HOW DO ELECTORAL SYSTEMS AFFECT REPRESENTATION
By
Tse-hsin Chen

A Dissertation
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
DOCTOR OF PHILOSOPHY
Political Science
2011

ABSTRACT
HOW DO ELECTORAL SYSTEMS AFFECT REPRESENTATION
By
Tse-hsin Chen
The project is to discuss the micro-foundations of how electoral institutions impact
political representation. The micro-foundations are built upon the citizens’ decisions on
how to express their policy preferences in elections. The beginning of political
representation is political participation, the decision of voting or not. Moreover, since not
all people decide to vote, the accuracy of the citizens’ preferences expressed through voter
turnout is essential in political representation. Furthermore, the authorization of the
citizens’ preferences is related to the selection of political agents who have the power to
speak for the people’s will in the government. These three topics are the main themes of
this project.
The central finding of this project is that various types of electoral systems (i.e.,
proportional representation (PR henceforth) and single majoritarian (SMD henceforth)
systems have their own advantages and disadvantages on three components of political
representation. I first show that the micro-foundations of why PR systems are associated
with higher turnout than SMD systems are built upon the calculus of voting and spatial
theory. Individual evaluations of the B term in the calculus of voting are affected by spatial
party competition framed by electoral institutions. Then I ask the question of how
electoral institutions affect the degree of political representation through the perspective of
comparing the distribution of voter preferences versus that of all electorate. Different types

of electorate according to their relative locations in the distribution of voter preferences
have various incentives to voting. Finally, I argue that electoral systems create the
convergent and non-convergent electoral incentives with substantial impacts on the
position-taking strategy of political parties through mechanisms of the electoral formula,
and the district magnitude. The pattern of party positioning is also modified by the type of
government (i.e., majority and coalition) and voter turnout rates depending on electoral
systems. These two aspects cause lower policy dependence under SMD and higher policy
dependence under PR.

To my father, and my mother

iv

TABLE OF CONTENTS
LIST OF TABLES ........................................................................................................................................viii
LIST OF FIGURES ........................................................................................................................................ix
CHAPTER 1
INTRODUCTION .........................................................................................................................................1
Why the Focus of Micro-Foundations of Political Representation.............................................4
Conceptualizations .............................................................................................................................9
The Arguments................................................................................................................................ 14
Contributions................................................................................................................................... 16
Outline of the Project...................................................................................................................... 17
Participation.............................................................................................................................. 17
Vertical Accountability............................................................................................................ 19
Competition .............................................................................................................................. 20
CHAPTER 2
UNCOVERING THE MICRO-FOUNDATIONS OF TURNOUT AND ELECTORAL
SYSTEMS....................................................................................................................................................... 24
Literature review .............................................................................................................................. 26
A Comparative View of the Calculus of Voting in Spatial Theory .......................................... 29
Why the Calculus of Voting ................................................................................................... 29
Reinterpreting the Calculus of Voting in Spatial Theory ................................................... 30
The Role of Electoral Systems................................................................................................ 36
Definition of Partial Change of the B Term ......................................................................... 41
Empirical Analysis........................................................................................................................... 43
Selection of Cases and Data .................................................................................................... 43
Measurement............................................................................................................................. 44
Binary Dependent Variable............................................................................................. 44
Main Independent Variable ............................................................................................ 45
Classification of Electoral Systems................................................................................. 47
The Institutional Effects on the B Term............................................................................... 50
A Voter Turnout Model ......................................................................................................... 51
Individual-level Control Variables ................................................................................. 51
Aggregate-level Control Variables ................................................................................. 52

v

Multilevel Methods .......................................................................................................... 55
Multilevel Model Results................................................................................................. 56
Conclusion ........................................................................................................................................ 63
CHAPTER 3
HOW IS POLITICAL REPRESENTATIOIN AFFECTED BY ELECTORAL SYSTEMS?... 66
Voting in Elections and Political Representation........................................................................ 70
The Influence of Electoral Institutions on Political Representation ........................................ 76
Background Research............................................................................................................... 78
Electoral Systems and Voter Turnout through Spatial Theory ........................................ 81
Electoral Systems and the Degree of Political Representation ........................................... 83
The Institutional Effects of Electoral Systems on Representation ........................................... 88
Selection of Cases and Data .................................................................................................... 88
Measurement............................................................................................................................. 89
The Dependent Variable................................................................................................. 89
The Classifications of Electoral Systems....................................................................... 92
Aggregate-level Control Variables ................................................................................. 93
Descriptive Statistics of KLD by Electoral Systems ............................................................ 94
Random Intercept Regression Model .................................................................................... 95
The Micro-foundations of Disproportionality of PR on Representation.............................. 100
Conclusion ...................................................................................................................................... 105
CHAPTER 4
A COMPARISON OF ISSUE VOTING ACROSS ELECTORAL SYSTEMS ......................... 108
Theoretical Consequences of Electoral Systems on Party Competition ................................ 114
Party Positioning Incentives and Government Type......................................................... 116
How Citizens Decide to Vote............................................................................................... 119
Linkage between Party Strategies and Voter Choice......................................................... 122
The Effects of Government Formation ....................................................................... 123
The Effects of Voter Turnout ...................................................................................... 125
Hypotheses and Statistical Models .............................................................................. 127
The Effects of Electoral Institutions on Voter Choice ............................................................. 133
The Voter’s Utility Function ................................................................................................ 133
Case Selection Criterion ........................................................................................................ 135
Bayes Factor Calculations...................................................................................................... 135
Results...................................................................................................................................... 136
Case Study: the 2004 Taiwanese Legislative Election .............................................................. 141

vi

Background ............................................................................................................................. 141
Model Specification................................................................................................................ 143
MNL and MNP Models by Bayesian Methods ................................................................. 146
Substitution Patterns of Voter Choice................................................................................ 150
Concluding Remarks ..................................................................................................................... 154
CHAPTER 5
CONCLUSION .......................................................................................................................................... 156
APPENDICES............................................................................................................................................. 163
BIBLIOGRAPHY ....................................................................................................................................... 171

vii

LIST OF TABLES

Table 2.1 Two Components of the B Term by Types of Electoral Systems........................................... 50
Table 2.2 Multilevel Model of Calculus of Voting in 64 Elections .......................................................... 61
Table 3.1 Summary Statistics of KLD by Types of Electoral Systems.................................................... 95
Table 3.2 Random-Intercept Regression Model of KLD in 68 Elections with 3 Types of
Electoral Systems ............................................................................................................................................ 98
Table 3.3 Random-Intercept Regression Model of KLD in 68 Elections with 4 Types of
Electoral Systems ............................................................................................................................................ 99
Table 3.4 Multilevel Model of Calculus of Voting in 64 Elections ........................................................ 104
Table 3.5 Bayesian Hierarchical Model of Calculus of Voting in 64 Elections .................................... 106
Table 4.1 Types of Governments by Separation of Power and Electoral Systems............................... 118
Table 4.2 The Comparison of Vote Choice Models across 59 Electoral Systems by Bayes Factor... 138
Table 4.3 Summary Statistics of Alternative-Specific Variables ............................................................ 144
Table 4.4 Bayesian Multinomial Logit Estimates, 2004 Taiwanese Legislative Election .................... 148
Table 4.5 Bayesian Multinomial Probit Estimates, 2004 Taiwanese Legislative Election .................. 149
Table 4.6 First Difference in the Voting Probabilities in 2004 Taiwanese Legislative Election ... 152

viii

LIST OF FIGURES

Figure 3.1 Examples of Distortion in Preference Distribution ................................................................. 74
Figure 3.2 Examples of KLD Computation................................................................................................. 92

ix

CHAPTER 1
INTRODUCTION
Political representation is one of the necessary requirements of democracy.
Representative democracy means that the government is delegated to a group of people
through regular elections. The idea of political representation is to realize the basic concept
of democracy — rule by the people — by asking delegates to express their constituents’
interests.
Political representation is a complex concept with conflicting sub-definitions. Any
analysis based on a single dimension of political representation is insufficient. This study
proposes to explain the meanings of political representation from the perspective of
responsiveness to bridge different characteristics of political representation. In particular, I
focus on three main components of political representation: electoral participation, vertical
accountability, and political competition. Meanwhile, this chapter intends to put these
components of political representation in the context of electoral systems and
systematically examine how electoral institutions affect political representation via various
mechanisms.
An electoral system is a collection of electoral rules, which function in an organized
way to decide how political representation works. A particular system contains many
separate electoral rules which may look disorderly but work together to achieve the
particularity of an electoral system. For instance, different combinations of the rules have
dissimilar effects on the degree of proportionality between votes and seats. The change of
one rule in the system may cause serious or unintentional consequences on political
representation.
The basic features of an electoral system include the number of votes that each citizen

1

can cast, how many delegates are selected within one district, and the electoral formula
which defines how the winner is determined. From the perspective of comparative rational
choice, ‘it pays attention to the constraints on and the strategic interactions among the
actors whose aggregated choices produce the outcome of interest’ (Levi 2009, 122). The
rules of electoral institutions not only frame how choices are presented to citizens but also
determine how choices are picked through preference aggregation. Importantly, electoral
institutions are a context factor framing the interactions between voters and parties.
Institution-induced incentives influence individual decision-making, i.e., electoral
participation, vote choice, and political competition in electoral campaigns and
policy-making process. Therefore, the filtering process of citizens’ preferences through
electoral institutions deserves investigation. The focus of this study is how disparate
equilibriums of electoral behavior created by the different rules of the game in electoral
institutions affect political representation.
The main thesis of the project is to discuss the micro-foundations of how electoral
institutions impact political representation.1 The micro-foundations are built upon the
citizens’ decisions on how to express their policy preferences in elections. This study adopts
the forward-looking aspect of political representation examining the integration of the
citizens’ preferences into final policy outcomes. The beginning of political representation is
political participation, the decision of voting or not, which is the first step of the linkage
between the citizens’ preferences and the government policies. Moreover, since not all
people decide to vote, the accuracy of the citizens’ preferences expressed through voter

1

The variable of electoral systems is treated exogenous in the project. The origin and
selection of varied types of electoral institutions are not the topic of this research. For
endogeneity of electoral systems, see Boix (1999) and Benoit (2004) for more information.
2

turnout is essential in political representation. The fidelity of the preferences in voter
turnout to the counterparts in the whole eligible citizens ensures the latter represented in
the policy outcomes faithfully. Furthermore, the authorization of the citizens’ preferences is
related to the selection of political agents who have the power to speak for the people’s will
in the government. These three topics are the main themes of this project.
The central finding of this project is that various types of electoral systems (i.e.,
proportional representation (PR henceforth) and single majoritarian (SMD henceforth)
systems have their own advantages and disadvantages on three components of political
representation. I first show that the micro-foundations of why PR systems are associated
with higher turnout than SMD systems are built upon the calculus of voting and spatial
theory. Individual evaluations of the B term in the calculus of voting are affected by spatial
party competition framed by electoral institutions. Then I ask the question of how
electoral institutions affect the degree of political representation through the perspective of
comparing the distribution of voter preferences versus that of all electorate. Different types
of electorate according to their relative locations in the distribution of voter preferences
have various incentives to voting. Finally, I argue that electoral systems create the
convergent and non-convergent electoral incentives with substantial impacts on the
position-taking strategy of political parties through mechanisms of the electoral formula,
and the district magnitude. The pattern of party positioning is also modified by the type of
government (i.e., majority and coalition) and voter turnout rates depending on electoral
systems. These two aspects cause lower policy dependence under SMD and higher policy
dependence under PR.2

2

The detailed definition of policy dependence is in Chapter 4. The wording of policy
3

1. Why the Focus of Micro-Foundations of Political Representation?
The object of political representation is the citizens’ preferences constituted by
individuals. In modern democracies, representatives are elected by the citizens’ action of
voting. The citizens’ preferences are revealed by the decision to vote and the selection of
political agents. The context of this process of political representation is electoral systems
to aggregate individual choices. The investigation of micro-foundations of political
representation restrained by electoral institutions should give us a better understanding of
the functioning of political representation.
How the represented is defined has long be ignored or assumed pre-existent in the
research of political representation. The citizens’ preferences expressed by voting are an
important dimension of the represented to facilitate democratic operation. The formation
of the represented is the judgment of good representation because the quality of the latter
is evaluated by the standard of the former. The importance of the object to be represented
hinges on itself as the starting point of the chain of democratic representation.
In the traditional research of political representation, the discussion of the content of
the represented is limited due to the attention to the typologies of the representatives. In
the classic work of Pitkin’s The Concept of Political Representation (1967), she implicitly
considers the represented as known and puts forward the meanings of types of political
representation. Recently, Mansbridge (2003) expands more categories of representation to
account for what representation does in practice. These categorizations point out the ways
the representatives perform their jobs. Moreover, Young ‘conceptualize[s] representation as
a differentiated relationship among political actors engaged in a process extending over

dependence is just a shortcut to indicate the contrasting policy-making processes under
SMD and PR (Martin and Stevenson 2001; Powell 2000).
4

space and time’ (Young 2000, 123). She argues that there are different social perspectives
from group representation to facilitate the democratic process. Saward considers the
formation of the represented important and ‘careful attention to how citizens can make
well-informed judgments about the ways in which they are represented (or not) is vital’
(Saward 2010, 30).
In the previous research of electoral systems, scholars discuss the effects of electoral
institutions on the relationship between seats and votes without putting the object of the
represented into consideration. These effects are measured by the proportionality between
seats and votes (Lijphart 1994; Rae 1967; Taagepera and Shugart 1989). The procedural
representation does not care about citizens’ needs (Powell 2004). Lately, some research of
electoral institutions has shifted their focus to the congruence of citizens’ preferences and
government policy (McDonald et al. 2004; Powell 2006; Powell and Vanberg 2000). This
development signifies the essential of the content of the represented.
With emphasis on looking at constitutive side of the represented, this research views
participation the core of political representation to characterize citizens’ preferences.
Participation in elections is rudimentary for democracy to work because it not only decides
what the people want but also determines the authorization of the representatives. Political
participation has a wide range of dimensions and this project narrows the topics down to
the decision to vote and the choice of politicians.
What do citizens’ preferences represent? After the justification of citizens’ preferences
as the ineradicable component of political representation, we need to pin down the
meanings of citizens preferences. Citizens’ preferences are a complex idea including
multiple aspects such as policy, gender, culture, economy, ethnicity and so forth. Each
attribute can be used as the criterion for representation efficacy. For instance, if the gender

5

perspective of male and female ratio is 1:1 in the population, a good representation is that
the men and women members of parliament should be 1:1 as well. This example indicates
that the qualities of representatives should mirror the same counterparts of citizens. In
other words, the characteristics of the representatives need to portray those important
qualities of the citizens. As Saward points out, ‘There is an indispensable aesthetic moment
in political representation because the represented in never just given, unambiguous,
transparent’ (Saward 2010, 74). This basic type of representation is denoted as descriptive
representation in Pitkin (1967). Thus, there are two requirements for democratic
representation to work. First is to understand how the object of the represented is formed.
Second is to represent what should be represented impartially through democratic
procedures. Only when both conditions are met can good democratic representation be
achieved.
Following the convention of Downs’ (1957) spatial theory analysis, I choose
policy as the main attribute of citizens’ preferences. I pick it for several reasons. First, the
influence of policy preference in citizens’ decision of voting is well-established. Spatial
theory specifies that voters have instrumental motivations for voting by evaluating policy
outcomes. Specifically, in the utility function for the judgment of their own welfare, voters
assess the distance between their own ideal points and the perceived policy position of
political agents. Rational voters, as utility maximizers, will always support the candidate
whose policy position is closest (Enelow and Hinich 1984). Then I am able to bulid my
arguments based upon past research. Second, research on the effects of electoral systems on
political parties is fully-fledged is past few decades. Since the target of this project is to
tackle the impacts of electoral systems, by picking the policy attribute I can connect the
institutional effects on voters’ decisions through party positioning strategies in campaign.
6

Spatial theory is an appropriate tool for my research because spatial theory has two useful
parts in my project: voting utility function and party positioning strategy. With the
combination of both pieces, I can investigate the effects of electoral systems on
representation. Furthermore, spatial theory can be used as a unifying theory accounting for
three subtopics of the project. By the usage of spatial theory for analyzing the policy
positions between voters and parties, I can develop more systematic assertions for various
aspects of voters’ decisions.
By confining my attention to the policy attribute, it means that other properties of
citizens’ preferences are not covered. This is not saying other components of citizens’
preferences unimportant. Every attribute of citizens’ preferences has its own significance.
For example, culture needs being common for the principal and agent to let them
communicate with each other because it put them under the same circumstance. The
practical reason of excluding other properties is the impossibility to discuss so much idea
in such a limited space of a dissertation project.
Even within the policy attribute of citizens’ preferences, there exists a problem of
multiple dimensionalities. There are different issues related to voters’ utility function, for
example, civil rights, health care, education, social welfare, defense and so forth. To make
cross-national analysis feasible, it is necessary to have a common issue spectrum. Left-right
ideology enables us to generate claims not constraining by country borders. The terms ‘left’
and ‘right’ have been shown that they are widely used in party competition and are
common language between citizens and political parties (Huber and Inglehart 1995). This
phenomenon exists not only in experts’ judgments but also in citizens’ minds with evidence
from survey data (Pierce 1999). The left-right issue dimension does serve as mutual

7

understanding between citizens and political parties. The recent research of electoral
systems on the congruence between citizens’ median and government policy also utilizes
left-right ideology as the common dimension for cross-country comparison (Blais and
Bodet 2006; Budge and McDonald 2007; Golder and Stramski 2010; Huber and Powell
1994; McDonald and Budge 2005; McDonald et al. 2004; Powell 2000, 2006, 2009;
Powell and Vanberg 2000). Following the heritage, I employ the left-right scale as the main
issue for its comprehensiveness.
To achieve commonality is to omit specifics because the salient issue varies across
countries and even across elections in the same country. Although the salient issue changes
across countries, it is not independent from the left-right scale. In other words, the
positions of the salient issue are correlated with those on the left-right dimension. The
major assumption I make is that the positions of the salient issue can be mapped onto the
left-right dimension without reversing their initial orders. This means that the variance of
positions on the left-right scale can explain most of the counterpart on the salient issue
(Jackman 2001; Poole and Rosenthal 1985). This idea is closely related to factory analysis
in statistics. The left-right scale is the hidden general dimension and the specific issues are
observable variables. Each issue should have some factor loadings on the left-right
dimension, with the situation that the salient issue is one of them. These scores on the
left-right scale are derived from distinctive issues because the original positions are
transformed spatially onto a more general dimension. Therefore, the left-right scale can be
used as the proxy for the salient issue in voters’ utility function.
The concentration of issue voting in the project restricts the applicability of my
arguments in some post-communist countries in Europe, new democracies in Latin
democracies and parts of Africa. The issue voting model, which is also called responsible

8

party model in the citizen-politician linkage, cannot explain the voting behavior in the
aforementioned areas. Citizens in these areas put more weight on clientelistic, party-voter
linkage in voting consideration (Kitschelt and Wilkinson 2007). To state the concept
alternatively, these voters increase their voting utility function by material inducements or
side-payments more than derived benefits from issue similarity with their identified
political parties. I do not dismiss this differentiated type of linkage, but it does show the
limitation of those mechanisms in my project. The extent of generalizability of my
dissertation does not include these areas. Let me unpack my thesis below.

2. Conceptualizations: Representation, Responsiveness, and Electoral Institutions
The concept of political representation needs to be clarified before any further
discussion. The formal definition is that the citizens (the principal) would like the
representatives (the agent) to act in their interest or on her behalf under the setting of
institutional contexts. According to this account, political representation implies that the
agent is selected to act in the government by aggregating the citizens’ preferences. In
democratic settings periodical and regular elections usually work as part of the
institutional mechanism for agent selection (Manin 1997) .3 The object to be represented
is the principal’s interest, whose best judgment is the citizens’ preferences. The agent, on
the other hand, faces a dilemma: should they function as a delegate acting for the
principal’s wish or as a trustee acting for the common good since citizens may not have
enough expertise to realize their best interests or because there is no Condorcet winner
among the majority of citizens’ preferences (Arrow 1951). The problem is further

3

For examples of nondemocratic representation, see Rehfeld (2006).
9

complicated by information asymmetry. The relationship between citizens and
representatives is a principal-agent one because the agent holds information not revealed
to the principal (Brennan and Hamlin 2000; Salanié 2002). The agent can shirk out of
self-interest and her action may not be detected by the principal.
To lessen the degree of these complications, this study follows the minimalist
definition of political representation. There are seldom universal substantive standards to
evaluate political representation, though there is an endeavor to derive what standards of
good representation should be (Dovi 2007). Unlike Manin, Prezworski, and Stokes who
define representation as ‘acting in the best interest of the public’ (Manin et al. 1999b, 2),
my definition emphasizes how the citizens’ preferences can be represented in an unbiased
way through democratic procedures. The citizens’ preferences can be represented only
when they are expressed in elections and are not altered by electoral institutions. This
definition is more in line with Christiano’s (1996) formal account of political responsibility
in which the agent is chosen in a certain way by the principal, with Riker’s (1982) in which
the practice of the democratic institution should be the focus, and with Mainwaring,
Bejarano, Pizarro, and Leongomez (2006) who defines representation as authorizing an
agent to act on a principal’s behalf. This kind of definition is minimal because it views
representation as merely requiring democratic institutions to work properly.
A successful political representation in democracies also provides responsiveness. The
representatives are aware of citizens’ preferences and are able to fulfill or employ those
preferences into policies under democratic institutions. To state this alternatively, the
agents respond to the principal’s need. This is what Pitkin describes as the meaning of
representation, to be ‘acting in the interests of the represented in a manner responsive to
them’ (Pitkin 1967, 209). To exemplify the process of political representation,

10

responsiveness connects citizen preferences and the outcomes of public polices through the
linkages of structuring choices, institutional aggregation, and policy making (Powell 2005).
This conceptualization of responsiveness amounts to the congruence between citizens’
preferences and policy outcomes (Stimson 1999).
Obviously, if the citizens have no means to remove bad agents or hold them
responsible for their actions in office, the representation is in crisis. The primacy of citizens
lies in voting in elections to control representatives and the electoral system decides how
agents are chosen. To further elucidate how electoral systems affect political representation,
we have to understand how elections serve as a mechanism for responsiveness. When
deciding for a candidate, citizens may engage in retrospective and/or prospective voting
(Manin et al. 1999b; Mansbridge 2003; Powell 2000). In the forward-looking version,
citizens look at whether representatives will act for the interests of the represented. Citizens
select agents who are competent enough to accomplish their campaign promises. In this
perspective, voters want to have a mandate government.
On the other hand, in the backward-looking perspective, citizens examine whether
incumbent agents have fulfilled their duty during the previous electoral term. Citizens are
empowered by the right to get rid of bad politicians who shirk their responsibility and hold
them accountable. Citizens' ability to punish or reward agents’ past behavior creates
accountability. In light of responsiveness, accountability shows that agents do not ignore
their constituents and do not just pursue their own goals or career. These two mechanisms
disclose that electoral systems are an essential part of democratic representation.
From the systematic perspective, responsive representation helps promote the
legitimacy of a democratic political system. Responsive representation maintains political
legitimacy through different dimensions of democracy. These dimensions can be divided

11

into two aspects: procedural and substantive. The procedural dimension involves
institutional arrangements that generate five features necessary for effective responsiveness:
the rule of law, participation, competition, vertical accountability, and horizontal
accountability (Diamond and Morlino 2005, xii). The rule of law shows every individual
agrees to play by the rules of the game which can be defined as the constitution;
participation means that citizens take their part in the decision-making process;
competition means that political parties and lobbyist groups are allowed to form and
compete with each other; vertical accountability indicates that political parties are
responsible to citizens who have the ultimate sovereignty under democracy, and finally,
horizontal accountability shows that the institutional design should have checks and
balances to curb government power in order to protect citizens’ basic political rights.
Among these qualities, participation, competition, and vertical accountability are
directly tied to electoral institutions. Voting in elections is considered a major form of
citizens’ political participation. Political parties need to compete for the voters’ support in
elections in order to form the government, and citizens control politicians through
elections. To put it different, electoral institutions influence political representation
through electoral behavior, party competition, and how voters hold political parties
responsible for their actions.
Finally, the substantive dimension involves freedom and equality. The responsiveness
of a political system supplies the connection between the procedural and substantive
dimensions designated as the important qualities of democracy (Diamond and Morlino
2005).
There are a lot debates related to how electoral systems affect political

12

representation.4 From the experience of established democracies, scholars compare the
advantages and disadvantages of SMD with those of PR over the citizens’ satisfaction of
how democracy works. Many researchers also have disagreements over whether those
observations in established democracies can be extended to either developing democracies
or ethnically-divided societies. The disagreement mainly comes from which electoral
system better produces a good representation beneficial to democratic consolidation. For
those who support SMD, they argue that SMD generates clearer accountability, creates a
tighter connection between the representative and constituents, and promotes cooperation
across ethnicity (Barkan 1995; Horowitz 2003; Lardeyret 1991). Conversely, other
scholars who prefer PR contend that PR has better minority representation and is more
suited for fragmented societies with a power-sharing political system (Amy 2002; Barber
2000; Lijphart 1991, 2004; Reilly 2002; Reynolds 1995). Some scholars take a moderate
position and argue that the solution to building up better representation in divided
societies is not unique (Bieber and Wolff 2007).
The controversies in past research arise because the effects of electoral systems on
political representation have not been compared systematically under a unified framework.
This study tries to access the three electoral institutional-related qualities of democracy
across developed and developing countries. This will help us answer the question on which
electoral institution will provide a better political representation and under what
circumstances.

4

The representation refers mainly to elections in parliament or in congress. In another
institutional dimension of parliamentary versus presidential systems, there is no
comparable election of executive chiefs.
13

3. The Argument
The representation of the electoral process can be broken down into three connected
elements: the individual decision to vote, the preference distribution of those who vote, and
how party competition seeks the support of those who turnout. Suppose there is only one
dimension policy space 5 and voters’ preferences are distributed uniformly. The first
component is how many voters decide to show up in the polling station. The second
component describes the post-election preference distributions of voters who actually go
out on Election Day. To put it in another way, the question is whether or not the
distribution of those regular voters in elections is biased against the whole range of the
distribution of the whole society. The third component indicates how political parties
compete for the market of those regular voters. These components will be the foci of three
empirical chapters and the more detailed idea will be explained in order in the following
paragraphs.
First, the incentives of participation are different across electoral systems. Individual
decisions of voting or not depend not only on many contextual-specific factors but also on
the effects of electoral institutions. The decision to participate or abstain in an election
shows whether the eligible citizens can select appropriate deputies to represent their
preferences. The central claim is that individual evaluations of benefits, what I refer to as
the B term,6 in the calculus of voting are affected by spatial party competition framed by
electoral institutions. While SMD reduces individual perceptions of the B term, PR helps
5

The assumption of unidimensionality is reasonable if the most salient issue exists within
a country. The most usual dimension can be assumed to be the left-right dimension. It may
be changed depending on the context.
6
There are two components in the B term, the F and H factors. The detailed discussion of
the two factors is in Chapter 2.
14

voters acquire higher estimates of the same term. As a consequence, a voter’s turnout
propensity should be increased more by PR than by SMD, ceteris paribus.
Second, not all eligible voters exercise political participation, and it is those who do go
to the polling station that hold representatives accountable. Do those types of voters who
show up for elections faithfully cover the full range of the policy space? We must know
whether voting turnout leaves some parts of the distribution unrepresented. If
representatives know that a certain portion of their constituents relinquishes their rights,
they may not include their interest in the policy-making process. Thus, after understanding
why people go to vote, we need to know the properties of these citizens who turn out to
vote. Only these voices are heard through elections and these preferences influence vertical
accountability. The relationships between voting turnout and electoral systems should be
investigated to understand which types of citizens express their preferences in elections.
Third, knowing which types of voters usually turn out, political parties choose their
campaign strategy to seek voter support under electoral systems. The main quest is to
know why political parties choose their positions in such a way under an electoral system
and how they position themselves under different types of electoral systems. Political
parties choose such positions because those are viable positions constrained by the
electoral institutions. Therefore, the resulting party position differs vastly under electoral
systems.
Alternatively, the aggregation process through electoral systems filters observable vote
counts into a small set of representatives also constrained by electoral systems. Political
agents positioning themselves differently act as proxies for their constituencies to bargain
with one another in the legislature. Since the number of political agents varies across
electoral systems, viable issue positions must obtain the majority support of voters. In a

15

majority system, a single agent occupies this position, while in other systems several
positions are needed to form a minimal winning coalition to maintain the majority.
The position-taking strategies under different types of elections are formed by political
parties by the recognition of the discussion in the previous paragraph. Electorates make
their choices of parties by responding to the relative locations of political parties. Voter
choice is the results between how political parties position themselves to attract voters’
support and the citizens’ response to the former. The patterns of voter choice across
electoral systems are the focus of the third chapter.

4. Contributions
Political representation has many paradoxical explanations when assessed from
different perspectives in the democratic process. To have a more comprehensive
understanding of political representation, the investigation of the concept should be
canvassed from multiple angles. This research suggests examining a consistent portion of
the meanings of political representation from the perspective of responsiveness. Moreover,
this chapter tries to place political representation in the context of electoral systems and to
ask how the variations of institutional factors influence the features of political
representation, because political representation cannot be isolated from the rules of how
representatives are selected. The effects of electoral institutions not only structure how
choices are presented to citizens but also determine how choices are picked through
preference aggregation. Therefore, electoral institutions have impacts on the interactions
between citizens and political parties and on their strategies in the process, which both
modify the qualities of political representation.
A few problems still have not been clarified by previous research. First, those studies

16

do not compare the effects of electoral systems systematically across established and
developing democracies. Second, usually aggregate indicators are utilized in exploring the
influence of electoral systems, which lack a micro-foundation.

Third, political

representation is based on individual behavior and the linkage between macro-institutional
context and individual decision is seldom explicitly specified.
This study tries to propose a research framework in order to address these deficiencies
in past studies. To build a stronger linkage between electoral systems and political
representation, we need to have general mechanisms penetrating country borders, but
accounting for essential features of how political representation works without the loss of
too much attention to contextual factors. Under this balanced approach, we can have a
better understanding of how electoral systems affect political representation in different
countries.

5. Outline of the Project
5.1

Uncovering the Micro-foundations of Turnout and Electoral systems
(Participation)

The second chapter intends to tackle the micro-foundations of why PR is associated
with higher turnout than SMD. The micro-foundations are built upon calculus of voting
and spatial theory.
The central claim is that individual evaluations of the B term in the calculus of voting
are affected by spatial party competition framed by electoral institutions. While SMD
constrains the number of political parties and creates large centripetal forces for party
competition, it reduces individual perceptions of the B term. In contrast, PR which allows
more political parties to survive does not generate many centripetal forces, and helps voters

17

acquire higher estimates of the B term. Building upon insights from spatial voting theories,
this chapter argues that a voter’s turnout propensity increases as the distance between her
position and the policy position of her most favored party decreases. Conversely, a voter is
more likely to turn out if the policy distance between her and her least favored party
increases.
This thesis is operationalized and tested by survey data from the round 1 and 2 of the
Comparative Study of Electoral Systems (CSES henceforth) across 64 recent elections. The
method is multilevel modeling because individual voting decisions are influenced by
aggregate contextual variables and personal characteristics at the same time. The empirical
findings confirm that the voting mechanism holds under both SMD and PR while PR has a
stronger tendency of voting due to the policy distance between her and her least favored
party. Moreover, the mechanism holds both in established and non-established
democracies.
Traditionally, the electoral institution school argues that countries with PR are
associated with higher turnout (Blais and Carty 1990; Jackman and Miller 1995; Franklin
et al. 1996; Radcliff and Davis 2000). Despite this strong empirical regularity, we know
little about the underlying mechanism that drives higher turnout under PR systems. In
addition, the effect of electoral systems seems to considerably weaken in the context of
new democracies (Blais and Dobrzynska 1998).
Previous research does not provide an explicit linkage between individual
characteristics and contextual variables (i.e., how aggregate factors affect individual
variables that also alter a citizen's propensity to vote). A more thorough procedure
includes the following: first, examining how institutions shape the incentives of individual
behavior; second, verifying how institutional effects change electoral behavior; third,

18

showing how individual incentives influence the decision to vote. This chapter intends to
bridge the gap and discuss the micro-foundations of voter turnout across electoral systems.

5.2

The Impacts of Electoral Systems on Political Representation
(Vertical Accountability)

Political representation is considered a basic requirement for democracy to work.
Citizens use elections as a means both to express their preferences and take the government
to account. However, there is no consensus regarding whether the PR or SMD system is
better in generating a more representative government. The disagreement has ignited a lot
of research over the past decade. The general argument is that SMD lacks minority
representation and PR produces obscure accountability.
Despite these known facts, there is no systematic research focusing on how
representative a government is based upon electorates who actually turn out to vote across
electoral systems. A representative government should have electoral support as a mirror
image of the whole country by the aspects such as issues, ethnicity, languages and religions.
The tenure of the government is also renewed by those who do vote in elections. In
particular, a representative government should be elected by a miniature of eligible
electorates.
The goal of the third chapter is to explore if political representation is biased by
electoral systems through comparison between the profiles of voter turnout and those of
the country as a whole. An electoral system induces a representative government when
voter turnout possesses features similar to the whole population. More specifically, in light
of spatial theory, the distribution of ideal points of voter turnout in an issue dimension
should be representative of the whole society by excluding those who do not vote. The

19

examination can be extended to other dimensions like ethnicity, languages, and religions.
Survey data from CSES the same as those in the previous chapter are utilized to investigate
which electoral system creates a more representative voter turnout.
The collective congruence analysis at the country level shows that PR has a higher
probability to induce biases into the distribution of citizen preference because more
extreme voters are more likely to find a viable political party to support. The previous
research which focuses on the congruence between the citizen preferences and the median
party in the legislature or the government policy outcome, basically conclude that PR has
the advantages at creating the congruence and thus, producing a better political
representation (Huber and Powell 1994; McDonald et al. 2004; Powell and Vanberg 2000;
Powell 2006).
These preceding studies do not take into account the effects of electoral institutions on
the voter side. By bringing the consideration of the influence of electoral systems on voter
participation back, I find that PR has a higher chance to generate the disproportionality
into voter preference distribution. The argument is in line with Blais and Bodet (2006) and
Golder and Stramski (2010). Although Powell (2009) conclude that the different
conclusions are due to the data in a later time period, this study provide another
explanation why the effects of PR in the congruence between the citizen preferences and
the government policy are balanced by the biases it introduces in the voter turnout.
Moreover, I discuss the micro-foundations of why PR introduces more biases thorough
higher voter turnout and corroborate the mechanisms by multilevel analysis.

5.3

Party Campaign Strategy under Electoral Systems (Competition)

Party campaign strategy is evaluated from the voter’s perspective to examine which

20

type of party campaign strategy is more effective in attracting support. The evidence for
how effective the party campaign strategy is voter choice because it is the results of
electorates’ response to political parties’ actions. I argue that electoral institutions influence
the patterns of political competition.
The SMD and PR electoral systems have institutional consequences on the interactions
among political parties in the decision-making process in parliament. SMD tends to
produce a manufactured majority held by a single political party while PR has a majority
coalition formed by several political parties with the principle of minimum winning
coalition (Powell 2000; Rae 1967). In other words, SMD usually creates a mandate
delegated to a single political party and PR has a power-sharing system with more than one
political party.
The policy implication of these properties of the two types of electoral systems is the
policy dependence of political parties within them. Under SMD, a political party can
foresee that if it wins the election, it can implement the policy position it campaigns for. On
the other hand, under PR, a political party usually needs other political parties’ help to
form a majority coalition and it has to compromise with other members in the coalition.
When voters ponder which political party to support, they can see whether or not there is
policy dependence among political parties under SMD or PR. Through the perspective of
spatial theory, the policy positions of political parties are represented a number in a
single-dimension issue space. Under SMD, the policy outcomes are more probable to be the
issue position of the winning party. In other words, the policy positions of political parties
under SMD can be viewed independently. But under PR, the policy outcomes are located
among a range of several issue positions of the coalition parties in government. Final policy
outcomes are closer to the issue positions of the coalition parties with higher correlation.

21

Thus, the degree of policy dependence is larger under PR than SMD.
The voting utility of a citizen to a political party is defined as random utility model
comprising two parts: systematic and unobservable utilities. The former is captured by
collectable and available variables in the data sets and the latter includes all remaining
properties influencing voter choice. Because the variable of policy dependence is not
measured in the survey data set, it is relegated into the error term. More specifically, the
error term of voting utility contains the institutional effects of electoral systems. The
concept of no policy dependence under SMD is equivalent to independence of irrelevant
alternatives (henceforth IIA) related to a statistical model called multinomial logit
(henceforth MNL). The multinomial logit deals with the problem of the dependent
variable with multiple unordered categories. The model assumption is that the error terms
of all choices are independent with each others. Another model which relaxes the IIA
assumption is multinomial probit (henceforth MNP) which allows policy dependence in
our case.
In order to fully capture the effects of electoral systems on vote choice, we have to
examine whether MNL or MNP has a better model fit under two types of electoral systems.
Since two statistical models are non-nested, we have to conduct the model comparison
through Bayesian factor with MNL over MNP. Bayesian factor can be standardized over
the range from negative infinity to positive infinity. A positive number means favoring the
model in the nominator, which is MNL in this case. We have to compare across different
electoral systems across countries to see if the pattern holds up. The purpose is to choose a
better fit model for each country to better control the effects of electoral systems.
The current research on political representation investigates the relationship between
voters’ preferences and the policy positions of political parties; research on the latter uses

22

either announced platforms in elections (Adams 2001; Adams et al. 2005; Kedar 2005;
Schofield and Sened 2006) or the compromise of party positions in the government
decision-making process resulting policy outcomes (McDonald and Budge 2005; Powell
2006). The first approach emphasizes the importance of party positioning strategies for
being elected while ignoring the policy-making process. On the other hand, the second
approach correctly focuses on the government process but fails to pay attention to how
political agents are chosen in elections in the first place. Although there is research that
discusses the consistency between election pledges and subsequent government policy
actions (Thomson 2001), these studies fail to take account of how voter choices in
elections are affected by the government policy-making process.
To measure the effects of party position-taking strategies, the policy distance between
political parties and voters is incorporated into the representative component. The policy
dependence among political parties is manifested in the correlation in the error terms.
While MNL imposes the IIA assumption to make the error terms uncorrelated, MNP
relaxes it. Therefore, MNL is suitable for voter choice under SMD but MNP is more
appropriate for voter choice in PR.

23

CHAPTER 2
UNCOVERING THE MICRO-FOUNDATIONS OF TURNOUT AND ELECTORAL
SYSTEMS
Voter turnout is arguably one of the fundamental features of democracy.
Normatively, turnout represents the most direct form of political participation and low
turnout reflects disenchantment among citizens. Declining rates can even indicate the
political system is experiencing a crisis of legitimacy (Powell 1982). Empirically, turnout is
often low and even eroding in most contemporary democracies. The continuing and
worrisome decline of turnout has raised serious concerns among scholars (Franklin 2004;
Norris 2004).
Such scholarly concern over voter turnout has spawned a large body of exciting
research over the past few decades.7 Among the various approaches, the importance of the
electoral system has received particularly strong attention from the scholarly community.
According to the electoral institution school, countries that use proportional
representation systems are associated with higher turnout (Blais and Carty 1990; Jackman
and Miller 1995; Franklin et al. 1996; Radcliff and Davis 2000). Despite this strong
empirical regularity, we know little about the underlying mechanism that drives higher
turnout under PR systems. In addition, the effect of electoral systems seems to considerably
weaken in the context of new democracies (Blais and Dobrzynska 1998). As Blais
forcefully puts it: ‘Most of the literature supports the view that PR fosters turnout, but
7

Briefly summarized, the determinants of turnout can be organized into three
complementary categories: social and economic, cultural, and institutional. One can also
categorize the determinants as individual or contextual depending upon the unit of
analysis. See Blais (2006) and Geys (2006) for a detailed review.
24

there is no compelling explanation of how and why, and the pattern is ambiguous when
the analysis moves beyond well-established democracies’ (Blais 2006, 116).
Previous research does not provide an explicit linkage between individual
characteristics and contextual variables (i.e., how aggregate factors affect individual
variables that also alter a citizen's propensity to vote). A more thorough procedure
includes the following: first, examining how institutions shape the incentives of individual
behavior; second, verifying how institutional effects change electoral behavior; third,
showing how individual incentives influence the decision to vote.
I use the spatial theory of voting as a unified framework in explaining individual
incentives to vote. The calculus of voting has a long history of development (Downs 1957;
Riker and Ordeshook 1968; Palfrey and Rosenthal 1983). The probable decisiveness of
one’s vote and its potential benefits are major components of self-interested voting
behavior. While the expected benefits account for turnout in one election, changes in
expected benefits from environmental variables are effective in explaining variations of
decisions regarding whether to turn out or not (Dowding 2005). A voter's belief, which is
the basis of her calculation, is shaped by the strategies that political parties or candidates
adopt to respond to political environments. For instance, political institutions should
induce separate equilibriums between political agents and voters, which are recognized by
voters, and thereby form different sets of beliefs across democracies. Hence, how
contextual effects influence individual perceptions in a political system is crucial to
understanding variation in voting rates across democracies.
This chapter seeks to uncover the micro-foundations linking electoral systems and
voter turnout. Building upon insights from spatial voting theories, this chapter argues that

25

a voter's turnout propensity increases as the distance between her preferred policy position
and the policy position of her most-favored party decreases. Similarly, a voter is more
likely to turn out if the policy distance between her and her least-favored party increases.
Utilizing survey data from the Comparative Study of Electoral Systems across 64 recent
elections and controlling for a set of individual as well as contextual factors, I find strong
empirical support for these claims. Furthermore, the mechanism works stronger under PR
than under single-member district systems. Moreover, this argument applies not only to
established democracies but also extends to non-established democracies.
In section two, I use calculus of voting and spatial theory to explain individual voting
decisions conditioned by contextual effects. Drawing on these theories, I derive three
hypotheses. Section three reviews the empirical measurement and operationalization of the
theory. To ensure that the political environment does shape the calculation of individual
incentives, a preliminary test will be performed using aggregate measures. The test provides
a brief illustration corroborating how rational choice theory helps us understand voting
motivations. Next, I develop a more comprehensive multilevel voting model to investigate
how electoral systems, social cleavages, and other political institutions influence voting
decisions. Finally, I review the study’s conclusions and make suggestions for future
research.

1.

Literature Review

Many studies identify electoral systems as an important factor in explaining
cross-national variation of voter turnout. The central argument in the literature is that PR
fosters voter turnout. Powell (1986) and Jackman (1987) find nationally competitive

26

districts, a feature of PR, important. Jackman (1987) also finds significant effects for other
characteristics of PR on the turnout rate, namely multipartyism and electoral
disproportionality. Following this research agenda, Jackman and Miller (1995) compare
institutional and cultural factors and corroborate the turnout-enhancing effect of PR.
Radcliff and Davis (2000) bring back the party-group linkage emphasized in Powell (1986)
and unionization, and find that district magnitude and multipartyism have substantial
effects on voter turnout. Blais and Dobrzynska

(1998)

inspect

country-level

socio-economic attributes and reiterate the importance of PR on voter turnout. Franklin
(2004) emphasizes the uniqueness of elections across countries and confirms that
disproportionality contributes to voter turnout.8 While the scope of previous studies is
confined to western democracies, the research in post-communist countries makes the
same inference (Kostadinova 2003).
Furthermore, scholars have proposed various research designs to validate the effects
of PR. Franklin, van der Eijk, and Oppenhuis (1996) test the same hypotheses on
European Parliament elections and conclude that proportionality is essential. Ladner and
Milner (1999) verify that PR enhances voter turnout using lower-level elections in
Switzerland when fully controlling for the country context. Perea (2002) computes an
individual incentive index formed by electoral institutions and shows that a lower average
of the threshold of representation boosts the incentive to vote. Norris (2004) employs
survey data to explore the effects of institutional and cultural explanations on voting
behavior and finds that institutional variables are indispensable.

8

Franklin (2004) proposes to control for majority status, margin of victory, time since last
election, postal voting and weekend voting.
27

Consequently, the underlying mechanisms that drive higher turnout under PR can be
summarized as three factors: nationally competitive districts, multipartyism, and electoral
disproportionality. The effect of these PR attributes on turnout hinges on an individual’s
rational expectation of how institutions work in a political system (Jackman 1987). The
mechanisms rely on the assumption how individuals will react to institutional contexts.
Nationally competitive districts lead to higher turnout because political parties have
incentives to mobilize voters widely across a country and thus, citizens have a higher
probability of voting. More political parties decrease voter turnout since the decisiveness
of a single vote is reduced. Finally, electoral disproportionality increases the propensity of
voting because people believe their votes will count under PR.
Further scrutiny, however, reveals that these mechanisms are less than satisfactory in
explaining why PR fosters voter turnout. First, they yield conflicting predictions regarding
the effect of PR (Blais and Carty 1990; Blais and Aarts 2006). On the one hand, PR is
predicted to foster turnout because voters have more choices with great mobilization and
also think that their ballots are more important. On the other hand, PR can be pernicious
to turnout because PR reduces the decisiveness of a single vote in light of a coalition
government. Second, these factors deemed beneficial to voter turnout do not work in
developing regions, such as Latin America (Pérez-Liñán 2001; Fornos et al. 2004). Blais
argues these results are evidence that the general pattern of PR having positive effects on
voter turnout is not robust (Blais 2006). Norris concurs, stating: ‘…The link between the
broader institutional context and how voters perceive and weigh the costs, choices, and
decisiveness of elections is poorly understood’ (Norris 2002, 63).
The modest goal of this chapter is to propose universal micro-foundations explaining

28

why people vote across established and non-established democracies. In the spirit of the
literature on the calculus of voting and spatial theory of party competition, I argue that a
citizen is more likely to go to the poll either when her favorite party or candidate has a
closer policy position to her own or when her least favorite political agent has a more
distant issue position. These hidden perceptions of party distance are individual
characteristics shaped by electoral institutions. I consider the variation in individual
perceptions about policy positions of political parties or candidates as the key to providing
the micro-foundation of higher voter turnout in PR systems.

2.

A Comparative View of the Calculus of Voting in Spatial Theory
2.1 Why the Calculus of Voting?

To uncover the underlying mechanism between PR and turnout, this chapter resorts to
the classic rational choice model. Accordingly, a citizen makes up her mind whether to vote
through a simple cost and benefit analysis. A voter’s calculus follows the well-known
P*B-C formula, where P is the probability of casting a decisive ballot, B is the benefit
derived from changing electoral outcomes from a voter's least preferred choices to her
most preferred choices, and C is the cost of voting. Specially, the rational choice model
predicts that a voter will vote when P*B-C is positive; namely, she decides to vote when the
expected benefits of voting are greater than the costs.
Because voting is individual behavior, cross-national variations in turnout should be
tracked back to how individual voting decisions are made. Thus, the calculus of voting
formula is utilized to explain a voter's voting propensity in an election within a specific
political system. It is critical to examine what individual variables might affect the P, B,

29

and C terms, to provide some understandings of why turnout rates vary across countries.
Interestingly, it is the rational choice model’s unintended implications, not the above
prediction, that echo most strongly within the scholarly community. The logical extension
of the rational choice model is that rational voters should never vote. The probability of
casting a decisive vote in a large electorate pool is extremely small, which in turn makes the
expected benefits lower than the costs. Yet, in reality, a substantial proportion of citizens
do vote, and this “paradox of voting” has become one of the most discussed issues in
political science.9
Note that this chapter does not seek to resolve the voting paradox; instead, this paper
follows the insight of the marginalist view (Aldrich 1993) and examines whether the
comparative statics derived from the rational choice model can shed any light on turnout
decisions.10 In a mathematical sense, this paper applies the concept of a partial derivative
to the P*B – C equation. The target relationship is how the small changes in the three
elements, especially B, will impact a citizen’s decision to vote. This paper examines
whether, ceteris paribus, the probability of turnout increases as the value of parameter B
increases. As stated by Blais, ‘the prudent solution is to focus on the core elements of the
model and to determine whether they do affect the decision to vote’ (Blais 2000, 10).

2.2 Reinterpreting the Calculus of Voting in Spatial Theory
The classic rational choice model conceptualizes the B term as the net benefit a voter
9

See Blais (2000) for more discussion of the voting paradox.

10

I recognize that issue voting only explains a portion of the B term because the whole
term includes other considerations. Nonetheless, I take the stance that the changing
benefits derived from issue voting represents the marginal effects of the B term.
30

would derive if her preferred candidate instead of the other candidate wins the election.
This paper extends this Downsian logic from the setting of simple plurality with two
candidates to multiple candidates. The key innovation of this paper is explicitly specifying
the B term by embedding spatial theory in the rational choice model.
Spatial theory states that voters have instrumental motivations for voting with an eye
toward policy outcomes. Specifically, voters assess the distance between their own ideal
points and the perceived policy position of political agents. The voter’s utility function is
assumed to be single-peaked and symmetric. Rational voters, as utility maximizers, will
always choose the candidate whose policy position is closest (Enelow and Hinich 1984).
This paper decomposes the two complementary parts of the traditional B term of
two-agent competition into two factors: (1) how close the policy position of a voter’s
preferred candidate is to her most preferred policy (henceforth F); (2) how far that of her
least-liked candidate is from her most preferred policy (henceforth H). The former
describes the degree of representation and the latter indicates the severity of threat. The
difference in final policy implemented by two agents with roughly equal vote shares
summarizes into a quantity to represent the voter’s recognition of the traditional B term,
the differential of the two components, F and H. The calculation depends on that the
expected vote shares of two agents are close. However, in a multi-agent game, the voting
utility depends upon several issue distances from agents with unequal vote shares and does
not hinge on a quantity as previously described. The voter’s derivation of F and H are the
weighted issue distances, the product of the issue proximity and the expected vote share of
agents, because agents with larger vote shares have the advantage in forming a coalition
government and pull the final policy outcome toward their issue platforms (Baron 1991).

31

Thus, regardless of two-agent or multiple-agent competition, the voter’s calculation of F
and H is the weighted distance based on the expected vote shares of agents and the
competition of multiple agents with unequal vote shares necessitates the decomposition of
the B term.
Voters acquire information regarding the agents’ issue positions and form
expectations about the distribution of vote shares through pre-election polls (Cox 1997;
Fey 1997; Myerson and Weber 1993). The assumption of the distribution of vote shares is
equal in two-agent spatial modeling and that of multiple-agent competition is model
specific.
Conditional on two-agent unidimensional competition, the calculation of the B term
can be referred to as how differently two candidates position themselves in the issue space.
If voters’ locations are more extreme than candidates’ positions, the differential quantity of
F and H factors is the identical length between the two candidates’ positions. Such voters
are called peripheral. If a voter’s stand is within two candidates’ positions, the segment is
divided into two portions. These voters are labeled interior. If the two segments are equal,
the disparity is zero. When they are not symmetric, their difference is the benefit of voting.
With three-agent competition, the calculation of the F and H factors relies on the final
policy implementation. Without loss of generality, suppose that the distribution of voters’
policy preferences is unimodal and three agents, denoted as L, M, and R, place themselves
from left to right. Voters expect that two parties are large, L and R, and one is small, M.
The six types of voters are two peripherals (a, f) and four interiors (b, c, d, e). It suffices to
discuss the calculation of the left side of the distribution because the right side is symmetric
and the same logic applies. First, when L or R obtains a majority of votes, the logic for

32

peripheral (a) and interior (b, c) voters, is the same as under two-agent competition by just
L and R. Second, when (L, M) or (R, M) reaches over 50% of votes under the principle of
a minimum winning coalition (Riker 1962), the policy outcome is the mean of the policy
locations of the two members in the coalition. The B term calculation of two-agent
competition still applies, depending on the compromise of two partners’ locations. The
voting incentive increases as the position of L or R gets further away from voter’s ideal
point.
In four-agent competition with similar assumptions that L1 and R1 are extreme and
L2 and R2 are moderate, voters evaluate the menace of extreme agents by the H factor
under the coalition-risk arrangement. Assume L2 or R2 is the core party (defined as more
than 0.33 vote share). The possible coalition combinations are (L1, L2), (L2, R2), and (R2,
R1). From left to right on the distribution’s left side, there are eight types of voters: a, b, c,
d with the right side’s mirror-image as h, g, f, e. The peripheral a (h) and interior b (g)
voters decide to turn out to increase the weight of their favorite agent L1 and to deter the
formation of other coalitions excluding their favorite. The interior c, d (f, e) voters cast a
ballot to get their favorite agent into the status of the plurality party or the policy result
will be pulled away by R1 (L1). Moreover, if no agent acquires more than a third of the
vote share, (i.e., all agents are about equal-size), the combinations of any two agents are
needed to build a majority coalition. Moreover, the additional logic, namely that voters
conceive of extreme parties as threats, also holds true in this case.
In spatial competition with more than four agents, the issue positions occupied by

33

candidates have a wider range (Eaton and Lipsey 1975), and thus, a political agent whose
platform is further from the median voter, may have a higher probability of influencing the
policy outcome. When some large agents obtain higher vote shares than others, albeit
without the majority, they need to form a coalition with agents whose voter share is
smaller. The moderate issue position of large agents is compromised by that of small
agents and smaller agents usually place themselves more extremely. On the other hand,
when the vote shares of agents are fragmented and nearly equal, the extreme small agents
have a higher chance to coalesce with others in order to govern; thus, the coalition
government becomes the norm under multi-agent competition. Downs clearly describes the
idea that ‘in a multiparty system, the victory of a party at the end of the scale opposite to a
voter’s position may usher in policies he bitterly opposes’ (Downs 1957, 148).
As these examples of multi-agent competition demonstrate, a more extremely
positioned agent can influence the final policy outcome of a PR election; given the
complexity of coalition outcomes, it is essential to disentangle the traditional B term. For
the voter in multiple-candidate competition, the segment between her most- and
least-preferable candidates’ positions varies by taking into account their vote shares, while
the focus of two-candidate competition is just the differential segment of two candidates’
policy positions.
The F factor, the first component of the B term, describes a voter's perception of how
closely her ideal point will be reflected in government policy as the proximity increases
between her position and the position of her most-favored party. This argument is valid
regardless of the number of candidates. Yet, the issue proximity only represents half of the
picture no matter how many candidates compete. Using Powell’s (2000) language, the

34

vision of two-candidate elections, mostly in SMD systems, is majoritarian and that of
multiple-candidate elections, usually in PR, is proportional. The former sees elections as
instruments to control the concentrated policy-making power and the latter consider
elections as an indirect route to influence factions in the dispersed counterpart.
In voters’ minds, they need to check the H factor, the second component of the B term,
in both types of elections. In the majoritarian view, citizens worry how distant their less
preferable candidate is since the policy-making power is delegated to either their favorable
or unfavorable candidate. In the proportional view, voters think about the policy positions
of all representative agents, who will enter the bargaining process and about how their
least preferable agent will weigh in after elections. More accurately, the attempt to
maximize issue proximity is similar across all types of elections; however, how voters
assess the seriousness of threats from their least preferable candidates under SMD and PR
relies on the second component—the perceived distance between their ideal point and their
least preferred candidate.
The H factor captures the distance between a voter’s ideal point and her least
preferred party under both SMD and PR. Assume that the issue positions of political
agents are predetermined and the first component, the F factor, is a constant. Under both
SMD and PR, citizens have higher incentives to vote when the second component is
larger.11 However, the mechanism under PR needs to include the post-election negotiation
process. If a voter’s least favorite party gets more ballots and her favorite one does not
have enough support, without her action the policy outcome will deviate further away
11

This argument also applies to SMD because if one party moves toward the median
voter position under two-party competition, the other party will be more moderate. This
results in less differentiation due to indifference (Adams and Merrill 2003).
35

from her position. If voters in multiple-candidate competition envision the negotiation
process with fully rational expectations, they are able to use their ballots efficiently to
achieve the desired final policy outcome. A similar line of argument can be found in
Kedar’s (2009) compensational voting model, where voters keep the policy position of the
viable extreme party in mind because it will pull the policy outcome away from the voters’
preferred direction. Citizens support a more extreme preferable political party to
counteract the effect of their least preferable one. The insight I draw is to include in the
calculation of the B term a measure of the degree to which a voter’s least favorite political
party is extreme.

2.3 The Role of Electoral Systems
Electoral systems are critical for turnout because they determine the policy positions
chosen by political agents, which cause the B term at the individual level to differ. In other
words, the B term is embedded in how political parties react to the institutional
arrangements, and voters evaluate their likely benefit from voting based on policy
positions held by agents under electoral systems. Hence, we bring electoral systems back
into the calculus of voting to capture the incentives of turnout among individuals.
Electoral systems shape the behavior of political agents. To maximize its electoral
support in an electoral system, political agents strategically choose a policy position after
considerations of other political actors' potential strategic responses. Adams et al. (2005),
and Schofield and Sened (2006) have demonstrated the applicability of the vote
maximizing assumption in multiparty competition under differing electoral systems. The
convergent or divergent positioning strategy is determined by an agent’s valence related to

36

its honesty and competence.12
Different electoral rules shape distinctive styles of competitions among political agents.
This suggests that the estimations of the B term are heavily dependent on the
characteristics of electoral systems. In other words, the voting decision process is
analogous to a Stackelberg game in which political agents move first and voters move
second. Political agents’ positions are made known to voters through campaigns. Hence,
the calculus of voting depends on a set of strategically configured policy positions chosen
by political agents responding to electoral institutions.
The political effects of electoral systems are the constraints they place on the number
of political parties. The effective threshold of representation in PR is lower than SMD
(Lijphart 1994; Taagepera 2007). The entry threshold of a political party in PR is shown
to be less restricted than SMD (Greenberg and Shepsle 1987; Palfrey 1984). As a result, the
effective number of parties is higher under PR (Amorim Neto and Cox 1997).
In addition, the parties or candidates under PR occupy a wider range of policy
platforms (Downs 1957). Cox (1990a) classifies electoral systems into centripetal and
centrifugal types based on whether electoral laws lead political agents to take converging
or dispersed positions in the electoral space. SMD is the most centripetal, whereas PR is
the most centrifugal. The more centripetal an electoral system is, the more convergent issue
positions political agents will choose. Empirical evidence confirms the existence of such a
pattern across electoral systems (Dow 2001).
The mechanical effects of electoral systems that constrain the number of political
parties and influence elites’ position-taking strategies produce different policy-making
12

See similar results in Adams, and Merrill (2009) with policy-seeking motivations.
37

processes. The distinction is between the marjoritarian vision under SMD and the
proportional vision under PR (Powell 2000).13 This difference is manifested by higher
disproportionality of vote-to-seat transformation under SMD than PR.
The contingent policy deviation fulfilled by electoral-institution-caused types of
government can be judged by the H factor. The threat under SMD comes from the
two-leading agents since one agent is usually delegated with policy-making power. While
the coalition government under PR includes the median party most of the time, the enacted
policy relies on its vote share (Laver and Schofield 1990; Martin and Stevenson 2001). The
influence exerted by its potential partners will be reduced as the median party gains more
votes. The median party faces a threat from the existence of small extreme parties who can
pull the policy outcome away if the median party does not have enough votes.
Furthermore, the policy outcome of the minority government controlled by the plurality
party must negotiate with other agents (Laver and Schofield 1990).
Moreover, the presence of pre-election agreements may appear among allied parties
which form the left or the right ideological coalition (Golder 2006). The exclusion of
specific extreme or antisystem parties may not always be the case due to the change of the
international circumstance such as the formation of European Union (Strøm et al. 1994,
315-319). These coalition conditions indicate that the government policy can be
represented by the weighted positions of coalition parties by seat shares which are
susceptible to more extreme agents with certain weights as a potential partner (Powell
2006).

13

SMD can also induce national multipartyism if the vote share of a political party is
concentrated in a region or several districts (as in Canada and India).
38

Citizens decide whether to vote by assessing both the vote share of their favorite
agents and the deviated issue distance of adverse agents capable of influencing government
policy outcomes. Voters will turn out to support their favorite party to increase the party’s
bargaining chips in the government formation. This is one type of expressive voting
(Brennan and Hamlin 2000). Voters balance the policy outcome by compensatory voting
with the recognition that the viable extreme parties are capable of changing the policy in
the opposite direction (Kedar 2009).
The psychological effects of electoral systems force voters to coordinate when voting
for political agents (Duverger 1954). The motivation for strategic voting lies in the
expected vote share of a political agent relative to its winning probability. The
coordination requirement is the most stringent under SMD because the district magnitude
(M) is one in SMD. Voters strategically support top-M+1 vote getters because these are
agents who will have influence on the policy outcome. The primary purpose of strategic
voting is to maintain the closeness of final policy outcome and a voter’s ideal position. For
example, in three-agent competition as described in the previous section, under SMD with
L and R as front runners, c (d) voters may choose L (R) and dessert M because they feel the
threat from R (L). Under PR, c (d) voters will not abandon M because they can make it
king-maker.
In the situation of four-agent competition with the assumptions that L2 is the core
party and R1 is a possible coalition partner, voters a, b, c, d all acknowledge the threat
from R1 if political agents on their side of the issue space do not get enough votes to form a
coalition, (L1, L2), (L2, R2) or (L1, L2, R2). In the second scenario (L2, R2), voters a, b

39

may vote strategically for L2 because L1 may not gain enough of the vote share to enter the
coalition. In the third scenario (L1, L2, R2) the final outcome, the average of the three
agents, is to the left of the position of L2; thus, although the closest agent to voters c is L2,
they may strategically support L1 to pull the policy closer to their ideal point. Accounting
for the vote shares of political agents and plausible coalitions, the evaluations of the F
factor may be affected by strategic voting, but not the H factor.14 A similar line of
arguments has been proven by Austen-Smith and Banks (1988) under three-agent
competition under PR.
In particular, in an electoral system with more median-convergent stimuli, the utility
derived from the first component of the B term tends to become smaller and decreases the
propensity of voting. In contrast, a more centrifugal electoral system increases the utility of
the second component of the B term and thus, enhances the incentive to vote.
Electoral institutions have two joint effects on the behavior of political parties via the
number of parties and position-taking strategies. The SMD system produces fewer viable
political parties and stronger centripetal forces for political parties to move toward
moderation. Conversely, in the centrifugal PR system, a political agent does not have to
choose the median voter position or to merge with other agents in order to win a seat.

14

Although strategic coordination is a common observation in various types of electoral
systems (Cox 1997), sincere voting can explain a significant portion of voting behavior
because compared to SMD, other types of systems suffer less from strategic voting (Cox
and Shugart 1996). Moreover, individual-level observations on voting behavior can be
explained by-and-large by sincere voting (Degan and Merlo 2006). Voting considerations
under a majoritarian system with one ballot are largely sincere and there is a reduction of
strategic voting in other electoral systems.
40

SMD tends to decrease the utility of the two components of the B term while PR is likely to
enlarge it. Thus, compared to SMD, PR shortens the average distance between a voter and
her most-preferred party while increasing the average distance between a voter and her
least preferred party.

2.4 Definition of Partial Change of the B Term
The B term is composed of two elements: (1) how close a voter’s most-preferred and
(2) least-preferred political agent are from her own ideal point. The first component,
denoted as F, can be written as the following equation:
(2-1)

Fij = –1/vk (Di – Sf )2

where Di is her ideal point, Sf is the issue standpoint of her most favorite political agent
and vk is the expected vote share. Following the conventional spatial voting framework,
the property of the utility function is a quadratic loss function such that the larger squared
distance with more disparity between Di and Sk, the less preferable it is to a voteri (Davis et
al. 1970). The F factor is inflated by the inverse of the vote share because the issue position
of an agent with a smaller weight will be counted as being counteracted by other larger
agents.
The second component of the B term, denoted as H, is defined as:
(2-2)

Hij = vk (Di – Sl)2

where Sl is the issue position of her least favorite political agent. The H factor is deflated
by the vote share since the severity of the threat perceived by voters depends on the weight

41

of a political agent. A smaller weight decreases the possibility to be influential on the
policy outcome.
Voters are more likely to vote when both the F and H factors are larger. Voters like to
raise their voice for their favorite party to give them greater weight in policy
implementation (Fowler and Smirnov 2005; Franklin 2004). Under SMD, if voters believe
that their favorite candidate has a chance to win, they turn out to vote to ensure her win
and to grant a firm mandate. Under PR, voters support their favorite parties to let them
have more chips in the negotiation process if no single party acquires a majority.
The H factor relates negatively to the degree of centripetal forces in an electoral
system. If there are more centripetal forces, political agents will tend to move toward the
median voter. The locations of political agents will be close and the H factor is smaller,
reducing the incentive to vote. If there are more centrifugal forces, political agents will tend
to spread out widely over the issue space. The positions of political agents will be more
diverse; thus, the H factor is larger, increasing the propensity of voting.
In short, relying on the type of electoral system and power-sharing institutional design,
a voter will assess and identify which party is likely to be influential in the next
government or parliament. Under SMD, her least favorite political agent who has some
leverage to move a policy outcome would be located in the farthest position away from her
ideal point. On the other hand, under PR, a voter's least favorite agent with a
seat-acquiring ability and the potential to participate in a coalition government should be
counted as a potential menace in PR.
Based on the discussion above, I derive three hypotheses as follows:
Hypothesis 1: Voters are more likely to vote when the F factor increases.

42

Hypothesis 2: Voters are more likely to vote when the H factor increases.
Hypothesis 3: On average, the F and H factors are both larger under PR than SMD.
All in all, when P is controlled across countries, B = F + H can be used as an
approximation of how electoral systems impact the propensity of voting. By breaking
down the B term we are able to theoretically articulate and empirically test the effects of
different mechanisms on turnout under different electoral systems. Importantly, this
method provides an explicit linkage between individual characteristics and contextual
variables.

3.

Empirical Analysis

3.1 Selection of Cases and Data
To substantiate the hypotheses, I analyze survey data from Comparative Study of
Electoral Systems. CSES fits our purpose since its research design collects individual-level
data reflecting macro-level variations of political systems. Both round 1 and round 2 of
CSES surveys from 1996 to 2006 are included. However, I did not include all available
elections for several reasons. First, the study focuses on free elections; thus, any country
with a negative Polity IV score is excluded.15 Second, any elections held in non-sovereign
regions are dropped.16 Third, the dependent variable is whether respondents voted in the
most recent election and any pre-election surveys are not used.17 Fourth, any surveys

15

This excludes the Belarus 2001 presidential election.

16

This excludes the Hong Kong 1998, 2000, 2004 legislative elections.

17

This omits the Russia 2000 presidential and Kyrgyzstan 2005 presidential elections.
43

missing questions that I use as independent variables are excluded.18
There are 64 elections left for analysis. Please see the appendix for more detail about
these elections. They constitute a representative sample of voting behavior from a variety
of electoral systems across the world. Not only does it allow us to compare the effects of
electoral institutions on individual behavior but it provides enough cases from both
established and non-established democracies to explore the difference between both types
of political systems.

3.2 Measurement
3.2.1 Binary Dependent Variable
The dependent variable is defined as whether or not a voter casts a ballot in elections
reported in the “Survey Turnout” of Table A.1 in the appendix. By comparing aggregate
turnout and self-reported turnout in the survey, we see a serious overreporting problem, as
found in Silver, Anderson and Abramson (1986) and Karp and Brockington (2005).
However, the tendency of overreporting is not confounded with our definition of the B
term (see below) and the degree of centripetal forces.19 Thus, the use of self-reported

18

This omits the Japan 1996, 2004 and Thailand 2001 because there is no
self-positioning question on a left-right scale. The Chile 1999 and USA 1996 elections are
discarded because respondents’ perceptions of the parties’ positions are unavailable. This
also drops Belgium 2003 due to no income variable being available and the Netherlands
2002 because the question asking whether a vote can make a difference was not included
in the survey.
19
This argument is supported by a regression analysis at the election level (not shown
here). The dependent variable is the discrepancies between aggregate and survey turnouts
in elections. The independent variables are the aggregate turnout, F, H, compulsory voting,
and the other controlled variables used in the final model. No independent variables had
strong enough effects to influence over-reporting biases in 64 elections.
44

turnout does not cause systematic biases in the estimations of effects of the main
independent variables of interest.

3.2.2 Main Independent Variable
The B term is operationalized with the following two items: “In politics people
sometimes talk of left and right. Where would you place yourself on a scale from 0 to 10
where 0 means the left and 10 means the right? Now, using the same scale, where would
you place a particular political party?” Two approaches are used to denote the party
position: subject and average party placements. The self-judgment of party positions is
potentially biased in favor of voters’ projection. Rabinowitz and Macdonald (1989) argue
that the party positions should be measured by the average of respondent perceived
positions by balancing the subjective biases. Yet, given the individualism emphasized in
this paper for the voting benefit calculation, the individual perceptions of party positions
are not constant and ‘the best source for both types of information is therefore the
individual voter’ (Westholm 1997, 870). Besides, the biases introduced by voters’
projections can be reduced by the inclusion of socio-demographic and party identification
variables in the model (Blais et al. 2001; Kedar 2009). Furthermore, Merrill et al. (2001)
demonstrate that the biases do not have systematic effects introduced by electoral systems.
Hence, this paper adopts the first approach as the primary method and the second
approach is to provide supplementary evidence.
To incorporate the viability of a political party, the two components of the B term (F
and H) are computed through separate processes with an emphasis on how voters evaluate
the proximate and opposite distances distinctly. The first step is to estimate that the

45

squared distances between voters’ ideal points and the locations of party platforms. To
incorporate the party weights into policy outcomes, the distance of the F factor is inflated
by the inverse of vote shares in the election. This represents the information voters
perceived from pre-election polls, and they utilize this information when judging the likely
importance of political parties after the election. Specifically, if a political party or
candidate is expected to receive strong support, its weighted distance, F, is inflated less,
meaning that its impact increases. For those agents with smaller expected vote shares, their
F factor is enlarged more to reflect a smaller influence. On the other hand, citizens
discount the H factor when considering a political party with weak support because they
expect it will have less of an effect in determining the government policy.
The calculation of the F factor can be written as:
(2-3)

Fij = – min[1/vk*(Di – Sk)2]

where vk is the vote share for party k in country j. The records of vote shares for main
political parties chosen by professionals in each CSES country team are collected in these
elections and applied to three electoral scenarios: the chief executive election, concurrent
presidential and parliamentary elections, and parliament only elections.20
The second component, the H factor, is also weighted by the percentage of vote shares.
When citizens measure the gravity of counter-effects from less favorable parties, they
analyze the probability of winning the election and the power that these parties might have
in the bargaining process. The H factor is defined as:

20

Sources are IFES Election Guide (http://www.electionguide.org/) and Election Results
Archive (http://cdp.binghamton.edu/era/).
46

(2-4)

Hij = max[vk*(Di – Sf)2].

I use vk because it indicates how far a specific political party is able to pull the policy
outcome away from a voter’s most preferred issue position.
In accordance with the principle of item equivalence, which is to ensure each
component of the B term is comparable across countries, each term is divided by the
standard deviation of the distribution of voters’ ideal points because the shape and spread
of that distribution varies over countries. This procedure removes specific measurement
units pertaining to countries even if they are originally measured by the same scale.21

3.2.3 Classification of Electoral Systems
In classifying electoral systems, the three major features are electoral formula (E),
ballot structure (V), and district magnitude (M). In 64 elections there are four electoral
formulae: SMD, combined-independent, combined-dependent, and PR. In majoritarian
systems including first-past-the-post or two-round 2nd ballot systems, the ballot structure
is per person per vote and the district magnitude is 1. These factors usually induce a
Duvergerian equilibrium in which two agents obtain substantial votes and other
ranked-below-three agents acquire very few ballots. Hence majoritarian systems should
have stronger centripetal forces than other types.
In non-compensatory mixed PR-SMD electoral systems, there are two separate

21

Davis et al. (1970) specify a voter’s utility function as Uij = −aij(Di − Pk)2 where aij is an
individual-specific weight to the issue. In my example, the assumption is that the weight aj
is country-specific. The standardization procedure intends to get rid of aj to fit the
principle of equivalence.
47

electoral rules to distribute seats. These systems can be represented by E = plurality and PR,
V = 2 and noncumulative, and M > 1 (i.e., the congressional elections in Russia and
Ukraine).

Total

seats

are

allocated

independently,

which

show

the

feature

“combined-independent.” Voters have two ballots to vote for candidates in the district and
for closed PR list. For the first ballot, the convergent incentives are similar as in a
majoritarian system. However, the second ballot for PR with district magnitudes larger
than 1 provides some incentives for political parties to deviate from the median voter
position. So the centripetal forces in combined-independent systems are weaker than those
in majoritarian systems.
In compensatory mixed electoral systems, their ballot structure and district magnitude
are similar to combined-independent systems (i.e., Germany). They have features similar to
the previous type except that the proportions of seats allocated to political parties are
entirely determined by the second ballot for closed PR list. Political parties’ shares of seats
are compensated by vote shares in the second ballot. These systems provide more driving
forces to deviate from the median voter. Hence we conclude that the centripetal forces in
compensatory mixed systems are weaker than those in combined-independent systems.
PR systems can be represented by E = PR, V = 1 and noncumulative, and M > 1.
Voters cast one ballot for candidates in an open PR list or for political parties in a closed
PR list. In the latter, seat allocation is based on vote shares among political parties. In the
former, a voter can select her favorite candidate and votes for candidates in the same
political parties are aggregated. The ranking of candidates of the same party is determined
by the votes that they acquire. Seats are allotted according to the ranking of candidates and
vote shares created by individual votes. Thus, the centripetal forces in PR are at least as

48

weak as those in compensatory mixed systems.
Next, I discuss the centripetal forces in concurrent elections with two levels,
chief-executive and congressional, held at the same time. If two levels adopt the same
formula as SMD, we classify it as the most centripetal. If they use different formulae, we
count the formula for presidential election as primary because these presidential elections
usually determine who will have the final say in a policy outcome under a presidential
system. Thus, we consider these elections to contain as strong of centripetal forces as
majoritarian systems. These include the following elections: Brazil 2002, Chile 2005,
Mexico 2000, Peru 2000, 2001, 2006, and Philippines 2004. However, this standard
cannot be extended to semi-presidential systems in which executive functions are shared
between the president and the prime minister. The presidential election is usually
majoritarian and the parliamentary election is PR (i.e., Romania 1996 and 2004). I treat
them as mixed electoral systems like a non-compensatory mixed system.
The special case is Australia. Its electoral system is the Alternative Vote (AV) with E =
AV, V > 1 and cumulative, and M = 1. Voters can cast preferential votes to rank
candidates in their district in order. The minimum threshold for being elected is 50%+1 in
the district for one seat. It can be classified as a majoritarian system (Norris 2004).
Therefore, it produces the most centripetal forces.
Thus, I divide the degree of centripetal forces of electoral systems into three categories
from the strongest to the weakest based on the degree of centripetal forces: the strongest is
majoritarian, concurrent SMD, and AV; the medium is non-compensatory mixed and
concurrent SMD and PR; the weakest is either compensatory mixed or proportional. This
categorization illustrates how electoral institutions shape party competitions.

49

3.3 The Institutional Effects on the B Term
We are ready to inspect hypothesis 3. Table 2.1 provides summary statistics of the F
and H factors by types of electoral systems. The unweighted figures are quadratic distance
on a scale of 0 to 10 and the weighted ones are computed with vote shares as described
above. First, the unweighted F factor is the largest due to weak centripetal forces induced
by the electoral systems. Examining the standard errors shows that the width is tightest. As
centripetal forces increase, the F factor gets smaller which means it is further from voters’
ideal points. The opposite trend is found in the H factor.
Second, the conclusion for the weighted F factor still holds with the confirmation of a
similar pattern. Although the pattern does not hold for the mean of the H factor, the
standard error of H in the least centripetal cases is smaller than the other two. A possible
explanation is that the vote shares in the third type are usually smaller because of
multipartyism. However, the weighted H factor is consistent at a similar strength.
Therefore, I consider the results in Table 2.1 as evidence supporting hypothesis 3.

Table 2.1 Two Components of the B Term by Types of Electoral Systems
Distance

Centripetal

F

Unweighted

Most
Medium
Least

-1.07
-0.78
-0.52

Weighted

Most
Medium
Least

-4.67
-2.95
-2.51

50

(SD)

H

(SD)

Cases

2.95
2.60
2.03

14.32
14.26
14.67

14.66
11.36
10.55

21676
12574
49766

14.98
8.68
10.39

3.95
4.08
3.23

4.53
3.97
3.25

21676
12574
49766

3.4 A Voter Turnout Model
Now that the influence of electoral systems on the B term is confirmed, I explore how
the motivation for voting is affected by individual perceptions of the B term. A more
sophisticated model explaining the individual decision to vote is necessary to control for
confounding factors in assessing the cost-benefit calculation. Controlling for variables
related to voting propensity is necessary or the impact of the calculus of voting cannot be
accurately assessed. Insights from previous research on electoral participation should be
included as intervening variables in the voting utility function.

3.4.1 Individual-level Control Variables
Each individual has her own socioeconomic status in a society, which affect how she
perceives the benefits of voting. Individuals have different endowments of resources
determined by socio-demographic variables such as sex, age, income, and education. Those
with more resources are presumed to care more about electoral outcomes because they
would like to influence government policy in the future. Moreover, since the voting act
bears costs of time and information, the wealthy are able to absorb the inevitable costs
more easily.
In addition, political attitudes should not be ignored. Those who have greater political
interest and stronger party identification are more likely to vote because they are more
concerned that the candidate or political party they support wins the election. Voters with
stronger party identifications are more easily mobilized. The effect is captured by a dummy
variable for party identification.
People with higher political efficacy are more likely to vote than others. This is

51

measured by two variables measuring a respondent’s political views: do people think who
is in power can make a difference (Inpower in Table 2.2); do people think who they vote
for makes a difference (makediff in Table 2.2). The above two variables are all ordinal
variables with 5 levels from “Strongly disagree” to “Strongly agree.”

3.4.2 Aggregate-level Control Variables
The P and B terms are endogenous to an election because they are determined by the
interplay between political agents and voters; however, the P and C terms are exogenously
fixed to the context of a political system since the decisive probability depends on
pre-existing demographic variables like population size. Moreover, the cost of voting is
subject to electoral laws, like the registration procedure and compulsory voting. Next,
voters adjust their perceptions of P and assess B through pre-election competition. This is
two-stage information acquisition. Hence, aggregate variables related to the P and C terms
contribute partially to variation of voting rates and should be controlled in the model
specification.
One socio-demographic variable is average district size related to the P term.
Individuals will feel their vote is more decisive if a representative is elected by a smaller set
of citizens. The larger the average district size, the smaller the P. Blais and Dobrzynska
(1998) and Geys (2006) find a negative association between voter turnout and the
logarithm of population size.
How political fragmentation measured by the effective number of political parties
changes voter turnout is inconclusive. Political fragmentation has positive effects because
there are more choices offered to voters, and more parties also mean more competitiveness.

52

Meanwhile, political fragmentation also has negative effects because more political parties
increase the need for coalition formation. The other reason comes from information theory:
more parties mean more complexity and higher information cost in the act of voting (Long
and Shively 2005). Brockington (2004) shows that the size of coalition government does
matter when it exceeds the rule of a minimum winning coalition. Conversely, after the
effects of coalition government are controlled for, the higher number of political parties
increases voter turnout. The main reason for the puzzling results is the lack of a
standardized cross-national measure of the information cost to individual voters.
I use three aggregate measures of political fragmentation: effective number of parties,
district magnitude, and the degree of political competition. I expect that the three variables
are all positively correlated with the propensity to vote.
Compulsory voting is an important factor in the voting cost calculation. In countries
with compulsory voting and high punishment of nonvoting, the voter turnout should be
larger than those without such procedures. Thus the coefficient for compulsory voting is
expected to be positive. The variable is measured at five levels from “No,” “Yes; without
sanction for violation,” “Yes; limited enforcement,” “Yes; weakly enforced sanctions,” and
“Yes; strictly-enforced sanctions.” To account for the nonlinearity of these five
categorizations, they are collapsed into 3 dummies: “Yes; without sanction”, “Yes; limited
or weak sanctions”, and “Yes; strict sanctions”.22
Acquiring information occupies a significant portion of the voting cost. Concurrent
elections reduce the information cost through the media coverage of at least one election
and the spending of more campaign funding (Cox and Munger 1989). The voting
22

I am indebted to an anonymous reviewer who clarified this point.
53

probability is empirically proven to be higher in systems with concurrent elections than
without (Long and Shively 2005). Following Geys (2006), I hypothesis that the dummy
variable of concurrent elections is positively correlated with voter turnout.
I also consider the individual perceived P term. Each voter’s observation of the P term
varies depending on information from pre-election competition. The individual assessment
of the P term is an adjustment of P at the aggregate level after voters form beliefs about the
expected vote shares of competing political agents. Therefore, the degree of
competitiveness also is controlled to partial out the effects of the B term.
One dimension of the individual judgment of the P term is decisiveness possibly
measured by the closeness of the election. Electoral closeness is the marginal victory of the
largest political party over the second largest party in terms of votes received. If political
parties are in a tight race, political elites will make a great effort to mobilize voters and
voters will also perceive a higher P term. The ex post vote shares are considered a
reasonable measure of how close voters perceive the race.
Another contextual variable is the frequency of elections. If there are more national
elections, citizens may feel that electoral contests are less decisive or citizen may develop
“burn out” from repeated voting. This variable is included as a control variable and the
sign is expected to be negative.
Finally, the socioeconomic environment is an important indicator for the measure of
individual resources. The economic development is usually hypothesized to facilitate voter
participation through higher education, the easy access to more information, and more
leisure time (Blais and Dobrzynska 1998). GDP per capita is included as a control variable.
However, there are arguments that the change in per capita GDP does not have the same

54

effects on turnout in the developing countries as in industrialized countries. A downturn in
the economy reduces the citizens’ willingness to vote in the advanced industrial countries
while the effects stimulate voter turnout in the developing democracies (Aguilar and Pacek
2000; Fornos et al. 2004; Radcliff 1992). Thus, the lagged change in per capita GDP
before the election year and its interaction term with the indicator of developing countries
are included.23
The socioeconomic claim illustrates the importance of the distinction between
developed and developing countries. But I expect that the micro-mechanism of the F and H
factors will work efficiently across the two groups of countries because their influences are
introduced by electoral institutions framing the same individual rational expectations that
penetrate country borders.

3.4.3 Multilevel Methods
The multitude of methods used in exploring the variations in voter turnout across
countries should be unified. Some studies focus on the aggregate level while others
concentrate on the individual level only. Moreover, some scholars integrate individual
characteristics and contextual effects to exploit joint their effects on voting rates across
political systems (Egmond et al. 1998; Perea 2002; Franklin 2002; Brockington 2004;
Norris 2004). The underlying assumption is that the propensity to vote is directly
influenced by aggregate-level variables. These methods still lack an important linkage
demonstrating to how institutional variables influence individual decisions. Matsusaka
23

The GDP per capita is the variable RGDPCH from the Penn World Table (PWT6.3) in
the election year. The change in per capita GDP is the variable GRGDPCH from the same
source.
55

and Palda (1999) argue that macro analysis suffers from an ecological fallacy so that
conclusions drawn from aggregate-level examination may be incompatible with
micro-level behavior.
The essence of voting is purely individualistic regardless of whether it is examined
from the aggregate perspective or not. Instrumental motivations have two sources of
variation: from individual characteristics that distinguish people from each other and from
the circumstance that they are situated in. Since electoral institutions influence how
political parties campaign, elites' strategies should shape voters' beliefs about the available
choices, which in turn affect their motives for voting. Individual perception of the
institutional impact of electoral systems is the second source of variation that needs to be
captured in the model. Thus, not only should the direct impacts of individual
characteristics on voting be included, but the repercussions of institutional variables on
individual perceptions as well.

3.4.4 Multilevel Model Results
To evaluate to what extent the B term explains individual voting decisions,
independent variables are divided into three groups: aggregate-level, individual-level, and
the two components of the B term. Aggregate variables include random effects of countries
and institutional properties. Individual variables are socio-demographic and attitudinal
variables. The B term is classified as its own category to test for its effects on voting
behavior. The level-1 model is as follows:
(2-5)

Prob(Voteij)=logit(β0j+β1*Femaleij+β2*Educationij+β3*Incomeij+β4*Inpowerij
+β5*Makediffij+β6*Partyidij+β7*Age26_35ij+β8*Age36_45ij
56

+β9*Age46ij+β10j*Fij+β11j*Hij+eij).
The fixed effects of β1 to β9 are assumed the same at country-level j because we expect
these variables work homogeneously regardless of country borders. Other β0j, β10j, and
β11j can be further specified:
(2-6)

β0j=γ0(0)+γ0(1)*Compulsory1j+γ0(2)*Compulsory2j+γ0(3)*Compulsory3j
+γ0(4)*Closenessj +γ0(5)*ENPj+γ0(6)*(District Magnitude)j+γ0(7)*Frequencyj
+γ0(8)*Concurrentj+γ0(9)*(LogDistrict Size)j+γ0(10)*(Political Competition)j
+γ0(11)*GDPj+γ0(12)*(Developing)j+γ0(13)*(L_GDP_Change)j
+γ0(14)*(L_GDPC_Developing)j+γ0(15)*PRj+γ0(16)*MIXj+ u0

where ENP is effective number of political parties; District Magnitude is the average seats
elected in each district; Frequency is the average of electoral frequency in the 1990s
including presidential and congressional elections; Concurrent is a 0, 1 indicator of if there
is another election running at the same time; Log District Size is logarithm of average
population size that the elected candidate represents in an election, and Political
Competition is the average of political competitiveness defined as the average margin of
the largest political party over the second largest in parliament in the 1990s; gross
domestic product (GDP) is introduced to account for the economic impacts on voter
participation at the country level.
To tackle the interaction effects between GDP growth and the group indicator of
being in the industrialized or developing world, I include three terms: the dummy of

57

developing countries not in the OECD, the lagged annual change in GDP per capita, and
the product of the previous two terms. To correctly estimate the effects of the interaction
term, the constitutive term, which is the dummy of developing countries, needs to be
included in the equation (Brambor et al. 2006).
The final group of variables is two indicators of electoral institutions: PR and MIX.
They are put into the equation for capturing any remaining effects not explained by the
individual institutional evaluations, F and H.
The random coefficients of two components of the B term can be written as:
(2-7)

β10j =γ10(0) +γ10(1)* PRj +γ10(2)* Developingj + u10;

(2-8)

β11j =γ11(0) +γ11(1)* PRj +γ11(2)* Developingj + u11.

The constrained model imposes the assumption that the slopes of F and H do not vary
across developed and developing countries. The model fit shows whether the
generalization of the two factors holds across the two groups of democracies.
The advantage of a multilevel model is the random coefficient. The random intercept
shows the effect of holding different institutional contexts constant and allowing the
coefficients of the F and H factors to vary across electoral systems and democracies. In
order to separate between- and within-country effects, I use a random effect hierarchical
generalized linear model to estimate the systemic relationship between the two components
of the B term and individual voting decisions. I use a generalized linear model with a
logistic link function due to the dichotomous property of the voting decision.
Table 2.2 shows the results of the multilevel model with two model specifications.24

24

To check the robustness of Table 2.2 from individual projection biases toward party
58

Notice that the random-effect estimation of country-specific differences is statistically
significant. Although the significant variance of the country effect is about 17% by
conditional intraclass correlation, we account for the fact that the institutional setting is
peculiar to a country. For aggregate institutional variables, four variables are significant at
the 5% level and are all in the expected direction. On average, without-sanction and
strictly-enforced compulsory voting, and close elections increase voter turnout. Frequency
of elections decreases average willingness to vote. Nevertheless, the two dummy variables
of electoral systems are not significant at the usual statistical level. Compared to SMD, the
level of voter turnout in PR and Mixed systems has no difference when other macro and
micro variables are controlled for.
The impacts of macro-economic development on micro-voting decisions as found in
previous aggregate research are verified (Blais and Dobrzynska 1998; Fornos et al. 2004).
Higher GDP per capita does increase the willingness to vote, albeit this finding is
statistically insignificant. Furthermore, the effects of lagged change in GDP per capita are
negative for both the industrialized and developing countries. The coefficients of lagged
GDP change (in the constrained model) are estimated at -0.0269+0.0008*Developing,
where Developing is the indicator variable. More specifically, the coefficient of lagged GDP
change in the industrialized countries is -0.0269 with 0.537 p-value and that in the

issue positions, the individual respondents’ perceptions are also replaced with the averages
of respondents’ evaluations (Rabinowitz and Macdonald 1989) because the experts’
judgments of party issue positions are not available for all countries included in the study
or are inconsistent with all individual perceived party positions in a country. After these
changes, the results remain and are, therefore, robust. See Table A.2 in the appendix for
details.
59

developing counterparts is -0.0261 with 0.492 p-value.25 A decrease of GDP per capita
fosters a voter’s motivation in both the industrialized and developing world, though not
statistically significant. This finding of economic voting is in line with the arguments of the
developing countries in previous research, but inconsistent with those of the industrialized
ones.
To explore the mechanism’s efficiency across non-established and established
democracies,26 the indicator variable dividing elections into two groups is included in the
intercept, and the slopes of the F and H factors. The dummy variable in the intercept is to
control for all remaining noninstitutional factors that fundamentally exist in the difference
between two groups of nations. The coefficient of the intercept indicator shows that
individual voting propensity is initially higher in the non-established nations with other
variables held constant. However, the binary indicators in the random coefficients of F and
H are not statistically significant at the 5% level. The two coefficient indicators
demonstrate that the relationship between the two components and voting propensity is
not substantially different in non-established versus established democracies. More
specifically, the institutional voting mechanism prevails in all of these elections. The
implication of the magnitude similarity is that electoral institutions create the same voting
incentives in the two worlds.

25

The standard error of the coefficient for lagged GDP change in the developing countries

is calculated by the formula,

ˆ
ˆ
ˆ
ˆ
var( r0 (13) ) + var( r0 (14 ) ) + cov( r0 (13) , r0 (14 ) ) , which is

0.0380 in this case. So the T-ratio is -0.6876 and the p-value is 0.4917.
26
I use the terms of industrialized and developing countries and those of established and
non-established democracies interchangeably.
60

Table 2.2 Multilevel Model of Calculus of Voting in 64 Elections (N: 66592) (Part 1)
Full Model
Fixed Part

Constrained Model

Coefficient

Robust SD

P-value

Coefficient

Robust SD

P-value

Intercept of β0, γ0(0)

-2.275

1.743

0.198

-2.318

1.741

0.190

Compulsory1, γ0(1)

0.797

0.302

0.012

0.794

0.301

0.012

Compulsory2, γ0(2)

0.139

0.236

0.560

0.141

0.229

0.541

Compulsory3, γ0(3)

1.284

0.211

0.000

1.306

0.209

0.000

Closeness, γ0(4)

-1.458

0.387

0.000

-1.452

0.386

0.001

ENP, γ0(5)

-0.072

0.047

0.132

-0.072

0.046

0.130

District magnitude, γ0(6)

-0.002

0.002

0.261

-0.002

0.002

0.298

Frequency, γ0(7)

-2.247

0.440

0.000

-2.483

0.440

0.000

Concurrent, γ0(8)

0.373

0.221

0.098

0.358

0.219

0.109

Log District size, γ0(9)

0.043

0.034

0.207

0.045

0.034

0.187

-0.002

0.007

0.739

-0.002

0.007

0.746

GDP per capita, γ0(11)

0.165

0.147

0.268

0.168

0.146

0.256

Developing, γ0(12)

0.970

0.243

0.001

0.989

0.244

0.000

-0.028

0.029

0.339

-0.027

0.029

0.357

L_GC_Developing, γ0(14)

0.002

0.039

0.962

0.001

0.040

0.983

PR, γ0(15)

0.086

0.187

0.648

0.079

0.188

0.674

MIX, γ0(16)

-0.283

0.280

0.318

-0.293

0.278

0.299

Female, β1

0.022

0.025

0.381

0.022

0.025

0.378

Education, β2

0.096

0.010

0.000

0.095

0.010

0.000

Income, β3

0.086

0.010

0.000

0.086

0.010

0.000

Inpower, β4

0.106

0.011

0.000

0.106

0.011

0.000

Makediff, β5

0.176

0.017

0.000

0.176

0.017

0.000

Partyid, β6

0.716

0.040

0.000

0.716

0.039

0.000

Age26_35, β7

0.274

0.036

0.000

0.274

0.036

0.000

Age36_45, β8

0.614

0.046

0.000

0.614

0.046

0.000

Age46 and above, β9

0.967

0.054

0.000

0.967

0.055

0.000

Politil Competition, γ0(10)

L_GDP Chang, γ0(13)

61

Table 2.2 Multilevel Model of Calculus of Voting in 64 Elections (N: 66592)
(Part 2, cont’d)
Full Model
Fixed Part

Constrained Model

Coefficient

Robust SD

P-value

Coefficient

Robust SD

P-value

Intercept γ10(0)

0.004

0.001

0.000

0.003

0.001

0.000

PR, γ10(1)

0.001

0.001

0.974

0.001

0.001

0.600

-0.001

0.001

0.228

Intercept γ11(0)

0.007

0.002

0.007

0.008

0.002

0.001

PR, γ11(1)

0.011

0.004

0.007

0.010

0.004

0.019

Developing, γ11(2)

0.003

0.004

0.428

F slope, β10

Developing, γ10(2)
H slope, β11

Random Part

2

χ

Std. Dev.

σ e (scale factor)

P-value

2

χ

Std. Dev.

P-value

1.81

3.29

σ u0

0.699

2342.21

0.000

0.699

2336.68

0.000

σ u10

0.003

102.30

0.001

0.003

104.69

0.001

σ u11

0.016

158.41

0.000

0.016

160.37

0.000

The likelihood ratio test between the full model versus the constrained model with
eliminating the 2 dummies of developing countries in the slopes of the F and H factors is
3.45,

which

is

smaller

than

the

threshold

of

.05

p-value

statistics,

10.6,

under χ distribution with two degree of freedom. Besides, the Bayesian information
2

criterion of the full model against the constrained model is 20.3, which shows the strong
support of the constrained model. This justifies the usage of the constrained model and
that the strength of the two components of the B term does not vary across non-established
and established countries.
The estimated results in Table 2.2 are a population-average model with robust

62

standard errors for making general inference toward the comparison of electoral
institutions. First, hypothesis 1 and 2 are confirmed after individual and contextual
variables are controlled for. The higher the individual components of the B term are, (i.e.,
the F and H factors), the more likely an individual decides to vote. This estimate offers us
promising evidence about the micro-foundations of the individual voting process. The
voting mechanism of benefit calculation considerations depends on institutional factors.
The linkage between the micro voting decision and electoral institutions is through how
electors evaluate the policy positions of political parties and their expected vote shares.
What is the connection between the micro-level voting mechanisms and electoral
systems? The PR dummy variable is not significant at the slope of the F factor. Regardless
of whether the voting decision is made under PR or non-PR systems, individuals use the F
factor in the same, positive way. Nonetheless, the PR dummy variable is significant at the
slope of the H factor. The relationship between the H factor and individual voting
decisions are stronger under PR systems. Thus, the H factor provides more incentives for
individuals to vote under PR and this is why PR fosters voter turnout.

4.

Conclusion

This paper tackles the micro-foundations of voting and addresses why PR systems are
associated with higher turnout than SMD systems. The micro-foundations are built upon
the calculus of voting and spatial theory. The central claim is that individual evaluations of
the B term in the calculus of voting are affected by spatial party competition framed by
electoral institutions. While SMD constrains the number of political parties and creates
large centripetal forces for party competition, it reduces individual perceptions of the two

63

components of the B term. In contrast, PR allows more political parties to survive and does
not generate many centripetal forces; thus, it helps voters acquire higher estimates of the
two counterparts of the B term.
This thesis is operationalized and tested using CSES data. The method employed is
multilevel modeling because individual voting decisions are influenced by both
aggregate-level contextual variables and personal characteristics at the same time. The
empirical findings confirm that the voting mechanism holds under both SMD and PR
while PR has a stronger tendency of voting due to the H factor. Moreover, the mechanism
holds across established and non-established democracies.
The calculus of voting helps us understand why voting rates differ across countries.
The cost-benefit approach under a synthesized spatial theory facilitates explaining citizens’
voting behavior driven by electoral institutions. Since every election is specific based on the
constraints of political institutions, and country-level contextual factors, interactions
between political agents and electorates are centrally important in explaining individual
voting behavior. Unless such an interplay among agents is accounted for, aggregate-level
interpretations miss the basic point that a decision whether to vote or not is fundamentally
individualistic. However, for future research, the data used in this paper do not control for
all relevant aggregate-level variables. More macro-level data should be collected. Moreover,
only cross-sectional data are used in Table 2.2. This dimension of the study is obviously
not sufficient because this model cannot clarify why voter turnout across countries declines
over time. As a result, panel data needs to be analyzed to investigate the universal trend of
sliding voter turnout.
Finally, the discrepancy between the effects of economic development on voter

64

turnout between macro- and micro-levels of research deserves more investigation. The
aggregate research may commit an ecological fallacy without a direct linkage between
individual behavior and economic change. Although the direction of the impacts of GDP in
the both worlds and of GDP change in the developing nations work as described in
previous research, the effects are not strong enough to be statistically significant.
Individual reactions to the changes in the economic environment are not explicitly
measured or captured in the model. Moreover, in the developed world, voters do not
reward success. This phenomenon is in contradictory with the findings of previous
research. It is likely that the economics works differently among distinct groups of voters,
and citizens also hold different views toward economic voting based on either a sociotropic
or pocketbook perspective. In addition, no consensus exists on what economic indicators
should be used in evaluating this question. Thus, future research needs to integrate possible
mechanisms to sort out the effects of economic voting.

65

CHAPTER 3
HOW IS POLITICAL REPRESENTATIOIN AFFECTED BY ELECTORAL SYSTEMS?
Political representation starts from political participation. The represented express
their preferences mainly through the act of voting in elections. As Dahl asserts: ‘citizen[s]
ought to have an adequate opportunity, and an equal opportunity, for expressing their
preferences as to the final outcome’ (Dahl 1989, 109); thus, effective participation is a
basic requirement of a democratic process. Equal opportunity implies that each citizen’s
preference has an identical weight, or as Verba puts it, ‘political equality refers to the extent
to which citizens have an equal voice in governmental decisions’ (Verba 2003, 663).
However, in the real world, not everyone turns out to vote and voter turnout rates vary
across countries with differing electoral systems. As the institutions of elections aggregate
individual preferences and influence how elected representatives act in the interest for the
represented (Powell 2000, 2005), it is thus essential to investigate whether the
electoral-system-caused bias between the preferences of the whole citizens and those of
who vote exists.
Procedural representation concentrates on the relationship between votes and seats
without considering citizens’ preferences. It investigates the mechanics of how electoral
institutions transform vote counts into seats (Rae 1967). The concept of proportionality
refers to the degree to which vote shares correspond to seat shares allocated to political
parties (Lijphart 1994; Taagepera and Shugart 1989).27 However, despite the merits of
understanding how electoral systems induce different proportionalities between seats and
27

Proportionality can be measured by the least-square index––calculated by taking the
square root of the half of the sum of squared difference between partisan vote and seat
percentages (Gallagher 1991).
66

votes under the principle of ‘one man, one vote, ’ procedural representation does not care
about citizens’ needs (Powell 2004). Since the object to be represented in political
representation is citizens’ preferences, it is necessary to bring the citizens’ preferences back
into consideration.
From the perspective of substantive representation (Powell 2004), the quality of
political representation hinges on the congruence between citizens’ preferences and policy
outcomes. In contrast to the view of procedural representation which focuses on the
disproportionality between votes and seats, substantive representation emphasizes the link
between citizens’ preferences and their representatives (Miller and Stokes 1963). Only
when the consistency of the link is ensured does successful political representation prevail.
More specifically, democratic responsiveness occurs when the government makes public
policies in accordance with what the citizens want (Powell 2005, 62-63).
Operationally, the research of substantive representation explores the congruence
between the citizen median and policy outcomes as defined either by the legislative median
or by government policies, and this perspective addresses how political representation is
affected by electoral systems. In the proportional vision associated with proportional
representation (PR) election rules, the government is usually formed in a coalition and the
policy outcome is generated from bargaining compromises (Powell 2000). The legislative
median accentuates its power in determining final policy (McDonald et al. 2004; Powell
and Vanberg 2000), while the role of government is emphasized in implementing the policy
outcomes (Huber and Powell 1994; Powell 2006). Both traditions of research conclude
that PR is advantageous over single member district (SMD) election rules.
Notwithstanding the effects of electoral systems on congruence, the literature has paid

67

little attention to how the effects of electoral institutions on voter turnout influence
political representation. The will of the people are realized mainly through political
participation in elections. Participation in elections is the essential quality of democracy for
reflection of responsiveness. Voting in elections reveals the citizens’ preferences, which is
one of the necessary conditions to ensure ‘government responsiveness to the expectations,
interests, needs, and demands of citizens’ (Diamond and Morlino 2005, xxix).
The primacy of political participation in elections depends upon the citizens’ decision
to vote or not. If voters evaluate the cost of showing up at the polling station as not
outweighing the benefit of expressing their preferences, they would abstain. Those who
do not show up to vote give up the right to make their voice heard. Assume that a certain
portion of eligible voters constantly do not vote and political parties also take this fact into
account while campaigning and making policies. Then the government is no longer
responsive to those abstaining from voting. This situation violates the basic principle of
political representation from the view that the government should be responsive to all
citizens. However, if voter abstention comes proportionally from different parts of the
society, the preference profile of voter turnout resulted from aggregation of electoral
systems may not be so dissimilar to that of the whole society. Thus, the understanding of
whether the discrepancy between the preferences of voter turnout and those of the whole
society exists is an important research agenda.
Moreover, voter turnout varies across countries with diverse electoral systems around
the world. Electoral systems have been identified by many studies to be an important
factor in explaining cross-national variation of voter turnout (Blais 2006); brutally
summarized, PR systems are associated with higher turnout (Blais and Carty 1990;

68

Franklin et al. 1996; Jackman and Miller 1995; Powell 1986; Radcliff and Davis 2000),
whereas the high disproportionality of SMD usually reduces voter turnout.
Nonetheless, as demonstrated in Chapter 2, the micro-foundations of voter turnout are
rooted in citizens’ evaluations of party issue positions (which are themselves structured by
electoral institutions), and citizens’ own policy locations in the voter distribution affect the
willingness to vote. The critical point is that if electoral institutions raise or lower the
voting propensities of different portions of the voter distribution, the resulting preference
distribution of those who actually cast the ballot may or may not be consistent with the
same distribution as the whole population eligible to vote.
Extending the emphasis on micro-foundations from the previous chapter, this chapter
will examine political representation within the context of electoral systems. The main
objective of this chapter is to explore whether political representation is biased by electoral
systems through comparison between the profiles of voter turnout and those of the country
as a whole.28 The key finding is that contrast to the conventional wisdom, this paper
shows that SMD systems induce a more representative government in the sense that those
who turnout possesses features similar to the whole population.
In section two, I will clarify the meaning of political representation and the focus of this
study. Next, I will demonstrate the mechanisms of how electoral systems influence the
degree of political representation through three steps in the third section: first, I briefly
review the past research on voter turnout; second, I show how voter turnout varies by
electoral systems; third, reinterpretation of the impacts of electoral systems on newly
28

In light of spatial theory, the distribution of voter turnout’s ideal points on an issue
dimension should be identical to the whole society by excluding those who do not vote in
the election.
69

defined political representation. To support and verify the theoretical arguments, I will
perform empirical analyses from aggregate and individual perspectives. It is important to
develop appropriate measurements and to operationalize the conceptualizations in the
theory to allow for hypothesis testing. In the country-level analysis, I will present a
preliminary examination of summary statistics by types of electoral systems and adopt a
more sophisticated regression model to explore the effects of electoral institutions. In the
mean time, in the individual-level investigation, I inspect the micro-foundations of data
analysis to complement and confirm the macro-level assertions. Finally, I shall conclude
and make some future research suggestions.

1. Voting in Elections and Political Representation
The citizens’ preferences are the objects made manifest through the complex,
responsive democratic process. To induce the government to do what citizens desire, the
latter vote in elections, the results of which are filtered through electoral systems. More
specifically, electoral systems not only define how citizens’ preferences are counted for
electing representatives, but also structure what kinds of choices are available to them. To
facilitate responsiveness, election outcomes are the bridge between the citizens’ preferences,
and government formation and policy outcomes. Famously, Schumpeter defines democracy
as ‘that institutional arrangement for arriving at political decisions, in which individuals
acquire the power to decide by means of a competitive struggle for the people’s vote’
(Schumpeter 1976, 269).
Specifically, the two purposes of voting in elections are preference expression and
delegate selection. Theories of substantive representation state that democratic

70

responsiveness works when the representatives are aware of citizens’ preferences and are
able to fulfill those preferences in forming policies under democratic institutions. The other
conception is that the agents (the elected) respond to the principals’ (the voters) needs.
Pitkin observes that democratic responsiveness comes from two angles: (a) authorization
of a representative and (b) accountability of the representative. The function of voting in
elections is to articulate the object, the citizens’ preferences, represented by the agents,
which constitutes how the people’s will is defined at the election time (Pitkin 1967,
225-226).
The two theories specify that the citizens wield elections to select representatives using
complementary prospective and retrospective visions: mandate and accountability (Manin
et al. 1999a; Powell 2000). In the forward-looking version, the citizens look at whether
representatives will act in accordance with the expressed desires of the represented. The
citizens select agents who are competent enough to accomplish their campaign promises.
The principal wants to prevent the selection of agents who are unable to perform their
tasks––a process known as adverse selection. In other words, voters want to have a
mandate government.29
This chapter adopts the standard of authorization to evaluate the quality of political
representation. The selection mechanisms mean that the voters at the current time period
authorize representatives the legitimacy to rule at the next time period. This notion refers
29

In addition, in the backward-looking vision, citizens examine whether incumbent
agents have fulfilled their duty during the previous electoral term. Voting empowers
citizens to get rid of bad politicians who shirk their responsibility and to hold them
accountable for their past performance. The citizens' ability to punish or reward agents’
past behavior creates accountability. Accountability shows that the incumbents do not
ignore their constituents and do not just pursue their own goals out of self-interest. This
dimension is important, but not the major concern of this chapter.
71

to promissory representation in which the agents campaign to keep their promises for
winning the principal’s support (Mansbridge 2003). Only those who exert their right to
vote do participate in the authorization process. For those who abstain in elections, their
preferences may be ignored by agents. Thus, the preference differences caused by not all
citizens’ votes being counted in elections can increase the probability that representatives
deviate from the distribution of whole citizens’ preferences.
Political participation’s centrality in elections is further enhanced by another
perspective on political representation called gyroscopic representation. Mansbridge
defines it as the following: ‘Voters select representatives who can be expected to act in
ways the voter approves without external incentives’ (Mansbridge 2003, 520). Due to
information deficiencies and the extreme cost of monitoring after elections, citizens tend to
focus more on selection of good types of politicians (adverse selection) than on sanctioning
bad performance of the incumbent (moral hazard) (Fearon 1999).
This paper proposes a previously unexplored notion of political representation. The
method is to compare the distribution of the citizens’ preferences expressed by voter
turnout and that of the whole society. The more consistent the two distributions are, the
higher the degree of political representation is. This notion of representation is built upon
the electoral participation – the focus of the previous chapter –, as voting provides an
important form of preference communication that helps or hinders the selection of
like-minded representatives and requires that the representatives be held accountable
(Bartels 1998; Miller and Stokes 1963). Lijphart argues that, ‘who votes, and who doesn’t
has important consequences for who gets elected and for the content of public policies’
(Lijphart 1997, 4). Moreover, representatives are more responsive or more likely to reward

72

voters than nonvoters in the policy-making process (Griffin and Newman 2005; Martin
2003). Therefore, voting in elections is an essential step in the representation of the
citizens’ preferences, and participation in elections can make a difference in who will be in
power.
The notion of representation proposed in this paper also takes the root in Downs’
(1957) spatial theory. In this framework, the citizens’ preferences can be measured from
the distribution of their issue positions. While the conventional wisdom equates
democratic responsiveness to congruence between the median of the citizens’ most
preferred issue positions and the outcomes of public policies, the initial determinant of
responsiveness is the consistency between the distribution of the voter preferences of those
who voted in elections and the counterpart of all eligible citizens’ preferences. If the
distribution of preferences represented through elections is distorted, the chance of
accurate responsiveness in policy outcomes will be lower.
Figure 3.1 displays examples of higher and less distortion in preference distributions.
The preference distribution of the whole society is plotted in red. The distribution of voter
turnout in the upper graph has less distortion compared to that in the bottom because the
green-dashed distribution of voter turnout has more area outside the population
distribution.

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0.4
0.2
0.0

Density

Population
Voter turnout

-6

-4

-2

0

2

4

6

0.2

Population
Voter turnout

0.0

Density

0.4

Less Distortion in Preference Distribution

-10

-5

0

5

10

Higher Distortion in Preference Distribution

Figure 3.1 Examples of Distortion in Preference Distribution

Indeed, one of the fundamental principles of democratic government is fairness and
equal representation (Dahl 1956). All individual preferences should be counted as
equivalent. As Mill argues, proportional representation ‘secures a representation, in
proportion to numbers, of every division of the electoral body: not two great parties alone’
(Mill 1862, 156). When this principle is applied to our case, it requires the consistency
between the preference distribution of voter turnout and that of all eligible citizens with

74

the right to vote. Verba argues that, ‘one of the bedrock principles in a democracy is the
equal consideration of the preferences and interests of all citizens’ (Verba 2003, 663).
Because all citizens do not vote, the more homogeneous the two distributions are, the less
misrepresentation occurs as a result of the partial voter turnout.
To sum up, this paper evaluates the degree of political representation in a polity by
comparing the preference distribution of voter turnout against the analogue derived from
all eligible voters. 30 Dalton depicts ‘the basic goal of representative government’ as
‘political decision makers enter[ing] the policy process with the same policy preferences as
the public’ (Dalton 1985, 275). Thus, the correspondence between the elites’ attitudes and
the overall citizens’ preferences in substantive representation hinges on an unbiased voter
distribution created by higher voter turnout.
Although voting in elections is based on geographical constituency voters belong to,
the discrimination among constituencies should be less distinctive on issues across different
locations, such as gender, environment, global trade and so on (Rehfeld 2005; Urbinati and
Warren 2008). Weissberg argues that the degree of representation measured collectively is
always no worse than that metered district by district (Weissberg, 1978). Following this
tradition, I calculate the degree of political representation by using a probabilistically
illustrative sample in a democratic country. Assuming that a quintessential issue dimension
of the citizens’ preferences is determined, this method requires the distribution be
congruent between two groups of voters along that issue dimension. This requirement

30

Although Miller and Stokes (1963) adopt the same viewpoint to examine preference
consistency in the dyadic representative-constituent relationship, this method may be
misleading due to randomness in the binominal matching process at the district level
(Achen 1977, 1978).
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means that the distribution of voter turnout should be a mirror of all eligible voters
because it is voter turnout that selects and authorizes representatives to rule. This can be
viewed as a preliminary step to reach Pitkin’s descriptive representation which asks that
the ‘legislature be a mirror of the nation or of public opinion’ (Pitkin 1967, 61).

2. The Influence of Electoral Institutions on Political Representation
The central focus of substantive representation is the reflection of citizens’ preferences in
final policy outcomes. The mandate theory of democracy requires that political
representatives, such as political parties, are a smaller set of delegates whose authority
comes from the aggregation of diverse citizens’ preferences expressed through voting in
elections (Converse and Pierce 1986).31 This defines the linkage between the citizens’
preferences and the government policy with the initial step of political representation is to
know the former.
With the emphasis on mandate theory, the means to reveal citizens’ preferences is
voting in elections. McDonald and Budge write vividly that the role of elections is ‘to
communicate where the median voter stands’ and that ‘voting is an expressive act with a
guaranteed value: every vote counts not in deciding the winner but in identifying the
median’ (McDonald and Budge 2005, 12). The policy-making process depends on the
plurality’s preferences of the policymakers, and their preferences should correspond to the

31

This definition does not exclude Edmund Burke’s view of the relationship between
voters and representatives as a trusteeship. According to the famous Diamond diagram in
Miller and Stokes (1963, 52), constituents’ sentiments have an impact on politicians’
opinions. Furthermore, the relationship between voters and their agents should not be
dichotomized; rather, it should be a combination of both types. (Converse and Pierce
1986).
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preferences of the citizens. This congruence demonstrates the importance of the position of
the median voter. However, the position of the median voter is not fixed and relies on those
voters who do go to the polling station to cast their ballots. Voter turnout decides what
political views are representational by the vehicle of political parties.
Meanwhile, Downs’ spatial theory provides a succinct model in which voters select
among political parties with alternative policy packages (Downs 1957). Political parties are
the devices offering various policy programs to represent the citizens’ preferences and enact
the policy position with a mandate in government policy (Converse and Pierce 1986;
Dalton 1985; Kitschelt et al. 1999; Schmitt and Thomassen 1999).32
Importantly, the position-taking strategies of political parties are not created out of a
vacuum but are chosen in response to the context provided by electoral systems. On the
one hand, the available range of policy packages varies across countries that have adopted
differing electoral institutions (Cox 1990a; Katz 1997). On the other hand, the effective
number of political parties is higher under PR compared to SMD because the effective
threshold of representation is usually lower under PR (Lijphart 1994; Taagepera 2007).
The two factors summarize the effects of electoral systems on the campaign strategies of
political parties.
Finally, instead of asking whether the congruence between the citizens’ preferences and
the final policy outcome, we need to take one more step back from the party’s policy
package to investigate the source of the mandate. Despite examining the coherence

32

At the electoral stage, different political agents propose contrasting policy programs to
allow voters to express their preferences. The linkage between the will of the citizens and
the government policy hinges on political agents’ carrying out their campaign promises
(Klingemann et al. 1994).
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between the two ends of the linkage process, the input of the fidelity of the citizens’
preferences is crucial. As explained in the previous chapter that electoral institutions have
impacts on individual voters’ decision-making on casting a ballot, so the essential question
to query is whether citizens’ preferences are expressed faithfully across various turnout
rates under electoral systems. The more consistent the preference distributions between
voters who turn out and the whole eligible electorate are, the more representative an
electoral system is. In other words, when the input of the citizens’ preferences is unbiased,
there is a higher chance that they can be integrated into the final policy outcomes.

2.1 Background Research
The studies of substantive representation shift the focus from dyadic representation to
collective representation. The tradition of substantive representation begins with Miller
and Stokes’ (1963) dyadic congruence between representatives and their constituents.
Converse and Pierce (1986) extend the theoretical underpinnings of dyadic representation
in their book on French electoral politics. Yet dyadic representation suffers the failure of
correlation coefficient to show the truthful relationship between the policy positions of the
representatives and those of their districts (Achen 1978; Weissberg 1978). While
investigating substantive representation dynamically or comparatively, scholars choose to
explore collective congruence between elites’ policy preferences and public opinion in a
political system (Fowler and Smirnov 2007; Holmberg 1999; Kitschelt et al. 1999; Stimson
et al. 1995; Thomassen and Schmitt 1999; Holmberg 2000; Thomassen and Schmitt 1997).
Moreover, Esaiasson finds that the extent of agreement between voters of a particular
constituency and the collective of party representatives is at least the same as between the

78

constituents and their own specific representative. His findings were valid in Sweden, West
Germany, France, and the USA (Esaiasson 1999). The main assumption that facilitates such
an observation is that the amount of geographical variation within a polity is smaller
compared to the variance within a district. The collective perspective also makes plausible
the examination of how characteristics of a political system influence political
representation.
Electoral systems are an important factor in explaining the correspondence between
popular preferences and government policy. The two stages in the linkage process that
produces substantive representation are: (1) citizens’ preferences select some agents and (2)
agents participate in the legislature or the government to make policies. The units of
analysis for comparison usually are two-fold: the issue position of political parties and the
policy position of the government. Under the concept of responsible party government,
parties carry the preferences of those who vote for them into the policy-making process.
Congruence is measured by the degree of correspondence between the collective of party
elites and its supporters’ preferences in a political system (Dalton 1985; Golder and
Stramski 2010; Luna and Zechmeister 2005; Wessels 1999). The assumption is that
political parties, as the device for preference aggregation, would represent their supporters
faithfully in the second stage.
On the other hand, the second type of units of analysis is institutions like government.
The government position is approximated by the weighted position of government parties
according to seat share in parliament (Blais and Bodet 2006; Huber and Powell 1994;
Powell 2000), or by the position of the median legislative party (Budge and McDonald
2007; McDonald et al. 2004; Powell and Vanberg 2000; Powell 2006). This model

79

connects the citizens’ preferences directly to the government without paying attention to
how the final policy is created. Thus, the model treats the two separate stages as one single
process.
Most congruence analyses reach the conclusion that PR systems produce better
representation than non-PR ones. With PR providing more diverse party choices and more
closely proportional vote-to-seat transformations, it is able to create a government that
better reflects the median voter. However, two recent studies find that PR does not
outperform SMD on the criterion of the congruence between citizens’ preferences and the
government policy (Blais and Bodet 2006; Golder and Stramski 2010). Although Powell
accounts for the anomaly as a difference in the data sources and the time periods covered
(Powell 2009), it is still puzzling why the effects of PR are not consistent across studies.
The proposed study argues that previous research does not take into account the
effects of electoral institutions on the citizens’ preferences at stage one. While the
congruence of the citizens’ preferences is compared with either political parties or the
government, the selection of these agents is determined partially by voter turnout, which in
the real world varies across countries. The mechanisms of PR and SMD work differently to
represent the citizens’ preferences. Under SMD, the government is delegated to a single
party determined by electoral competition whereas under PR, the government is formed
through postelection negotiation (Lijphart 1999; Powell 2000). In other words, the effect
of electoral institutions on the degree of congruence depends on the coordination of
political parties at both stages. While the representation of citizens’ preferences under
SMD needs more stringent coordination at the first stage, the counterpart under PR
happens mostly during the second stage. As Cox explains, “if coordination is more likely to

80

fail at the electoral stage, then majoritarian systems will be more erratic. If coordination is
more likely to fail at the government formation stage, then PR systems will be more
erratic” (Cox 1997, 237).
In short, political representation is a product of the interactions between voters and
political parties through the process of electoral competition. Previous research
concentrates only on the effects of electoral institutions on political parties but not on the
voters. The acting agents under either PR or SMD are based on the preferences expressed
by the total number of voters who turnout during the election. Since electoral systems also
influence higher or lower turnout in a polity, the bias introduced by electoral systems affect
not only how political agents represent the citizens’ preferences, but also which citizens
express their preferences by turning out to vote in elections. Therefore, electoral systems’
effects on political parties and political representation should not be the only target of
research. I propose to incorporate the effect of voter turnout via electoral systems on the
expression of citizens’ preferences and thus, policy responsiveness.

2.2 Electoral Systems and Voter Turnout through Spatial Theory
The representation of the electoral process can be broken down into three connected
elements: the individual decision to vote, the preference distribution of those who vote, and
how party competition seeks the support of those who turnout. The first component is the
focus of this study.
Suppose that the citizens’ preferences are distributed in one dimension policy space33

33

The assumption of unidimensionality is reasonable if the most salient issue exists within
a country and it coincides with the left-right scale. The most usual dimension can be
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(see the next section). The structure of the dimension is to set up a common frame for
communication between voters and political parties. In the literature, the left-right
dimension has become the focus of the analysis since it is most applicable (McDonald and
Budge 2005; Powell 2000).34
The forces of electoral system on political representation through voter turnout are
contingent on the collective congruence between the preference distribution of voter
turnout and that of the citizens as a whole. If nonvoters includes some certain groups of
disadvantaged citizens such as low income, or ethnic minority, the elected agents may not
be responsive to include their needs in the government policy. Thus, the initial inquiry of
the degree of political representation is to ask the question whether or not the distribution
of those regular voters in elections is biased against the whole range of the distribution of
the whole society.
First, the incentives of participation are different across electoral systems. Individual
decisions of voting or not depend not only on many contextual-specific factors but also on
the effects of electoral institutions. The decision to participate or abstain in elections shows
whether eligible citizens can appropriate deputies to represent their preferences. The
central claim of Chapter Three is that individual evaluations of the B term in the calculus
of voting are affected by spatial party competition framed by electoral institutions. While
SMD constrains the number of political parties and creates large centripetal forces for
party competition, it reduces individual perceptions of the B term. In contrast, PR allows
more political parties to survive and does not generate many centripetal forces and helps
assumed the left-right dimension. It may change depending on the context.
34
Scholars also prove that voters do have an understanding of where their self-position
and the stands of political on the left-right space (Converse and Pierce 1986; Pierce 1999).
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voters acquire higher estimates of the B term. Building upon insights from spatial voting
theories, Chapter Two argues that a voter’s turnout propensity increases as the distance
between her position and the policy position of her most favored party decreases.
Conversely, a voter is more likely to turn out if the policy distance between her and her
least favored party increases. Taken together, a voter’s turnout propensity should be
increased more by PR than by SMD, ceteris paribus.
However, not all eligible voters exercise political participation, and it is those who do
go to the polling station that select representatives and hold them accountable. Do those
types of voters who show up for elections faithfully cover the full range of the policy space?
We must know whether voting turnout leaves some parts of the distribution unrepresented.
If representatives know that a certain portion of their constituents relinquishes their rights,
they may not take into consideration their interest in the policy-making process. Thus, the
resulting policy outcomes may be biased against those who abstain in elections. Based on
aforementioned mechanisms of voter turnout, the relationship between electoral systems
and substantive representation measured by preference distribution consistency
contrasting voter turnout versus all eligible voters, needs to be explored.

2.3 Electoral Systems and the Degree of Political Representation
The focus of this section is to discuss how electoral systems influence different portions
of the electorate’s voting propensity in a unidimensional policy space. We ask the question
whether the rates of participation and abstention spread evenly or disproportionally
among all electors under electoral systems. Put it briefly, this amounts to comparing the
relative positions of voters and nonvoters in the issue space. If the rates of participation

83

and abstention are pretty close across the whole range of the distribution, the resulting
preference distribution of voter turnout will be similar to that of electorate.
The main argument acts on the following assumptions: (1) Electoral systems and the
number of political parties are fixed before each election and are treated as exogenous; (2)
Political parties or candidates campaign by choosing issue positions in the issue space; (3)
Voters respond to information and messages sent by political agents and decide whether or
not to cast their ballot. Then, the key question is: what portions or segments of the
preference distribution of voters on the main issue are more likely to vote or abstain?
Next, political parties choose their issue positions to solicit voters’ support. Cox
(1990a) classifies electoral systems into centripetal and centrifugal types based on how
electoral laws lead political agents to take converging or dispersed positions in a
one-dimensional issue space. Cox finds that SMD is the most centripetal electoral system,
whereas PR is the most centrifugal one. Obviously, the more centripetal an electoral system
is, the more convergent are the issue positions political agents will choose. Moreover,
political parties decide their issue positions in response to rival parties’ policy shifts and to
public opinion. In the former, political parties are more likely to diverge from the median if
other parties do so, especially those in the same ideological families (Adams and
Somer-Topcu 2009). In the latter, the centrist and rightist parties react to public opinion
more quickly than the leftist ones (Adams et al. 2009). These patterns of the parties’
positioning strategies confirm the institutional effects of electoral systems.35

35

The positioning strategies under SMD and PR can also be explained from the angle of
entry problem. In equilibrium, the strategy under SMD is convergent toward the median
while that under PR is candidate dispersion over the policy space. This is the best response
under both types of electoral institutions because the threat of entry from new candidates
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Voters react to political parties’ campaign promises by two classes of electoral models:
the moral hazard model and the adverse selection model. Voters make their decision to
participation based either on the former with available information about candidates like
incumbent government performance and campaign promises, or on the latter with
anticipation about how they would behave in office (Ferejohn 1993). In particular, the
citizens derived their voting utility from the combination of both sources of information.
Hence, the issue positions taken by candidates under SMD or PR provide useful hints to
voters’ decision of political participation.36
Thus, the citizens use their right to vote as the means for controlling politicians by
responding to campaigning strategies structured by electoral systems. The B term of voting
in elections largely includes two parts: the F factor, how closely a voter’s ideal point will
see implementation in government policy; the H factor, how far the distance is between a
voter’s ideal point and her least preferred party. More specifically, in an electoral system
with more median-convergent stimuli, the utility derived from the first component of the B
term tends to become smaller and decreases the propensity of voting. On the contrary, in a
more centrifugal electoral system, the induced utility of the second component of the B
term is likely to become larger and increases the incentive of voting. In conclusion, on
average, SMD tends to induce a smaller F factor and a smaller H factor than PR does in a
does not exist (Greenberg and Weber 1985; Palfrey 1989).
36
The classes of electoral models both have equilibriums under unidimensional issue
space. The politicians are uncontrollable in a multidimensional issue space (Ferejohn 1986,
1993). Usually the dimensionality can be reduced to one because the single dimension can
explain an essential part of variance of many issues. In other words, many issue positions
can be mapped into the most salient issue space. This argument has been confirmed in
empirical research of roll call data in American (Jackman 2001; Poole and Rosenthal
1985). In the comparative research of substantive representation, the single issue space is
the left-right dimension (Huber and Powell 1994; McDonald et al. 2004; Powell 2006).
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unidimensional space.
Using Powell’s language, the vision of two-candidate elections, mostly in SMD
systems, is majoritarian, and that of multiple-candidate elections, usually in PR, is
proportional (Powell 2000). The former vision sees elections as instruments to control the
concentrated policy-making power and the latter consider elections as an indirect role to
influence factions in the dispersed counterpart. In voters’ minds, they need to take into
account both components of the B terms in both types of elections. In the majoritarian
view, citizens only need to worry how distant their less preferable candidate is since the
policy-making power is delegated to either her favorable or unfavorable candidate. In the
proportional view, voters have to think about the policy positions of all representative
agents, who will enter the bargaining process. Although their votes in the
multiple-candidate competition only exert indirect influence on the final policy outcome, a
voter must consider how her least preferable agent will weigh in after elections. More
specifically, the minimization of the issue proximity is the same across all types of elections,
but how voters perceive the seriousness of threats from their least preferable candidates
under SMD and PR relies on the second component.
Classifying voters based on the relative location along the distribution of their ideal
points helps analyze the question about which segment of voters are more likely to turn
out. The distribution of voter preferences can be divided into three segments: the leftist, the
moderate, and the rightist from minimum to maximum. The classification of left and right
does not matter because the same categorization can be obtained by reserving the direction.
I define three types by voters’ relative locations on the issue spectrum: the leftist toward the
left end, the moderate, and the rightist toward the right end. The categorization is to define

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three types of voters and their actual locations are not the main concerns here.
The effects of electoral systems on three types of voters vary through different
evaluations of two components of the B term. Under SMD, the moderate type has a
satisfactory F factor and a low H factor because two agents converge toward the median.
In the mean time, the other two types have an unsatisfactory F factor and low H factor
because two agents are not only far from their ideal points but also cluster together. Hence,
all three types of voters have low incentives to go to the polling station. Furthermore,
under PR, the moderate type has a similar incentive scheme to their counterpart under
SMD because they can find a political agent to represent and also because the extreme
types of agents are not so threatening to them. The story of the leftist and rightist is
different under PR because they would not only have a satisfactory F factor but also have a
high H factor. The F factor is satisfactory because there are extreme types of agents staying
at out of interquartile range. The H factor is high because they sense the threat from the
other extreme of the distribution. Thus, the incentives of turnout for different types of
voters are universally low under SMD. However, they are low only for the moderate type
under PR but are high for two extreme types of voters.
Based on discussion above, the degree of political representation defined by the
distortion of the distribution of voter preferences induced by turnout variation across
electoral systems is higher under SMD than under PR. The preference distribution is more
biased because more extreme types are more likely to vote while they locate at the lower
density area of the distribution. Therefore, the main research hypothesis is as follows:

The degree of political representation is higher under SMD than under PR because the

87

resulting distribution of voter preferences is more consistent against that of the citizens’
under SMD than under PR.

3. The Institutional Effects of Electoral Systems on Representation
3.1 Selection of Cases and Data
To explore the institutional effects of electoral systems on substantive representation
from a collective perspective, it is necessary to compare the preference distributions
country by country. The unit of analysis is a polity. The advantage to compare the degree
of political representation at the country level is that the institutional impacts on citizens’
decision to vote in elections are the same to everyone in a political system. Moreover, to
make the distribution comparatively equivalent, the issue space needs to be measured on
an identical scale. The citizen preference distribution should be a quintessential sample
within a polity. Survey data across countries can approximate reasonably the preference
distribution. Thus the data sets of comparative study of electoral systems (CSES) meet our
requirements of empirical analyses.
Following the case selection criteria in Chapter Two for the round 1 and round 2 of
CSES project from 1996 to 2006, there are 64 elections included. The same 64 elections
are used to calculate of the F and H factors for multilevel analysis. However, for the
collective representation at the country level, those elections with the measure of the
citizens’ preference distribution can enter the congruence analysis without any concerns
because the analysis only require voters to identify their policy stands on the issue
spectrum and their decision to vote in an election. These elections are Chile 1999, Belgium
2003, Netherlands 2002, and the USA 1996. Thus, there are 68 elections for collective

88

congruence analysis. Please see appendix for more detail about these elections.

3.2 Measurement
3.2.1 The Dependent Variable
In order to measure the degree of representation of voter turnout vs. the whole eligible
voters, two steps should be taken. First, pick an essential dimension of the citizens’
preferences to compare across two groups. Second, decide how to measure the discrepancy
between the distributions of voter turnout and the whole population.
The dimension picked for analysis is the left-right issue space. The battery question is
“In politics people sometimes talk of left and right. Where would you place yourself on a
scale from 0 to 10 where 0 means the left and 10 means the right?” The question measures
the citizens’ preferences over the left-right and provides us with a distribution for
comparison across voters against all eligible voters. While the issue dimension is
determined, the next step is to discriminate two groups of respondents. The group
indicator is the binary variable: whether the respondent voted or not in the previous
election.
In order to calculate the discrepancy between two distributions and take the
consideration of variable equivalence across countries into account, the frequency of
probabilistic samples within one country from 0 to 10 is computed to be proportions.
Another reason for calculating proportions is so that sample sizes across countries and
sample numbers will not affect the discrepancy between distributions. These proportions
are summed up to 1 according to Kolmogorov axioms of probability because they
represent the discrete mass at each point from 0 to 10. The same method can be applied to

89

two groups of samples.
The congruence between the distribution of voter turnout and that of all eligible
voters display how the effects of electoral institutions on voter turnout transform the
citizens’ preferences. If the preference distribution communicated by voter turnout is
identical with that of all citizens, it means that there is no bias introduced by electoral
systems. This approach is similar to previous research that it checks the relationship
between the citizens’ preferences and their representatives from a collective perspective, but
it is dissimilar in that it examines the effects of electoral institutions on the voter side. The
reason for the focus on voters is because their preferences are the object to be represented
and the fidelity of preference communication through the electoral competition should be
the guarantee of the quality of the democratic process.
The measure of the congruence of two preference distributions is the distance between
two distributions. The idea of comparing two distributions for the degree of political
representation is fairly new, except in Golder and Stramski (2010), in which they called it a
‘Many to Many’ relationship and focus on the congruence between the distributions of
citizen and representative preferences. The concept is to compute the difference between
two distributions. Golder and Stramski adopt the method of calculating the difference in
area of the cumulative distribution functions of the two distributions (Golder and Stramski
2010, 96). The shortcoming of this method is that the distribution needs to be transformed
first and the left-right ideological measure in the survey is usually from 0 to 10, which is
discrete, not continuous. Therefore, the transformation may be problematic.
I utilize a more intuitive approach to evaluate the difference between the two
distributions, the Kullback-Leibler distance (KLD henceforth) is a good choice to measure

90

the closeness of two distributions (Gill 2008). KLD can be computed directly using
probability distribution functions and no transformation is needed. Suppose that the
distribution function of all eligible citizens’ preferences is normal. If the resulting
distribution of voter turnout is also normal but with another mean and a different
standard deviation, the KLDs of the two indicate how far apart the two distributions are.
Another example is the distribution of turnout is uniform. KLD between normal and
uniform distributions is greater compared to that of the former example.
KLD is used to measure the degree of political representation between voter turnout
against all eligible voters. The formula is defined by:

(3-1)

⎡ f ( x) ⎤
I ( f , g ) = ∫ log ⎢
⎥ f ( x)dx
⎣ g ( x) ⎦

for two candidate distributions (Robert and Casella 1999, 222). The Kullback-Leibler
distance is computed by using the distribution of voter turnout, f(x), compared to the
distribution of all electorate, g(x). So the distance indicates the degree of deviation of the
distribution of voter turnout preferences from the whole electorate. This is a measure of
disproportionality at the country level. The total number of observations is 68.
Examples of KLD are shown in Figure 3.2. From top to bottom, the degree of
similarity is from the greatest to the least and KLD ranges from small to large. Smaller
KLD, which the distance between two distributions is close, means that they look alike.
The measure of larger KLD indicates that two preference distributions are different in their
locations and shapes.

91

0.4
0.2
0.0

Density

g(x)
f(x)

-6

-4

-2

0

2

4

6

0.2

g(x)
f(x)

0.0

Density

0.4

Small KLD

-10

-5

0

5

10

0.2

g(x)
f(x)

0.0

Density

0.4

Moderate KLD

-5

0

5

Large KLD

Figure 3.2 Examples of KLD Computation

3.2.2 The Classifications of Electoral Systems
The classifications of electoral systems follow the standards specified in Chapter Two
into four categories: majoritarian, combined-independent, combined-dependent, and
proportional representation. Majoritarian systems include the first-past-the-post or the
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two-round 2nd ballot systems. Second, combined-independent systems contain two tiers of
districts using SMD and PR formulae to allocate seats separately. Third, compensatory
mixed electoral systems have the same features as the previous type except that the seat
allocation is according to the vote shares in the PR tier. Forth, PR systems cover those
countries with larger district magnitude and a variety of PR formulae to distribute seats to
political parties. Furthermore, for presidential and parliamentary elections held
concurrently, if the formulae are not the same in both levels, the centripetal effects of SMD
will be contradicted by those of PR.
I further arrange the electoral systems by the degree of centripetal forces into three
categories from the strongest to the weakest: the strongest is majoritarian, concurrent
SMD, and AV; the medium is non-compensatory mixed and concurrent SMD and PR; the
weakest is either compensatory mixed or proportional. This categorization illustrates how
electoral institutions will shape party competitions. Thus, these definitions give us three
types as SMD1, Mixed1, and PR1 (see Appendix Table A.3 for detail).
In order to test the robustness of the categorization, compensatory mixed electoral
systems are not combined with PR according to Shugart and Wattenberg (2001).

Thus

we have four categories: SMD2, MMM, MMP, and PR2, where MMM stands for
mixed-member majoritarian and MMP stands for mixed-member proportional.

3.2.3 Aggregate-level Control Variables
Three aggregate measures of political fragmentation are used, which are effective
number of parties, district magnitude, and the degree of political competition. These three
variables should be negatively related with the KLD because these are all beneficial to

93

proportionality.
Compulsory voting is considered as an important factor in the voting cost calculation.
In those countries with compulsory voting and high punishment of nonvoting, the voter
turnout should be larger than those without compulsory voting or those with lower
punishment of nonvoting. Thus the coefficient for compulsory voting is expected to be
negative. The compulsory voting is measured at five levels from ‘No,’ ‘Yes, without
sanction for violation,’ ‘Limited enforcement,’ ‘Yes, weakly enforced sanctions,’ and ‘Yes,
strictly enforced sanctions.’ If more voters are forced to go to the polls, KLD will be
smaller.
Another contextual variable is the frequency of elections. If there are more national
elections, citizens may feel that electoral contests are less decisive or citizen may develop
“burn out” from repeated voting. This variable is put in as a control variable and the sign
is expected to be positive. The same logic of compulsory voting appears again here. Since
voters are more likely to abstain their rights due to too many elections, the possibility that
the difference of two distributions of turnout versus all eligible voters will be higher. More
frequent the elections, the larger the KLD.
Developing is a dummy variable of developing countries which includes all countries
not in the OECD. This dummy variable can let us compare whether the degree of
disproportionality varies across established and non-established democracies.

3.3 Descriptive Statistics of KLD by Electoral Systems
The summary statistics by different types of electoral systems are shown in Table 3.1. As
expected, the mean level of the degree of disproportionality is ranked by PR, Mixed, and

94

SMD from the highest to the lowest. The degree of disproportionality in PR is twice the
number of SMD by our measure. This preliminary result confirms our main hypothesis
that though PR induces higher voter turnout, it generates more discrepancy between the
preference distribution of voter turnout and that of the electorate. The main reason for this
phenomenon is that those voters at the interquartile range of the preference distribution
have lower incentives to cast their ballot.
To verify the robustness of the previous finding, mixed electoral systems are
reclassified by Shugart & Wattenberg’s typology. The summary statistics are displayed at
the bottom of Table 3.1. Basically we make the same conclusion as the original
classification. Surprisingly, compensatory mixed PR-SMD electoral systems have the
lowest degree of disproportionality. Maybe this is the consequence of the combination of
both kinds of electoral systems, but the conclusion is tentative due to there only being 5
cases in this category.

Table 3.1 Summary Statistics of KLD by Types of Electoral Systems
Catogory
Types
Mean (SD)
Cases
Centripetal
SMD1
0.154 0.183
21
Mixed1
0.261 0.233
12
PR1
0.365 0.562
35
Shugart &
SMD2
0.154 0.183
21
Watternberg
MMM
0.261 0.233
12
MMP
0.127 0.136
5
PR2
0.405 0.597
30

3.4 Random Intercept Regression Model
In order to explore whether the disproportionality of PR is higher than SMD, a more
sophisticated method is necessary to eliminate the impacts of other confounding variables.
Since KLD is a measure on a continuous scale, a linear regression model fits the need. To

95

control for unobservable country-specific characteristics, random intercepts assumption is
reasonable. Each intercept can be interpreted as anything belonging with a country and not
generalizable across borders. There are 37 countries with 68 elections. A common intercept
is estimated for one country with several elections and a particular one is estimated for
those countries with just one election in the data set. This method amounts to putting a
dummy variable into the right hand side and will not cause the identification issue. Since
the goal of the model is to control for those country-specific effects, we should not focus
on explaining these coefficients. Bayesian methods are used in model estimation because
this avoids the problem of degrees of freedom that would otherwise result from the small
number of cases. The main assumption of Bayesian method is that all estimated coefficients
are assumed to have a non-informative prior.
The estimation results of the first categorization of electoral systems are shown in
Table 3.2. The statistics presented in the table are the means and various quantiles of the
posterior distribution. The mean indicates the centrality of distribution while the quantiles
contain information about how the posterior distribution spreads among its range because
not all posterior distribution is symmetric. Several observations can be made:
(1) The coefficient mean of the PR variable is 0.152. This is consistent with our
conjecture in Hypothesis 1 that compared with SMD PR does have a higher
disproportionality through higher voter turnout mechanisms. The positive range of
the PR posterior distribution is around 80%. This means that we have a
reasonable, though not strong evidence to support Hypothesis 1.
(2) The average coefficient of Frequency is 1.299. The more frequent the elections, the
higher probable the disproportionality. This shows that voters will be tired of

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elections and less likely to turn out if elections are too many. More frequent
elections will cause larger disproportionality. The evidence of this argument is
strong because the 95% range of the posterior is positive.
(3) Political competition reduces disproportion, though the mean effect is -0.06, which
is smaller when compared with the previous two variables. Around the 90% range
of the posterior is negative.
(4) The developing countries have a lower disproportionality than the developed
countries. The mean coefficient is -0.286 and the 95% range of the posterior locate
in the negative area. The possible explanation is that there are fewer voters who
customarily abstain and voters are less inclined to relinquish their right to vote
across the whole range of the distribution. So the resulting distribution of voter
preferences is less distorted.
(5) The results of the second categorization of electoral systems are shown in Table
3.3. Similar conclusions can be derived from these coefficients. For electoral
institution variables, PR has a stronger positive effect on disproportionality with
the mean coefficient at 0.205 and with the 90% positive range. At the same time,
MMP also has a moderate negative effect on disproportionality with 80% negative
range.

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Table 3.2 Random-Intercept Regression Model of KLD in 68 Elections with 3 Types of
Electoral Systems
Mean
1.299
-0.006
-0.286
0.152
0.053
0.006
-0.001
-0.036

5%
0.618
-0.013
-0.541
-0.096
-0.219
-0.057
-0.002
-0.112

10%
0.776
-0.011
-0.483
-0.039
-0.158
-0.042
-0.002
-0.095

15%
0.881
-0.010
-0.444
-0.004
-0.117
-0.033
-0.001
-0.083

20%
0.958
-0.009
-0.414
0.025
-0.085
-0.025
-0.001
-0.074

80%
1.641
-0.002
-0.286
0.278
0.053
0.038
0.001
-0.035

85%
1.722
-0.002
-0.157
0.307
0.192
0.046
0.001
0.002

90%
1.821
-0.001
-0.090
0.344
0.266
0.055
0.001
0.023

95%
1.971
0.001
-0.034
0.401
0.326
0.069
0.002
0.040

σIntercept

0.175

0.017

0.047

0.072

0.092

0.179

0.252

0.288

0.319

σResidual
Deviance

0.375

0.305

0.319

0.328

0.336

0.412

0.422

0.434

0.452

57.766 38.619

42.52

45.36

47.63

67.94

69.63

71.66

74.74

Variable
Frequency
Politic competition
Developing
PR
Mixed
ENP
District magnitude
Compulsory
Variance Part

The main point of the collective congruence analysis at the country level is that PR has
a higher probability to induce biases into the distribution of citizen preference because
more extreme voters are more likely to find a viable political party to support. The
previous research which focuses on the congruence between the citizen preferences and the
median party in the legislature or the government policy outcome, basically concludes that
PR has advantages at creating congruence and thus, producing a better political
representation (Huber and Powell 1994; McDonald et al. 2004; Powell and Vanberg 2000;
Powell 2006). The mechanisms proposed in these studies mainly explain the different
degrees of congruence in political representation through the actions of political parties.
SMD requires the majority party to move toward the position of the median voter. While
this requirement is more stringent, political parties may often fail to fulfill it. On the other
hand, under PR, the reduction of the distance between the median parliamentary party or
the government policy hinges on the postelection bargaining process, but not on the party
coordination at the electoral stage (Powell 2006). From the time dynamic aspect, the

98

adjustment to get closer to the median voter is higher under SMD than PR because
political parties are able to propose a policy platform with more freedom. However, in the
long run, the congruence between citizen preferences and the government policy is closer
under PR than SMD (Budge and McDonald 2007).
These preceding studies do not take into account the effects of electoral institutions on
the voter side. By bringing the consideration of the influence of electoral systems on voter
participation back, I find that PR has a higher chance to generate disproportionality into
voter preference distribution. The argument is in line with Blais and Bodet (2006) and
Golder and Stramski (2010). Although Powell (2009) concludes that the different
conclusions are due to the data in a later time period, this study provides another
explanation: the effects of PR in the congruence between the citizen preferences and the
government policy are balanced by the biases it introduces in the voter turnout.

Table 3.3 Random-Intercept Regression Model of KLD in 68 Elections with 4 Types of
Electoral Systems
Mean
1.273
-0.005
-0.282
0.205
-0.222
0.068
-0.002
-0.001
-0.028

5%
0.590
-0.012
-0.537
-0.060
-0.598
-0.205
-0.067
-0.002
-0.106

10%
0.747
-0.011
-0.479
0.001
-0.515
-0.143
-0.052
-0.002
-0.089

15%
0.847
-0.010
-0.442
0.040
-0.459
-0.102
-0.042
-0.001
-0.077

20%
0.930
-0.009
-0.412
0.072
-0.415
-0.069
-0.035
-0.001
-0.067

80%
1.617
-0.002
-0.152
0.339
-0.031
0.208
0.030
0.001
0.011

85%
1.697
-0.001
-0.123
0.370
0.014
0.240
0.038
0.001
0.020

90%
1.798
-0.001
-0.085
0.409
0.073
0.281
0.048
0.001
0.032

95%
1.949
0.001
-0.028
0.466
0.161
0.344
0.063
0.002
0.049

σIntercept

0.174

0.027

0.051

0.070

0.090

0.251

0.268

0.288

0.321

σResidual
Deviance

0.376

0.306

0.320

0.330

0.337

0.413

0.423

0.435

0.453

39.12 43.189

46.00

48.25

67.82

69.55

71.65

74.80

Variable
Frequency
Politic competition
Developing
PR
MMP
MMM
ENP
District magnitude
Compulsory
Variance Part

58.109

99

4. The Micro-foundations of Disproportionality of PR on Representation
To understand the source of why the biases of voter turnout toward the distribution of
citizen preference are higher under PR, we need to investigate the individual decision to
vote more thoroughly. The mechanism of higher disproportionality in PR is that voters
with a more extreme location in the preference distribution are more likely to go to the
polls than their counterparts in SMD. While extreme voter preferences have a higher
possibility to be expressed under PR than under SMD, the preference distribution of voter
turnout is more likely to have more biases under PR as compared to the preference
distribution of all citizens.
The operationalization of the relative location of voters in the preference distribution
is the transformation of the cumulative distribution function. Since the preference
distribution of the left-right is discrete from 0 to 10, there are many voters positioning
themselves at the same point. The voters with the same location should be ranked the same
in the indicator. Furthermore, for the purpose of comparison across countries, the different
shapes and spreads of preference distributions need to be standardized. The first step is to
transform each distribution into a cumulative distribution function (F(x)). Each voter then
has her own relative location in the distribution within a country. The range of F(x) is from
0 to 1 with extreme voters locating on the both ends close either to 0 or to 1. A second
transformation is necessary to capture the voters’ extremeness in the preference
distribution. The variable is defined as:

(3-2)

X=abs|F(x)-0.5|.

100

The second transformation is to take the absolute value of subtracting 0.5 from the
location in the cumulative distribution function. The X variable measures the extremeness
of voters’ location compared to other voters in the same country. We expect that X has
positive impacts on citizens’ decision to vote because when voters’ location is further from
the center of the distribution, they are more likely to have higher benefits in the calculus of
voting. Yet the institutional effects work differently under PR and under SMD. As PR has
more effective political parties and more extreme political parties, the extreme voters have
more incentives to support their favorite agents under PR than under SMD. In other words,
the effects of the X variable are hypothesized to be larger under PR.
Following the multilevel modeling method in Chapter Two, assume that the
coefficients of the X variable vary across elections. Using the model specification in
Chapter Two, I use all variables as control variables now. The model is written:

(3-3)

Prob(Voteij)=logit(β0j+β1*Femaleij+β2*Educationij+β3*Incomeij+β4*Inpowerij
+β5*Makediffij+β6*Partyidij+β7*Age26_35ij+β8*Age36_45ij
+β9*Age46ij+β10j*Fij+β11j*Hij+β12j*Xij +eij).

The intercept includes all control variables at the country level, which is:

(3-4)

β0j = γ0(0)+γ0(1)*Compulsory1j+γ0(2)*Compulsory2j+γ0(3)*Compulsory3j
+γ0(4)*Closenessj +γ0(5)*ENPj+γ0(6)*(District Magnitude)j+γ0(7)*Frequencyj

101

+γ0(8)*Concurrentj+γ0(9)*(LogDistrict Size)j+γ0(10)*(Political Competition)j
+γ0(11)*GDPj+γ0(12)*(L_GDPC_Developing)j+γ0(13)*(L_GDPC_Industrial)j
+γ0(14)*PRj+γ0(15)*MIXj+ u0.

For the random coefficient specification, I continue to assume that the F and H factors
differ across elections. The same assumption applies to the X variable as well. In order to
test for the institutional effects of PR versus non-PR, I put a dummy variable of PR as the
group predictor for the effects of the X variable. The formulae are as follows:

(3-5)

β10j =γ10(0) + u10;

(3-6)

β11j =γ11(0) + u11;

(3-7)

β11j =γ12(0) +γ12(1)* PRj + u11.

I utilize the hierarchical modeling method to estimate the calculus of voting under
electoral systems. Table 3.4 displays the maximum likelihood estimation results and Table
3.5 shows the results by Bayesian methods. Both tables tell a similar story about the effects
of the extreme variable. The micro-foundations of the effects of electoral systems on
political representation lie in the influence of X. The random coefficients of X, which is the
relative location of a voter in the preference distribution, demonstrate the individual
propensity to vote, controlling for relevant variables at both micro- and macro-levels. The
average coefficient estimate of X is positive and also significant at the 95% confidence

102

level. This shows that no matter what electoral institutions voters are situated in, on
average, they have a higher probability to decide to express their preferences by the act of
voting as their issue positions are more extreme in the distribution. Moreover, the indicator
variable of PR versus non-PR exhibits a positive coefficient which is statistically significant
as well. The meaning of the greater influence of PR in X is that those extreme citizens are
more likely to vote compared to those under SMD, despite of positive coefficients in both
circumstances. Thus, the consequences of X demonstrate the micro-foundation
mechanisms of PR.

5. Conclusion
The purpose of this paper is to explore the question of how electoral institutions affect the
degree of political representation through the perspective of comparing the distribution of
voter preferences versus that of all electorate. The effects of electoral systems on political
representation are based upon voters’ response to party competition under spatial theory.
The main argument is that different types of electorate, according to their relative locations
in the distribution of voter preferences, have various incentives to vote. The moderate type
of electors with location in the middle range has lower benefit evaluations for voting
across PR and SMD. However, the extreme type of electors with locations in smaller or
larger quantile has dissimilar profit schemes under PR and SMD. The profit calculation for
the extreme type is lower under SMD than PR because of indifference and alienation for
political parties’ policy position convergence toward the median voter. Thus, due to
inconsistent benefit evaluations among different types of electorate, PR has a higher
probability to induce disproportionality defined above.

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Table 3.4 Multilevel Model of Calculus of Voting in 64 Elections (Part 1)
Fixed Part

Coefficient

Robust SD

T-ratio

D.F.

P-value

Intercept of β0, γ0(0)

-0.656

1.816

-0.362

48

0.719

Compulsory1, γ0(1)

0.247

0.268

0.921

48

0.362

Compulsory2, γ0(2)

0.263

0.217

1.207

48

0.234

Compulsory3, γ0(3)

1.132

0.227

4.978

48

0.000

Closeness, γ0(4)

-1.443

0.447

-3.227

48

0.003

ENP, γ0(5)

-0.009

0.045

-0.205

48

0.838

0.002

0.001

1.552

48

0.127

Frequency, γ0(7)

-1.880

0.396

-4.748

48

0.000

Concurrent, γ0(8)

0.376

0.225

1.673

48

0.100

Log District size, γ0(9)

0.045

0.034

1.313

48

0.196

Political Competition, γ0(10)

-0.002

0.007

-0.300

48

0.765

GDP, γ0(11)

-0.007

0.146

-0.052

48

0.959

L_GDPC_D, γ0(12)

0.036

0.018

2.011

48

0.050

L_GDPC_I, γ0(13)

-0.062

0.025

-2.422

48

0.019

PR, γ0(14)

-0.081

0.182

-0.444

48

0.658

MIX, γ0(15)

-0.257

0.251

-1.024

48

0.312

Female, β1

0.024

0.022

0.708

66632

0.280

Education, β2

0.090

0.009

9.268

66632

0.000

Income, β3

0.082

0.009

8.588

66632

0.000

Inpower, β4

0.098

0.010

9.526

66632

0.000

Makediff, β5

0.167

0.015

10.689

66632

0.000

Partyid, β6

0.657

0.036

18.200

66632

0.000

Age26_35, β7

0.266

0.034

7.787

66632

0.000

Age36_45, β8

0.590

0.043

13.495

66632

0.000

Age46 and above, β9

0.922

0.052

17.560

66632

0.000

F slope, β10, Intercept, γ10(0)

0.007

0.001

6.714

63

0.000

H slope, β11, Intercept, γ11(0)

0.011

0.005

2.042

63

0.045

X slope, β12, Intercept γ12(0)

0.035

0.011

3.095

62

0.003

0.059

0.017

3.437

62

0.001

District magnitude, γ0(6)

PR, γ12(1)

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Table 3.4 Multilevel Model of Calculus of Voting in 64 Elections (Part 2, cont’d)
Random Part

Std. Dev.

Variance

1.81

σu0

0.722

0.522

σu10

χ

2

P-value

3.29

σe (scale factor)

D.F.

48 2708.7

0.000

0.006 0.00004

63

98.06

0.003

σu11

0.039

0.001

63 133.31

0.000

σu12

0.085

0.007

62 126.74

0.000

105

Table 3.5 Bayesian Hierarchical Model of Calculus of Voting in 64 Elections (Part 1)
Fixed Part

Posterior
mean

Intercept of β0, γ0(0)

Bayesian Confident Interval
Low(2.5%)

Median(50%)

High(97.5%)

They are 64 random parameters and not reported here.

Compulsory1, γ0(1)

1.398

-3.928

1.412

5.558

Compulsory2, γ0(2)

0.406

-0.339

0.401

1.149

Compulsory3, γ0(3)

0.678

-0.032

0.667

1.374

Closeness, γ0(4)

1.478

0.767

1.478

2.184

ENP, γ0(5)

-1.672

-3.350

-1.660

-0.034

District magnitude, γ0(6)

-0.005

-0.178

-0.016

0.224

Frequency, γ0(7)

0.003

-0.004

0.002

0.009

Concurrent, γ0(8)

0.376

-0.015

0.375

0.551

Log District size, γ0(9)

-0.006

-0.038

-0.005

0.024

Political Competition, γ0(10)

-0.399

-1.156

-0.393

0.359

GDP, γ0(11)

-0.132

-0.518

-0.146

0.364

L_GDPC_D, γ0(12)

0.035

-0.038

0.035

0.107

L_GDPC_I, γ0(13)

-0.073

-0.154

-0.072

0.007

PR, γ0(14)

-1.524

-2.734

-1.514

-0.346

MIX, γ0(15)

-0.158

-0.731

-0.164

0.404

Female, β1

0.025

-0.022

0.025

0.073

Education, β2

0.104

0.088

0.104

0.119

Income, β3

0.094

0.075

0.094

0.115

Inpower, β4

0.113

0.094

0.113

0.133

Makediff, β5

0.191

0.171

0.192

0.210

Partyid, β6

0.765

0.711

0.766

0.818

Age26_35, β7

0.300

0.222

0.301

0.376

Age36_45, β8

0.676

0.598

0.677

0.756

Age46 and above, β9

1.063

0.987

1.063

1.138

F slope, β10, Intercept, γ10(0)

0.006

0.003

0.005

0.009

H slope, β11, Intercept, γ11(0)

0.002

-0.011

0.001

0.017

X slope, β12, Intercept γ12(0)

0.043

0.005

0.042

0.083

0.062

0.013

0.061

0.110

PR, γ12(1)

106

Table 3.5 Bayesian Hierarchical Model of Calculus of Voting in 64 Elections (Part 2,
cont’d)
Random Part

Variance

σu0

0.746

0.604

0.739

0.935

σu10

0.073

0.034

0.073

0.111

σu11

0.004

0.001

0.004

0.009

σu12

0.035

0.021

0.035

0.051

This thesis is operationalized and tested by survey data from CSES in the macro level
of 68 elections and across the multi-levels of 64 elections. Summary statistics and a
random intercept regression model are utilized to examine the argument. Evidence is found
that PR has higher chance to produce disproportionality than SMD. Furthermore, a
multilevel model of the calculus of voting elucidates the micro-foundations of PR. The
reason that PR causes a higher disproportionality through the decision to vote is because
more extreme voters under PR have a higher voting propensity as compared to their
counterparts under SMD.
The future research agenda will need to include more elections with more diversity.
The 68 elections in this dataset are still close to a small N case, and their information will
not be sufficient to implement a more complex model. Furthermore, related to the data
issue, race, ethnicity, language, and religion variables are not available in all countries
included in CSES studies. This difficulty makes comparison of these properties across voter
turnout and all electorate impossible. If the data problem can be solved, a more thorough
examination can be executed toward different dimensions of voter turnout preferences.

107

CHAPTER 4
A COMPARISON OF ISSUE VOTING ACROSS ELECTORAL SYSTEMS
Electoral competition means that political parties seek the citizens’ support in a
representative democracy, which is the process of selecting policy makers as an
intermediate step linking voters’ preferences to policy outcomes. Political parties connect
voters to the government with two requirements: voter participation and elected officials’
responsiveness (Powell 2005). Political agents are responsive to citizens’ policy preferences,
which are expressed through voter participation. To represent the people, political parties
campaign with announced platforms to gain votes, which are subsequently transformed by
the electoral system into seats. The intermediate steps linking citizens’ preferences to policy
outcomes are from the electoral campaign to government policy-making. The current
research on political representation investigates the relationship between voters’
preferences and the policy positions of political parties; research on the latter uses either
announced platforms in elections (Adams 2001; Adams et al. 2005; Kedar 2005; Schofield
and Sened 2006) or the compromise of party positions in the government decision-making
process resulting policy outcomes (McDonald and Budge 2005; Powell 2006). The first
approach emphasizes the importance of party positioning strategies for being elected while
ignoring the policy-making process. On the other hand, the second approach correctly
focuses on the government process but fails to pay attention to how political agents are
chosen in elections in the first place. Although there is research that discusses the
consistency between election pledges and subsequent government policy actions (Thomson
2001), these studies fail to take account of how voter choices in elections are affected by
the government policy-making process.

108

The positioning strategy of political parties in elections is for the purpose of being
elected. When voters decide which parties to select for, they have expectations of how the
platforms of elected parties will be changed due to types of government (i.e., majority or
coalition). The process of political representation is to delegate agents to express
principals’ preferences. This definition has two properties: authorization and the truthful
transformation of the citizens’ preferences. The first determines who has the mandate to
voice for the people’s desires and the second means that representatives should support
policies that fit the people’s need. From the voters’ point of view, they would like the
policy outcome as closer to their own issue positions as possible. Therefore, when the
citizens cast their ballots for political parties, they take account of the change of their
positioning strategy in elections after parties enter the government.
The party strategies in election campaigns and in the government policy-making
process are heavily influenced by electoral institutions. District magnitude is an important
variable that shapes electoral competition in different electoral systems. The defining
feature of a single-member district system is that only one candidate can be elected, while
that of a proportional representation system is that multiple posts are filled. Under the
assumption of the single issue dimension in spatial theory, political parties and candidates
have electoral incentives to converge toward the center under SMD and to diverge under
PR (Cox 1990a). Furthermore, electoral systems are associated with contrasting
government policy-making processes. The government in SMD is delegated to a single
party, while the counterpart in PR is a coalition government comprising several political
parties as the result of bargaining. The former electoral system is majoritarian, and the
latter is called proportional (Huber and Powell 1994; Powell 2000). In other words, the

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policy position of political parties to be fulfilled in the government is picked by the
electorate at the election stage under SMD but the policy position of the government under
PR is adjusted by the negotiations among elites without any control by the electorate. As a
consequence, electoral institutions influence how political parties choose their positioning
strategies in campaigns and the consideration of how the policy positions of all winning
political parties will be executed in the government. Conditional on the policy positions of
political parties structured by electoral institutions in elections and in the government,
citizens make their choice of which political party to support. Thus, issue voting under
various types of electoral systems includes the possible trajectory of the formation of
postelection policy because the information related to how the policy is made is politicized.
Institutions matter. Spatial party competition describes how political parties pick their
issue positions with vote-maximizing motivations under different institutional settings.37
The most famous argument of spatial theory is the median voter theorem with political
party convergence to the center of the distribution of voters’ preferences (Downs 1957).
When extended to multiple competitors, candidates deviate from the centrist location in
equilibrium (Eaton and Lipsey 1975). These position-taking strategies are based on the
plurality rule with one seat elected. Where multiple seats are at stake, political parties
locate themselves across the issue space and top-vote getters’ victory is not guaranteed
(Greenberg and Shepsle 1987). The rule of how many seats are elected in one district can
change the positioning strategy. Electoral laws define the rules of the game which

37

The goal of vote-maximizing for political parties is common under two-agent
competition. Adams et al. (2005) and Schofield and Sened (2006) adopt the assumption
under multiple-agent competition. For the model of political parties with policy
motivations, the results are similar (Adams and Merrill 2009).
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influences political parties’ positioning strategies. 38 In modern democracies, electoral
systems specify basic rules such as the electoral formula, the district magnitude, the ballot
structure, and the electoral threshold (Lijphart 1994; Taagepera 2007).
Electoral systems produce centripetal and centrifugal incentives to political parties’
position-taking strategies (Cox 1990a). The former situation is linked with single-member
district systems which are also called first-past-the-post and the latter happens under
proportional representation systems. Under PR, a political party or candidate needs to
obtain a quota of votes defined by the electoral formula for winning a seat. Spatial theory
states that political parties spread across the issue dimensions with roughly equal vote
shares (Greenberg and Weber 1985; Sugden 1984). Hence, depending on the number of
agents entering the election race, convergence or dispersion campaign strategy will occur.
Under the plurality rule with two agents competing, a convergent equilibrium exists.
However, when the number of candidates is more than two under the plurality rule, there
are multiple dispersion equilibriums. Moreover, with multiple candidates contending for
seats under the plurality rule or under PR, party issue positions diverge (Cox 1990b).
The aforementioned spatial models assume that voters respond to party issue
positions deterministically, meaning that voters cast their ballots for political parties whose
policy positions are the closest to their own. Since this vision of deterministic voting may
not fit the real world properly, a model of probabilistic voting is developed to present a
voter’s utility as the summation of parts derived from issue distance, individual social
demographic properties, and error terms. Using the probabilistic voting model, the
equilibrium of multi-candidate competition under the plurality rule is that all candidates
38

See, e.g., Cox (1987).
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converge to the mean of voter distribution (Lin et al. 1999). Recent research also shows
that the model of probabilistic voting is an appropriate tool to investigate multiparty
competition under different electoral systems (Adams et al. 2005; Schofield and Sened
2006). I take the assumption that citizens decide how to vote based on the utility they
derive from each political party. This is one version of probabilistic voting, which is also
called the random utility model.
This chapter aims to explain the patterns of the degree of policy dependence among
political parties’ issue positions across electoral systems. The policy dependence means
whether the policy positions of political parties are correlated with each other during the
policy-making process. The main argument is that the degree of policy dependence is
higher under PR than SMD due to two reasons: the types of government and voter turnout
rates. When political parties think about their campaign strategies and how to position
themselves on the ideological spectrum, they need to take the postelection government
structure and how to acquire voter support into account. First, SMD usually creates a
single majority government while PR encourages a coalition government. The distinction
comes from majoritarian and proportional visions of democracy (Powell 2000). This
means that the policy outcomes of a majority government are determined by a political
party without compromise among political parties represented in the parliament. Second,
seeking to maximize voters, a political party selects an issue position where it can capture
enough votes to win seats under the electoral system. The electoral threshold is higher
under SMD while PR usually needs a quota to guarantee a seat. Political parties think
about their electoral market defined as potential supporters. They may move to a more
extreme position since extreme voters are more willing to vote and feel more threatened

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from the political parties locating at the opposite end of the issue space (Kedar 2009). In
other words, when political parties recognize the facts that turnout rates are higher under
PR and that voters are willing to vote for more extreme political parties, they respond with
placing themselves at a more extreme position. When a coalition government needs to be
formed with majority, moderate political parties have to bargain with those minority
parties. Therefore, the policy dependence is higher under PR than under SMD.
The vote choice under SMD and PR is affected by the policy dependence from various
degrees. The citizens view vote choice as substitutable or independently under SMD, since
the policy dependence is low from the fact that a single political party can execute their
policy position without bargaining. Conversely, the citizens treat vote choice as correlated
under PR because the policy dependence is high since the policy outcome results from the
negotiation among several political parties to form a majority coalition. If the degree of
policy dependence is measurable, it can be used as an independent variable in the voter’s
utility function. Under such a circumstance, the residual terms in the voter’s utility toward
each political party are stochastic. However, contemporary scholars of electoral
competition do not conduct surveys to measure policy dependence. The current survey
data of voter choice cannot control for the effects of policy dependence by using it as a
random variable in the systematic component of the voter’s utility function. Given the
constraints of the current survey data, the effects of policy dependence must be relegated
into the residuals. More specifically, the error terms of the voter’s utility functions toward
political parties are prone to be independent under SMD but correlated under PR after the
relevant variables that influence voter decision-making are taken into account.
The subsequent sections of the paper go as follows. The second section discusses

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how electoral systems influence political competition. To elucidate the effects of electoral
systems on the issue positions of political parties in a campaign, I discuss how various
types of government formation produce the final policy outcome. Next, I show how
citizens decide their vote choice. The linkage between party positioning strategies and
voter choice functions through the two perspectives of electoral institutions: the types of
government and voter turnout rates. Following theoretical expectations, the hypotheses
are based on the implications of statistical models, (i.e., multinomial logit and multinomial
probit models). The index for comparison of the model fit between multinomial probit and
multinomial logit of voter choice under SMD and PR is Bayes factor. Moreover, to
investigate the difference in the substitution pattern of voter choice predicted by
multinomial probit and multinomial logit, the Taiwan 2004 legislative election is used as a
case study. The final section ends with concluding remarks and suggestions for future
research

1. Theoretical Consequences of Electoral Systems on Party Competition
An electoral system produces convergent or non-convergent position-taking incentives
for political parties. This argument is derived from the mechanical effects of electoral
institutions regarding how votes are transformed into seats (Duverger 1954). Electoral
systems tend to defractionalize the allocated seats in the parliament but the intensity of this
process depends on the electoral formula (Rae 1967, chapter 4). The disproportionality
between votes and seats is the product of electoral rules, with PR usually having a lower
degree of disproportionality than SMD. The main features which characterize PR and
SMD are the electoral formula and the district magnitude, which jointly produce the

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electoral threshold. Thus PR can support more political parties and provide incentives for
them to locate at the periphery of the policy space.
The proportionality between votes and seats is higher under PR than SMD (Taagepera
and Shugart 1989; Taagepera 2007). The electoral formula decides the quota of votes
required to award a seat in a district. The quota to secure a seat is Droop quota calculated
as 100%/(M+1) + 1 where M is the district magnitude. The plurality rule associated with
SMD is sometimes termed first-past-the-post. The district magnitude under SMD is 1
required Droop quota of 50% of votes + 1 to win a seat. As the district magnitude
increases (which is the case under PR), the quota decreases. With different PR formulae
like d’Hondt, Sainte-Languë, or Hare-LR, the threshold would be slightly different. This
most stringent condition is the upper bound of the threshold. As the number of political
parties or candidates competing in a district goes up, the quota will decrease. This most
favorable condition is the lower bound of the threshold. Thus, the effective electoral
threshold is between the former two criteria (Taagepera 2007) and the lower effective
electoral threshold has a strong influence on multipartyism (Lijphart 1994, 83-86).
The argument that multipartyism is highly correlated with PR has been proven
empirically. The effective number of political parties is measured either by the inverse of
the sum of square of voter share percentages or by the same definition of seat shares. PR
allows more parties to gain seats in the parliament conditional on the effects of social
cleavages (Cox 1997; Ordeshook and Shvetsova 1994). Since the rise of the third-wave
democracies in the 1990s, there is a new trend of combining PR and SMD formulae called
mixed electoral systems (Massicotte and Blais 1999; Shugart and Wattenberg 2001). The
institutional effects of mixed electoral systems have been shown to lie between PR and

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SMD (Ferrara et al. 2005, chapter 8).
The electoral threshold is influenced directly by the district magnitude, which produces
convergent or divergent electoral incentives (Cox 1990a). When the district magnitude is
one, the electoral threshold becomes high. When the district magnitude is multi-member,
the electoral threshold gets lower. As Colomer states, ‘the large prefer the small and the
small prefer the large’ (Colomer 2004, 3). When the district magnitude is set at one, it
reduces the viable number of political parties or candidates down to two (Cox 1997;
Palfrey 1989). The large parties move to the center location of the policy space because of
the high electoral threshold imposed by having only one seat at stake. In PR with a large
district magnitude M>1, the number of viable parties or candidates is restricted to M+1
(Cox 1994; Cox and Shugart 1996). The small parties can acquire seats even when
advocating a more extreme issue position, conditional on a larger district magnitude.
These convergent and non-convergent electoral incentives across electoral systems are
provided with evidence in early research (Cox 1997; Dow 2001). Therefore, electoral
institutions are an important factor influencing how political parties choose their
campaign strategies.

1.1 Party Positioning Incentives and Government Type
Political parties represent the voter policy preferences expressed in elections in the
policy-making process. As just discussed, the selection of policy makers is determined by
electoral systems, which produce convergent and divergent electoral incentives. However,
the position-taking strategy for being elected does not work in isolation. Position-taking
strategies in elections for being elected are related to how voters make their decisions and

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the policy making process. The first component regards how voters choose a political party
to support and the second is how the policy positions of parties are incorporated into final
policy outcomes. Since citizens’ voting considerations concerns the product of policy
execution, how the types of governments influence party campaign strategies will be
examined first using backward induction (Austen-Smith and Banks 1988; Shepsle 1991,
chapter 8).
Following Powell (2000), the democratic political systems in the world can be mapped
onto the dimension of marjoritarian vs. proportional visions depending on the
constitutional design and the electoral system.39 The majoritarian vision means that a
single political party dominates policy-making while all authorized political parties are
allowed to influence the policy outcome under the proportional vision. The constitutional
design regards the separation of power whether the president is elected by popular votes
with a fixed term, not dependent on the parliament confidence vote, and whether the
president is granted lawmaking authority (Shugart and Carey 1992). On the other hand,
electoral systems induce either two-party or multiple-party seat getters in the parliament.
Three typologies follow. First, a combination of parliamentarism and SMD is
marjoritarian because the ruling party has the authority to implement its policy position.
The other example of the marjoritarian vision is that the president and the congress are
controlled by the same party under the mixture of presidentialism and SMD. Second, the
composite of parliamentarism and PR is proportional in the sense that the coalition

39

Lijphart (1999) adopt a similar method to classify democracies into the criterion of
Westminister and consensus models. Nohlen (1984) also argue that the categorizations of
the electoral systems such as SMD and PR should not be mutually exclusive and they are
rather on a continuous scale like the degree of proportionality.
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government often takes place with compromises among the issue positions of parties in it.
Third, other situations that do not fit into the previous two categories are regarded as a
mixed type located within two extremes. The combination of presidentialism and PR
under the situation of a unified government is mixed because more political parties are
represented in the congress and the coalition building is needed to support the president’s
policy. On the other hand, if two political parties hold the power in the executive and
legislative branches, the issue position of the party in the executive branch is checked by
the other holding the majority in the legislative branch. Thus, in the third type of mixed
systems, the policy position of the presidency must accommodate that of the congress. The
combination of PR and presidentialism with a unified government happens very seldom
because it is difficult for a single political party to acquire the majority of seats in the
congress.

Table 4.1 Types of Governments by Separation of Power and Electoral Systems
Unified Power Separated Power with Separated Power with
a unified government a divided government
SMD
PR

Majoritarian
Proportional

Majoritarian
-

Mixed
Mixed

The degree of centripetal electoral incentives hinges on the government formation
process structured by electoral systems. The convergent electoral incentives are the
strongest under the marjoritarian vision of democracy associated with a majority
government created by SMD. Conversely, the non-convergent electoral incentives
produced by PR from the coalition government are the weakest. However, the divergent
incentives produced by PR are modified by the combination of presidentialism and a

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coalition government. The final policy outcome under such a political system is an
accommodation between the convergent electoral incentives driving the president and the
divergent ones permeating in the congress. Specifically, the ranking of centripetal force
generated by electoral systems from the strongest to the weakest is from the majoritarian,
mixed, and proportional visions of democracy.
The generalization of the aforementioned argument is based on the assumption of the
policy space being unidimensional. The politics of the real world works within the multiple
dimensions of many issues, and it is argued that at least two dimensions are needed to
better display the issue positions of political parties across countries (Dow 2001).
Although the two-dimension model has the advantage of showing more information
regarding diversified party issue positions, evidence from the US Congress roll call and
comparative issue voting analyses shows that the one-dimension model can capture most
of variance of party issue positions (Jackman 2001; Schofield and Sened 2006). Thus,
unidemsionality is a reasonable assumption.

1.2 How Citizens Decide to Vote
Citizens decide which party to support according to the proximity between their ideal
points and the party issue positions framed by electoral institutions and the government
formation process. The deterministic voting model with its emphasis on policy distance is
insufficient to explain the vote choices made by all voters. The advantage of the
probabilistic voting model is that its inclusion of a random term helps explicate individual
voting behavior. Social demographic variables and partisanship should also be
incorporated into the model for a more thorough understanding (Adams et al. 2005;

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Schofield and Sened 2006).
The random utility model (henceforth RUM) specifies that an individual, labeled n,
obtains a utility by facing a set of J alternatives and that an individual selects an
alternative with the highest utility. These choice-specific utilities Unj, j = 1,…J, are
unobservable variables and only the indicator of final choice can be observed by the
researcher. The observed choice made by the decision maker is a manifestation of t h e
underlying utilities. Accordingly the behavioral assumption is that one chooses
alternative i if and only if Uni > Unj ∀ j = i. Since only one final choice made by each
individual is observed and each individual’s utility functions of choices are latent, the
utility of alternative j is divided into two components: representative utility Vnj and a
stochastic term (Train 2003; Walker and Ben-Akiva 2002):
Unj = Vnj + εnj.

(4-1)

This formulation of the utility function is consistent with the definition of a
probabilistic voting model. The probability that the nth individual selects the ith
alternative is the probability that the utility for the ith alternative exceeds the utilities of
all other alternatives in the choice set:
(4-2)

Pni = Pr(Uni > Unj ∀ j = i)
= Pr(Vni + εni > Vnj + εnj ∀j = i)
= Pr(εnj − εni < Vni − Vnj

∀j = i).

By this formulation, only the differences between utilities matter for which one to

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choose and the scale of utilities is irrelevant (Train 2003, 23-33). Another feature is that
the distribution of εnj − εni determines how Pni is computed.
The first component of utilities toward political parties is assumed to be a
function of a set of observable independent variables. The researcher observe the
representative utility composed of the attributes related to alternatives xnj ∀j and those
related to the decision maker sn. In other words, Vnj = V(xnj, sn) ∀j contains two parts:
alternative-specific

and

individual-specific

preferences.

The

alternative-specific

preferences are related to how an individual evaluates the properties of each choice, i.e.,
assessments attached to each option derived from how an individual appraises them by
how far the policy locations of candidates are from his own ideal point. The first
element corresponds to issue voting which is how political position-taking strategies
influence the voter’s choice. The second individual-specific element is measured by social
demographic variables and partisanship.
All factors that cannot be explained by the representative utility are included in the
error term εnj. According to Train, ‘The characteristics of εnj, such as its distribution,
depend critically on the researcher’s specification of Vnj. This distribution becomes
relevant when evaluating the appropriateness of various specific discrete choice models’
(Train 2003, 19). To state it another way, how the researcher can observe or specify
representative utility determines what factors are relegated into the error term.

If the

researcher believes that the function of the representative utility is thorough and that no
omitted variables are excluded, then the error terms across utilities are assumed to be

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independent. Conditional on the specification of the representative utility, the distribution
assumptions on εnj induce different behavioral patterns. Thus whether the assumption of
independence among error terms holds relies on measurement. When some variables of
theoretical importance cannot be collected, they cannot be captured in the representative
utility, which causes correlated error terms.
The proximity voting model is simple and intuitive but has some limitations. The
proximity model has been criticized by directional and discounting voting models
(Grofman 1985; Lacy and Paolino 1998; Rabinowitz and Macdonald 1989). Although the
effects of added complexity to the proximity model may not be substantial (Lewis and
King 2000; Westholm 1997), I assume that the other types of issue voting not captured by
the proximity voting model are not correlated with the systematic component. Thus these
unmeasured properties of issue voting are relegated into the error term.

1.3 Linkage between Party Strategies and Voter Choice
Party position-taking strategies under electoral systems are influenced by voter
choice from two perspectives: the type of government formed and the voter turnout rate.
The first component reinforces the non-convergent electoral incentives through the
bargaining process in the coalition government. The second component affects political
competition as a result of citizens’ voting decision since the degree of diversified issue
positions is modified by which part of the voter distribution will actually cast the ballot.
The argument is that higher voter turnout under PR also gives political parties electoral
incentives to take a more extreme position. These two patterns will be discussed in order.

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1.3.1 The Effects of Government Formation
The voting behavior of electorates in periodical elections in democracy determines
which political party holds power and which one is to step down. Voters use elections as
tools to express their preferences in future policy and their satisfaction with status quo
policy. Citizens utilize elections as instruments to hold politicians accountable and to
prevent the government from infringing on their own civil rights (Powell 2000). At the
same time, how voting decisions are made is framed by electoral institutions. More
specifically, the decision-making process of voting behavior is contingent on electoral
institutions from two aspects: the choice set available to voters and the methods of how
votes are translated into seats.
The first aspect concerns about entry problem, which is how many candidates
compete in an election. The higher portion of votes in a district that are needed to be
collected by candidates to ensure a seat, the fewer candidates that will enter the election.
For example, in SMD, only the leading candidate with the most votes is awarded the seat.
The number of serious candidates with substantial vote support usually converges to two
because of mechanical and psychological effects (Duverger 1954; Myatt and Fisher 2002;
Palfrey 1989). Moreover, in a single nontransferable vote system (henceforth SNTV), the
district magnitude (M) is larger than 1 and electorates cast one vote for each candidate.
Depending on the size of district magnitude which is the number of candidates elected out
of the district, the number of candidates with positive vote shares tends to be close to the
size of district magnitude plus one. When under PR, there are usually M + 1 viable
candidates in an M-seat district (Cox 1997; Cox and Shugart 1996). Therefore, how
many candidates are available in the choice set is constrained by the types of electoral

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systems.
The second aspect is related to how voters’ preferences are transformed into policy
outcomes. There are different degrees of disproportionality across electoral systems. The
disproportionality of SMD is higher than its counterpart of PR. Since one candidate is
elected in SMD, the delegate represents opinions from those who vote for him. Voters in
SMD know that the winning candidate will be the only one expressing their policy
preference in the government. However, when more than one delegate is chosen in SNTV
and PR, different segments of voters are voiced in the government. The final policy
outcomes must be compromises among these representatives. For instance, in a
one-dimension issue space of Downsian spatial theory, the median voter position is the
policy outcome generated by SMD. While there are several agents standing for different
weights of preferences over the whole issue space, the policy outcome is a negotiation
process. The preference aggregation procedures are also influenced by the types of
electoral systems and hence, the impacts of votes on policy results are not the same across
electoral systems.40
How do electoral institutions influence voter choice models? The classifications of
electoral systems depend on two features. First, the number of alternatives in the choice
set is dichotomized into two categories: two viable candidates and more than two. The
former happens usually in SMD and the latter can appear sometimes in SMD and usually
in SNTV and in PR. According to sizes of districts in electoral systems, these choice sets

40

In SMD, voters usually use proximity voting to judge how closer a political party is. But
in a multi-member system like SNTV and PR, voters may prefer to support more extreme
political parties because the final policy outcome depends on compromise among political
parties in the parliament. This is called compensational voting (Kedar 2005).
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can be arranged from the fewest to the most as two alternatives in SMD, more than two in
SMD, more than two in SNTV, and more than two in PR.
Second, conditional on the vote preference transformation process, voting utilities
of alternatives depend on the linkage of voter preference and prevailing postelection policy.
In SMD, electorates evaluate voting utilities of candidates by knowing that the candidate
whom they support will implement their preferred policy. In other words, the voting
utility of one candidate cannot be replaced by picking up the other candidate. However,
this is not the case under SNTV and PR. The delegates all play roles in setting government
policy and the voting benefits of candidates rest on the policy locations of other
candidates too. The interdependency of candidates’ policy positions in resulting policy
outcomes in SNTV and PR indicates that electorates have to take not only their favorite
candidate into consideration but also other candidates. Similarly, the degree of vote choice
substitutability is the second dimension to categorize electoral systems. The degree of vote
choice dependence in SMD is lower than that in SNTV and PR. Hence, there are four
types of choices sets with two related to SMD and with the other two related to SNTV and
PR. These choice sets are combined with a lower degree of choice dependence in SMD and
a higher degree of choice dependence in SNTV and PR. In conclusion, this order also
shows the degree of convergent incentives ranked from the strongest to the weakest in
four scenarios.

1.3.2 The Effects of Voter Turnout
The convergent and non-convergent party strategies are influenced by varied turnout
rates across electoral systems. The fact that PR is linked with higher voter turnout is

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well-documented (Blais and Carty 1990; Jackman 1987; Jackman and Miller 1995; Powell
1986). The utility of a voter’s decision to choose a political party is based on the
cost-benefit calculation with benefits derived from party policy differentials. Political
parties’ goal of maximizing vote support is constrained by voter abstention. The
configurations of party policy issues induced by electoral institutions are adjusted by voter
abstention to be less convergent under SMD and to be more divergent under PR for small
political parties.
Under SMD, the electoral force that political parties converge toward the median
voter position is mitigated by voter abstention. If political parties all occupy the same
position at the median voter, the voting benefits of the policy difference to voters will be
zero. Voters will have no incentives to cast their ballots either due to alienation or due to
indifference (Adams and Merrill 2003). The former reason is that voters think the political
parties are too far from their own ideal points and the latter reason is because the policy
outcome implemented by the two parties will be alike. Moreover, when two main political
parties are too close to the median voter position and look too similar in their policy
positions, they are vulnerable to the emergence of a third political party (Palfrey 1984).41
Therefore, the convergent electoral incentives of SMD are reduced but still significant.
Under PR, political parties have incentives to take extreme positions in elections when
voters consider the larger voting benefits of supporting more extreme, small political
parties. Voters located at the two extreme ends of the electoral space have motivations to
vote because the policy outcome can be pulled toward their favored direction if small
parties gain enough vote shares to exert influence in the coalition government. Voters have
41

See, e.g., Lacy and Burden (1999).
126

this sort of calculation because they would like the final policy outcome created by the
coalition government to be as close as possible to their ideal positions (Kedar 2009). On
the other hand, small parties also acknowledge this kind of voting intention and have
electoral incentives to move to a more extreme position to extort the government
(Schofield and Sened 2006). The reciprocal calculations between voters and smaller parties
under PR generate more divergent electoral incentives. Furthermore, political parties have
their loyal or activist supporters located more diversely along the electoral space under PR.
Political parties usually move toward the mean or the median of these groups in order to
attract more votes in elections (Adams et al. 2005).
In sum, convergent and divergent incentives by electoral institutions are affected by
voter turnout by various degrees depending on the context. The general pattern of
electoral institutions which move political parties stay similar, but with caution regarding
how to stimulate more voters to go to the polls.

1.3.3 Hypotheses and Statistical Models
Party positions are perceived by voters differently. The average positions of all voters
are argued to be a better estimate of where political parties locate themselves because in
theory, political positions should be unique (Rabinowitz and Macdonald 1989). However,
in fact, citizens have their own judgments of party positions due to voter heterogeneity.
The approach of different party positions perceived by voters is not inferior (Blais et al.
2001; Westholm 1997). The measurement of party position is:
(4-3)

Znj = Zj + Δnj,

where Zj is the average party position for party j and Δnj is drawn from a random
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distribution.
Policy dependence between political parties can be viewed as how voter choice is
correlated with each other at the final policy stage. Conditional on the representative
utility of voter choice, the degree of the correlation between alternatives tells how much
citizens view the dependence between political parties’ issue positions. Remember that the
policy dependence between parties is induced by electoral institutions. The policy
dependence is higher under PR than under SMD.
The controversy between applications of multinomial logit (henceforth MNL)42 or
multinomial probit (henceforth MNP) persists. Some scholars advocate that MNP is a
better model in explaining voting behavior than MNL because the former relaxes the
independence from irrelevant alternatives (henceforth IIA) assumption which is implicitly
adopted by the latter (Alvarez and Nagler 1998; Alvarez et al. 2000). Other scholars argue
that MNL is a better model than MNP since the estimation results of MNL are not so
different from those of MNP and MNL is easier to estimate and more efficient than MNP
(Dow and Endersby 2004). In addition, some scholars also argue that the implementation
of MNL or MNP depends crucially on the data available (Quinn et al. 1999). The essential
factor that underlies voting behavior is the electoral institution. The electoral institution
structures the choice set of how many candidates compete in an election and the
calculation process of voting behavior.
According to the effects of electoral institutions on voter choice, what statistical
methods should be used to analyze voting behavior in different scenarios? The focus of this
42

Depending on model specifications, multinomial logit includes another version called
conditional logit. We do not discriminate between the two types of multinomial logit
models.
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paper is on multiparty competition which means that there should be at least three
alternatives in the choice set. This excludes the first condition in the four classifications
with only two candidates in the race. MNL with the IIA assumption should be used to
analyze voting behavior with a lower degree of choice dependence in SMD. MNP without
the IIA assumption is more appropriate in investigating voting patterns with some degree
of choice interdependence under SNTV and PR. The IIA assumption imposes restrictions
on the random term of voting utility and implies that the choice between MNL and MNP
amounts to what the degree of policy dependence that researchers select to explain voting
behavior. Explaining the patterns of voting behavior under various electoral circumstances
relies on assumptions of statistical models imposed by researchers. The target of
investigation is the underlying process generating observed data. The understanding of a
primary mechanism behind voting behavior is necessary for selecting correct statistical
methods since the latter should approximate the former as closely as possible but not the
other way around. In other words, when an inappropriate statistical model is applied,
some needless assumptions are added on the voting behavior of interest. Unwanted
assumptions either distort the explanation researchers intend to uncover or conceal the
real patterns of voting behavior. Choosing correct voting choice models derived from
electoral institutions is thus essential in understanding of the perceived party positions by
voters.43

Hypothesis 1: MNP is more appropriate for voter choice under PR than MNL.

43

See more discussion about how voters make decisions when facing the uncertainty of a
large population in Myerson (1999), Myerson (2000), and Martinelli (2002).
129

The substitution patterns of voter choice between MNL and MNP differ.
Remember that the utility function contains two components: the systemic components,
Vnj, developed by the researcher with the observed variables and the error components
defined as the difference between the utilities that the individual in fact acquires, Unj, from
different political parties. If the researcher could specify the best systemic utility, the error
components left are essentially “white noise”. In multinomial logit, only individual-specific
characteristics

are

utilized

in

the

specification

of

systemic

utility,

but

not

alternative-specific variables. As a result, in multinomial logit, the IIA property is not
avoidable. A feasible way to get rid of the IIA property is to improve the specification of
the systemic component. However, when some variables are immeasurable, the IIA
assumption becomes an unnecessary restriction on the statistical model. For example, the
policy dependence between political parties is not measured directly by survey questions,
but the perceptions exist in voters’ minds and the policy dependence is taken into account
in party position-taking strategies. To evaluate tradeoffs between logit and probit models,
the restrictions of substitution patterns under the IIA assumption should be explored.
Two ways to investigate the substitutions pattern of RUM are how a new choice
entering a choice set changes the existing probability distribution among choices and how
the increase of representative utility of a choice decreases the proportions of other choices.
The first scenario is how a new candidate entering an election influences the support of
preexisting candidates. For example, suppose that there are two political parties, L and R,
occupying the left and the right position along a left-right issue dimension. Their vote
shares are PL = 0.5 and PR = 0.5 with the ration PL/PR = 1 where PL and PR are

130

probabilities of voting for the left and right parties. Suppose another right political party
R2 emerges. We can expect that voters have no particular preferences over the two right
parties: PR/PR2 = 1. The IIA assumption imposed by MNL says that PL/PR = 1 does not
change even though there is a new right party. It follows that PL = PR = PR2 = 1. However,
we should expect that the two right political parties split the same political segment. It is
more reasonable to reach a distribution of vote shares like PL = 0.5 and PR = PR2 = 0.25.
Although this exercise can help investigate counterfactual scenarios about how the
votes of one candidate can be distributed to other candidates, this situation does not
usually happen in a real election because the number of candidates is exogenous to an
election. The decision of whether to enter a campaign takes place before the beginning of
an election. More importantly, it is required for citizens to register in order to qualify for
being a candidate. The registration requirement implies that the number of alternatives in a
choice set is fixed. The number of candidates can only decrease as the election goes on and
it cannot increase in an opposition direction. But giving up in a campaign seldom happens.
In other words, the number of alternatives can be viewed as unchanging. Hence, the first
interpretation of substitution patterns cannot tell us how voters make their decisions when
facing a fixed number of candidates.
The second way to interpret the IIA assumption is proportional substitution about
altering the probability distribution when the probability of one choice varies. The
elasticity of Pni related to a derivative that influences the representative utility of
alternative j (Train 2003, 51-64):

131

(4-4)

Eiznj =

∂Vnj
∂Pni z nj
=−
z nj Pnj ,
∂z nj Pni
∂z nj

where znj is the characteristic of alternative j assessed by person n.
This cross-elasticity is the same for all i choices since there is no quantities related to

i in

Eiznj . This shows that the decreasing proportion is the same for all other i choices

while there is an increase of representative utility j. Suppose that there are three political
parties, labeled L, C, and R, positioning themselves along the left-right single dimension
from left to right under the condition that the distance between positions of C and R is
smaller than its counterpart of L and C. Their initial vote shares are PL = 0.4, PC = 0.4,
and PR = 0.2.44 This implies that PL/PR = 2. If the vote share of the central party C
increases to 0.46 by 10%, proportional substitution stipulates that PL = 0.36 and PR =
0.18. Since the ratio of PL and PR must not change by the IIA assumption, the decreasing
percentage must also be the same as 10% and the deceasing percentage of PL must be
larger than that of PR. However, this pattern of substitution imposed by the IIA
assumption is possibly incorrect because we expect the increasing vote share of C comes
more from R than L by spatial theory. Facing a fixed set of alternatives, the voting
behavior is restricted by the IIA assumption even though electorates see that some
candidates are more similar than others. This unrealistic IIA assumption of the error terms
44

Myerson and Weber (1993) claim that the voter’s choice depends not only on his own
preference but also on the winning probability of each candidate obtained by pairwise
comparison. The winning probability is induced by types of electoral institutions.
132

in voting utilities has serious consequences by using a misspecified model. Under the
condition that error terms are interdependent imposed under MNL, MNP must be used to
discover a correct substitution pattern while the policy dependence exists.

Hypothesis 2: The substitution pattern among political parties predicted by MNP is
better than that by MNL because of the degree of policy dependence is higher under
PR than under SMD.

2. The Effects of Electoral Institutions on Voter Choice
To investigate how electoral institutions affect voter choice, I use survey data from the
Comparative Study of Electoral Systems (CSES) project. The project contains survey data
across varied electoral systems which allow having a valid comparison across different
types of electoral systems. Furthermore, the issue dimension common in the survey data is
the left-right scale and it enables us to estimate and compare issue voting across countries.

2.1 The Voter’s Utility Function
The voter’s utility function is the expected utility that the voter will receive by voting
for a particular political party. The utility function includes two components: the
systematic term and the disturbance. The former represents those factors which are
measurable by other questions included in the survey. The latter is the error term including
all factors which can not be controlled for. Within a political system, a voter i’s utility

133

function to political party j is written as45:
(4-5)

Uij=Intercept+β1*Issueij +β2*Femaleij+β3*Educationij+β4*Incomeij
+β5*Age26_35ij +β6*Age36_45ij+β7*Age46ij+β8*Partyidij+β9*Inpowerij
+ β10*Makediffij+eij.

The systematic component has eleven variables classified into 5 categories: valence,
issue, socio-demographic, party identification, and political efficacy. The valence is the
electorate’s average judgment of the component or the integrity of a political leader (Stokes
1963, 1992). The valence is usually independent of the issue evaluation and it is
appropriate to use an intercept to capture it (Schofield 2008). Second, the issue variable is
the quadratic distance between a voter’s ideal point and the policy platform of a political
party. This independent variable is alternative-specific, meaning that its measure has
information about a voter’s distance to every political party. Third, a voter’s
socio-demographic characteristics determine how he or she derives the utility from each
vote choice. This group of variables contains sex, age, education, and income. Forth, the
core supporters of a political party can influence their party’s positioning strategies.
Political parties may move toward the policy location preferred by their party activists
(Adams et al. 2005). Therefore, it is necessary to control for the effects of party
identification. Fifth, the final group of variables concerns whether a voter thinks that his or
her one vote impacts the electoral or policy results. The variable of interest is the issue
45

I exclude those political parties receiving less than 5% of the vote share from the choice
set because they have a smaller chance to influence the policy outcome even if they win
seats.
134

variable. The sign of the coefficient is hypothesized to be negative because a voter is less
likely to choose a political party whose policy position is further from the voter’s ideal
point.

2.2 Case Selection Criterion
To insure a valid comparison between MNP and MNL, some elections are excluded
because of the constraints of the choice set or because of the political reality in a polity.
First, the choice set must have more than two options, and at least three for multinomial
model estimation, which excludes the Russia 2004, Taiwan 2004 and the USA 2004
presidential elections. Second, in a political system with too many candidates running as
independents or fluid party systems, the issue position estimates of political parties are not
stable. This standard excludes the Lithuania 1997 presidential and the Ukraine 1998
parliamentary elections.

2.3 Bayes Factor Calculations
The Bayes factor of two models, M1 versus M2, is defined as ratio of the marginal
likelihoods f(y|M1) and f(y|M2) where y is the observed data. The marginal likelihood
f(y|M) for

M ∈ {M 1 , M 2 }

is calculated by integrating out the model parameters as

(Gill 2008):
(4-5)

f ( y | M ) = ∫ f ( y | θ M , M ) f (θ M | M )dθ M

.

I approximate the marginal likelihood of the posterior distributions of the MNP

135

and MNL models by Newton and Raftery’s (1994) harmonic mean method. To avoid the
instability of the harmonic mean estimator, I further adopt the iterative algorithm to reach
a more accurate estimation of the marginal likelihood (Congdon 2006; Kass and Raftery
1995). The posterior distribution of MNP is a truncated multivariate normal distribution.
To evaluate the marginal likelihood, I follow Rossi, Allenby, and McCulloch’s (2005)
GHK simulator46 to estimate the marginal likelihood of MNP.

2.4 Results
Table 4.2 displays the Bayes factor of MNP over MNL across 59 elections. This is the
step to verify whether the patterns of voter choice vary across electoral systems. For each
country, two statistical models of voter choice are estimated by Bayesian methods. The
advantages of Bayesian methods are two-folds: First, the posterior distribution of
parameters of interest can show more information about the estimated coefficients. We can
make more valid inferences, not like traditional methods relying on hypothesis testing;
second, since we have posterior distributions of all parameters, we are able to calculate
marginal likelihood more precisely.
There are two points worth making in details. First, the coefficients of issue voting
shown in Table 4.2 are almost significant in 95% of Bayesian confident interval. Except
the Chile 2005 and South Korea 2000 elections, the effects of issue voting are essential in
determining the voter choice in other 57 elections. At the same time, the importance of
issue voting holds across various electoral institutions. Therefore, issue voting does

46

The GHK simulator is developed by John Geweke, Vassilis Hajivassiliou, and Michael
Keane.
136

influence the voter choice. Second, the magnitudes in Bayes factor of MNP over MNL
within three types of electoral systems shows a pattern from positive to negative as the
institutions change from PR to SMD. The average of Bayes factor in PR is 7.591, that of
mixed systems is -2.000, and that of SMD is -6.5. This shows that the MNP model is more
suitable for voter choice under PR while the MNL model is for SMD. Hence, this provides
some evidence to substantiate the hypothesis 1.

137

Table 4.2 The Comparison of Vote Choice Models across 59 Electoral Systems by Bayes
Factor (Part 1)
Log Mag Bayes
Country
Year Type # Model Mean 2.5% 97.5% Likelihood Factor Average
Belgium
1999 PR 6 MNL -0.0673 -0.0760 -0.0590 -1720.8010
6 MNP -0.0130 -0.0167 -0.0105 -1718.6240 2.1770
Bulgaria
2001 PR 5 MNL -0.0840 -0.0950 -0.0750 -587.9487
5 MNP -0.0190 -0.0260 -0.0140 -584.4877 3.4610
Czech Rep
1996 PR 6 MNL -0.1227 -0.1404 -0.1060 -746.1125
6 MNP -0.0146 -0.0177 -0.0121 -744.1069 2.0056
Czech Rep
2002 PR 4 MNL -0.1707 -0.2020 -0.1440 -318.2120
4 MNP -0.0280 -0.0420 -0.0200 -316.0631 2.1489
Denmark
1998 PR 5 MNL -0.2076 -0.2300 -0.1870 -1084.0110
5 MNP -0.0543 -0.0647 -0.0440 -1079.6750 4.3360
Denmark
2001 PR 5 MNL -0.1520 -0.1687 -0.1368 -1285.4540
5 MNP -0.0620 -0.0773 -0.0482 -1283.5540 1.9000
Germany
1998 PR 5 MNL -0.0796 -0.0913 -0.0690 -1268.6200
5 MNP -0.0150 -0.0210 -0.0120 -1261.7840 6.8360
Germany
2002 PR 5 MNL -0.0662 -0.0759 -0.0570 -1512.9170
5 MNP -0.0189 -0.0235 -0.0150 -1509.6470 3.2700
Iceland
1999 PR 4 MNL -0.1220 -0.1380 -0.1067 -684.8749
4 MNP -0.0430 -0.0580 -0.0330 -684.0060 0.8689
Iceland
2003 PR 5 MNL -0.1520 -0.1753 -0.1308 -697.5130
5 MNP -0.0398 -0.0487 -0.0320 -695.2284 2.2846
Israel
1996 PR 5 MNL -0.0780 -0.0960 -0.0604 -347.0964
5 MNP -0.0329 -0.0710 -0.0170 -338.6494 8.4470
Israel
2003 PR 6 MNL -0.1000 -0.1180 -0.0818 -382.6424
6 MNP -0.0202 -0.0270 -0.0130 -373.3548 9.2876
Finland
2003 PR 6 MNL -0.1220 -0.1410 -0.1040 -887.1411
6 MNP -0.0250 -0.0322 -0.0190 -883.7840 3.3571
Ireland
2002 PR 4 MNL -0.0660 -0.0800 -0.0530 -780.9008
4 MNP -0.0192 -0.0299 -0.0130 -779.9333 0.9675
Italy
2006 PR 4 MNL -0.0580 -0.0894 -0.0330 -189.6867
4 MNP -0.0048 -0.0083 -0.0016 -189.5646 0.1221
Netherlands 1998 PR 5 MNL -0.1878 -0.2090 -0.1670 -1335.4800
5 MNP -0.0330 -0.0520 -0.0220 -1334.3900 1.0900
New Zealand 1996 PR 5 MNL -0.1260 -0.1370 -0.1152 -2045.4371
5 MNP -0.0355 -0.0411 -0.0298 -2044.6580 0.7791
New Zealand 2002 PR 5 MNL -0.1060 -0.1225 -0.0880 -479.5482
5 MNP -0.0193 -0.0247 -0.0124 -478.2426 1.3056
Norway
1997 PR 6 MNL -0.1358 -0.1490 -0.1221 -1722.6670
6 MNP -0.0265 -0.0308 -0.0223 -1720.3360 2.3310

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Table 4.2 The Comparison of Vote Choice Models across 59 Electoral Systems by Bayes
Factor (Part 2, cont’d)
Log Mag
Bayes
Country
Year Type # Model Mean 2.5% 97.5% Likelihood Factor Average
Norway
2001 PR 6 MNL -0.1364 -0.1510 -0.1230 -1663.5621
6 MNP -0.0478 -0.0580 -0.0396 -1662.4490 1.1131
Poland
1997 PR 4 MNL -0.0750 -0.0880 -0.0630 -553.3134
4 MNP -0.0191 -0.0240 -0.0140 -551.3992 1.9142
Poland
2001 PR 6 MNL -0.0670 -0.0792 -0.0550 -535.6088
6 MNP -0.0211 -0.0288 -0.0153 -533.1723 2.4365
Portugal
2002 PR 4 MNL -0.1280 -0.1500 -0.1100 -382.2072
4 MNP -0.0445 -0.0570 -0.0340 -378.6974 3.5098
Portugal
2005 PR 5 MNL -0.0611 -0.0692 -0.0530 -1256.9630
5 MNP -0.0108 -0.0134 -0.0087 -1255.1183 1.8447
Sweden
1998 PR 5 MNL -0.1310 -0.1490 -0.1130 -636.6120
5 MNP -0.0291 -0.0408 -0.0221 -635.4533 1.1587
Sweden
2002 PR 6 MNL -0.1731 -0.1980 -0.1500 -814.5072
6 MNP -0.0221 -0.0290 -0.0163 -810.6247 3.8825
Slovenia
1996 PR 6 MNL -0.0510 -0.0628 -0.0390 -552.9481
6 MNP -0.0226 -0.0337 -0.0150 -548.8174 4.1307
Slovenia
2004 PR 6 MNL -0.0550 -0.0640 -0.0380 -241.3974
6 MNP -0.0129 -0.0230 -0.0045 -224.7552 16.6421
Spain
1996 PR 4 MNL -0.0470 -0.0590 -0.0360 -441.5405
4 MNP -0.0218 -0.0330 -0.0140 -433.3279 8.2126
Spain
2000 PR 4 MNL -0.1459 -0.1770 -0.1200 -327.6002
4 MNP -0.0225 -0.0360 -0.0160 -323.9329 3.6673
Spain
2004 PR 3 MNL -0.1400 -0.1700 -0.1160 -234.6854
3 MNP -0.0236 -0.0278 -0.0190 -233.6746 1.0108
Switzerland
1999 PR 4 MNL -0.1206 -0.1375 -0.1050 -783.3624
4 MNP -0.0437 -0.0515 -0.0320 -782.5713 0.7911
Switzerland
2003 PR 5 MNL -0.1110 -0.1270 -0.0953 -718.6000
5 MNP -0.0398 -0.0550 -0.0256 -716.3860 2.2140 3.4876
Albania
2005 Mixed 5 MNL -0.0409 -0.0484 -0.0350 -369.8226
5 MNP -0.0173 -0.0240 -0.0130 -393.6514 -23.8288
Brazil
2002 Mixed 3 MNL -0.0125 -0.0160 -0.0090 -825.9670
3 MNP -0.0040 -0.0053 -0.0027 -824.1888 1.7782
Chile
2005 Mixed 4 MNL -0.0048 -0.0100 0.0009 -854.1580
4 MNP -0.0023 -0.0060 0.0024 -855.8812 -1.7232
Hungary
1998 Mixed 5 MNL -0.1020 -0.1190 -0.0850 -618.4877
5 MNP -0.0240 -0.0290 -0.0188 -616.5464 1.9413
Hungary
2002 Mixed 4 MNL -0.0622 -0.0840 -0.0430 -200.9694
4 MNP -0.0180 -0.0300 -0.0085 -195.4531 5.5163
Mexico
1997 Mixed 6 MNL -0.0230 -0.0261 -0.0207 -730.5618
6 MNP -0.0120 -0.0160 -0.0081 -753.9203 -23.3585

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Table 4.2 The Comparison of Vote Choice Models across 59 Electoral Systems by Bayes
Factor (Part 3, cont’d)
Log Mag
Bayes
Country
Year Type # Model Mean 2.5% 97.5% Likelihood Factor Average
Mexico
2000 Mixed 3 MNL -0.0258 -0.0310 -0.0209 -596.4166
3 MNP -0.0091 -0.0127 -0.0057 -595.4128 1.0038
Mexico
2003 Mixed 4 MNL -0.0240 -0.0290 -0.0190 -529.7419
4 MNP -0.0076 -0.0108 -0.0048 -534.2830 -4.5411
Peru
2000 Mixed 5 MNL -0.0310 -0.0390 -0.0240 -604.1493
5 MNP -0.0130 -0.0240 -0.0068 -601.5447 2.6046
Peru
2001 Mixed 4 MNL -0.0377 -0.0446 -0.0310 -910.9695
4 MNP -0.0133 -0.0163 -0.0100 -916.9777 -6.0081
Peru
2006 Mixed 6 MNL -0.0195 -0.0240 -0.0150 -1124.3140
6 MNP -0.0048 -0.0063 -0.0034 -1132.1340 -7.8200
Philippines
2004 Mixed 5 MNL -0.0095 -0.0160 -0.0025 -645.6324
5 MNP -0.0033 -0.0061 -0.0012 -641.8285 3.8039
Romania
1996 Mixed 4 MNL -0.0208 -0.0300 -0.0120 -341.1735
4 MNP -0.0098 -0.0150 -0.0044 -340.6212 0.5523
Romania
2004 Mixed 5 MNL -0.0371 -0.0470 -0.0280 -432.6715
5 MNP -0.0235 -0.0357 -0.0150 -426.9113 5.7602
Russia
1999 Mixed 6 MNL -0.0551 -0.0650 -0.0460 -702.4708
6 MNP -0.0168 -0.0234 -0.0113 -700.2422 2.2287
S. Korea
2000 Mixed 4 MNL -0.0120 -0.0210 -0.0076 -325.4625
4 MNP -0.0013 -0.0044 0.0007 -327.1485 -1.6860
S. Korea
2004 Mixed 4 MNL -0.0240 -0.0290 -0.0190 -526.2679
4 MNP -0.0076 -0.0108 -0.0048 -529.7419 -3.4740
Taiwan
2001 Mixed 5 MNL -0.0600 -0.0717 -0.0410 -529.0898
5 MNP -0.0251 -0.0350 -0.0130 -514.3441 14.7457 -2.2308
Australia
1996 SMD 5 MNL -0.0960 -0.1100 -0.0820 -963.2401
5 MNP -0.0314 -0.0380 -0.0260 -964.7504 -1.5103
Australia
2004 SMD 4 MNL -0.1250 -0.1430 -0.1072 -998.6099
4 MNP -0.0914 -0.1350 -0.0580 -996.3808 2.2291
Canada
1997 SMD 5 MNL -0.1070 -0.1224 -0.0920 -902.8433
5 MNP -0.0344 -0.0464 -0.0233 -910.8321 -7.9888
Canada
2004 SMD 4 MNL -0.1238 -0.1404 -0.1100 -811.5547
4 MNP -0.0570 -0.0704 -0.0460 -837.1024 -25.5477
France
2002 SMD 6 MNL -0.0588 -0.0720 -0.0460 -457.7811
6 MNP -0.0153 -0.0240 -0.0110 -463.1364 -5.3553
UK
1997 SMD 3 MNL -0.0960 -0.1080 -0.0846 -1039.2630
3 MNP -0.0230 -0.0313 -0.0165 -1048.4950 -9.2320
UK
2005 SMD 3 MNL -0.1305 -0.1630 -0.1030 -271.5710
3 MNP -0.0280 -0.0550 -0.0150 -272.7975 -1.2265
Taiwan
1996 SMD 3 MNL -0.0430 -0.0651 -0.0227 -239.3537
3 MNP -0.0193 -0.0280 -0.0122 -236.4446 2.9091 -6.9474

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3. Case Study: the 2004 Taiwanese Legislative Election
3.1 Background
In 2000, Taiwan experienced the control of a new political party for the first time.
The Koumington (KMT) that was in government from 1949 stepped down and Chen
Shui-bian from the Democratic Progressive Party (DPP) was elected as president of Taiwan.
After the 2000 presidential election, KMT split into three parts. In addition to the old one,
the two new parties are the People First Party (PFP) and the Taiwan Solidarity Union
(TSU). 47 This means that Taiwan has a multi-party system. One important factor
attributed to this is the electoral institution of the legislature, which is a SNTV.
The plurality rule system promotes a two-party system and the PR system does not
prevent a multi-party system from emerging. The plurality rule system has a higher elected
threshold than does the PR system and there is only one candidate elected from one district
under SMD. The parties or candidates must form a coalition to compete the position.
Under this mechanism, in the long run, the party system is prone to a two-party system
unless there are serious social cleavages. Under the PR system, there is no such mechanism.
So the PR system does not have any incentives to make such a coalition because the party
or candidate does not need to be the first pass the post. The SNTV system is similar to the
PR system if the party nominates its candidates in each district efficiently based on the
expected vote shares the party will receive. The multiparty system that forms under the
SNTV system is an equilibrium outcome.

47

The other political party in 2000 was the New Party (NP), but it did not amass a large
vote after the 2001 legislative election. There are other independent candidates too. The
former is excluded because of its small vote share and the latter are not included because of
a data restriction in the lack of issue positions.
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The policy positions of political parties will not converge to the median voter
position under the SNTV system because they only need to get the support of enough
specific electorates in order to win. The threshold to win a seat is not fixed in each district.
There are two parameters that influence the threshold to win a seat in a district. The first
parameter is the size of a district which is how many seats will be elected in this district.
We use M to represent the size of a district. When M increases, the threshold to win a seat
will decrease. The second parameter is the number of candidates in a district. The vote
share distribution of each candidate in a district will have higher variance when there are
more candidates entering the election. If there are more candidates entering the SNTV
system in a district, the threshold to win a seat will be lower. Because of this mechanism
under the SNTV system, we can expect that there will be different kinds of parties or
candidates who represent different parts of the electorate. The policy positions of parties
will spread over the entire issue space. The parties or candidates who can occupy the
positions that can get enough support to win a seat in a district will survive. The
distributions of electorate ideal points in different issue dimensions will be the basic issue
space. Then different parties or candidates will emerge to represent different voices in
various issue positions. In equilibrium, only the M +1 vote getters within the district are
viable under the SNTV system. The implication of this kind of equilibria means that the
proximity between the candidate’s position and the voter’s ideal point decides voter
behavior. The voter will choose the candidate or party whose position is closest to his own.
According to the Taiwanese constitution, the highest chief executive is not president.
The appointment of the chief executive is nominated by the president, who does not need
the consent of legislature; the president can nominate any politician who can conduct his

142

policy. The Taiwanese electoral system is close to a mixed regime. After the DPP was in
government from 2000, they formed a minority government because the DPP did not have
a majority in the legislature. Moreover, the major parties in Taiwan are divided into two
pan-green and pan-blue coalitions to fight each other in the legislature. Consequently, the
central government did not operate efficiently since 2000. Therefore, voters know that the
official government policy must be generated through a negotiation process in the
Legislative Yuan.

3.2 Model Specification
There was a legislative election in 2004. The data source is the Taiwan’s Election
and Democratization Study (TEDS2004LB), which conducted postelection face-to-face
interviews. The total sample size is 600 after excluding any missing case values. In the 600
sample size, 34% of voters reported casting a ballot for the KMT, 45.33% for the DPP,
15.85% for the PFP, and 4.83 % for the TSU. The utility function of individual n toward a
political party j is as following:
(4-6)

Unj = TDnj + Likenj + Sexn + Agen + Educn + TWn + Chenscoren + εnj ,

where TDnj is the total issue distance from a political party j, Likenj is the affection toward
a political party j, TWn is Taiwanese identity, and Chenscoren is satisfaction with Chen
Shui-Bian’s government.
In the top of Table 4.3, the survey respondents perceive two groups of political parties
that the KMT and the PFP are more similar while the DPP and the TSU are closer in the
three issue dimensions of independence versus union with the Chinese mainland,

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environmental protection versus economic growth, and reform versus stability. In the
dimension of non-welfare state versus welfare state, the DPP supports a welfare state more
than the other three parties. Hence, the DPP and the TSU belong to the pan-green camp
and the KMT and the PFP can be classified into the pan-blue camp according to their
positions in the four-dimension issue space.

Table 4.3 Summary Statistics of Alternative-Specific Variables
Issues
TSU
Independence v.s. union
1.61(1.99)
Environment v.s. economy
5.29(2.51)
Non-welfare v.s. welfare state 5.29(2.65)
Reform v.s. stability
3.63(2.55)
Total Euclidean distance
between voters and parties
2.22(0.73)
Party affection
3.77(2.63)
Source: TEDS2004LB.
Standard errors are in parentheses.

DPP
2.18(1.96)
5.58(2.55)
6.05(2.66)
3.79(2.67)

KMT
7.43(1.92)
7.09(1.98)
5.63(2.68)
7.01(2.54)

PFP
7.50(1.95)
6.48(2.12)
5.52(2.52)
6.31(2.45)

2.10(0.71)
5.20(2.62)

1.93(0.77) 1.93(0.74)
5.04(2.48) 4.19(2.49)

In order to capture the issue distance between voters and political parties in the
four-dimension issue space, the total issue distance is included as an alternative-specific
variable in the utility function. The total issue distance is computed by the square root of
the square distance between voters’ ideal points and the positions of political parties.
According to Downsian spatial theory, a voter will acquire lower benefits when a political
party is farther from his ideal point. Therefore, the sign of coefficient estimate of total issue
distance expects to be negative.
The other alternative-specific variable is party affection. It is choice-specific because
this question was asked four times toward each political parties measured by a 0 to 10
scale. This variable indicates voters’ political orientation about party identification. Since

144

party affection measures the same concept as “which political party do you identify with?”,
the question battery about party identification is excluded in the utility function to avoid
the collinearity problem. When two variables catch almost the same variance in the sample,
the variance will be inflated to make estimates of standard errors less efficient. This
problem can be solved either by collecting more samples or by demeaning related variables.
Under the condition that the limited sample size contains restrict information and the
second method of centering variables is not feasible, the traditional dummy measure of
party identification does not enter the model.
To assess other dimensions of political orientation, Taiwanese identity is used to
capture the heterogeneity of ideology among voters. Although there are many factors
influencing the ideology, whether a voter identifies himself as a Taiwanese would be the
most important in the case. No matter what a voter’s ethnicity is, he would think that
pan-green parties are closer to his own ideology once he considers himself as more
Taiwanese than Chinese. The attitude about whether Taiwan should go for independence
or union with Mainland China should be also important too. But this factor is already
contained in the issue dimension related to “independence versus union.” Therefore, only
Taiwanese identity is utilized in the systematic component of the utility function.
To explore whether the IIA assumption holds in voting for four political parties in
the

2004

Taiwanese

legislative

election,

the

multinomial

logit

model

with

alternative-specific variables treated separately in all party contrasts is performed.48 Then
the null hypotheses that any two political parties can be combined are all rejected at the
0.05 significant level. As one kind of the test of the IIA assumption, the six p values of
48

The result is not shown here.
145

likelihood ratio tests of combining the DPP and the PFP, the DPP and the TSU, the DPP
and the KMT, the PFP and the TSU, the PFP and the KMT, and the TSU and the KMT
range from 0.000 to 0.049.49 This means that some preliminary evidence is found to
prove the violation of the IIA assumption. In other words, under the usual circumstance of
a SNTV election, the chance that the IIA assumption holds is low. This gives us the first
reason to choose MNP over MNL.

3.3 MNL and MNP Models by Bayesian Methods
Bayesian methods are applied to estimate MNL and MNP models explaining vote
choice in the Taiwanese 2004 legislative election. One of the advantages of Bayesian
methods is that the distribution of coefficient estimators can be acquired. This avoids some
traditional problems in explaining the significant level of the null hypothesis.
The MNL and MNP models computed by Bayesian methods are presented in Table
4.4 and Table 4.5. A Monte Carlo Markov Chain simulation is used to estimate Bayesian
models. The chain of each simulation has time-series properties and the convergence of
model is a very important criterion to judge whether the parameter estimates are correct or
not. The criterion of Gelman and Rubin’s is lower than 1.1. We can see that the diagnostic
of the two models does not have any serious problems. As for the substantive
interpretation, parallel arguments can be made according to Table 4.4 and Table 4.5.
First, the coefficient interval of total issue distance is statistically significant negative.
This means that when a voter’s issue is further from the locations of all political parties, on
average, it is less likely that the former will vote for the later. More specifically, if a voter’s
49

All statistics are computed in Stata 9.
146

total issue distance is further to the DPP than to the KMT, or closer to the PFP than to the
KMT, or more distant to the TSU than to the KMT, s/he has a higher expected probability
to vote for the KMT, but not for the other three parties.
Second, voters have a higher expected probability to cast their ballot for their
favorite political party. In other words, if a voter likes the DPP more than the KMT, s/he
tends to support the DPP probabilistically. Third, Taiwanese identity influences how
voters choose between the DPP and the KMT, instead of making decisions between the
PFP and the KMT, or the TSU and the KMT. Fourth, satisfaction with Chen Shu-Bian’s
government impacts how electorate selects which party to vote for among the three pairs.
If a voter is more satisfied with the government, s/he is more likely to elect the DPP over
the KMT or the TSU over the KMT. In contrast, when a voter is less satisfied with the
government, s/he has a higher probability to vote for the PFP over the KMT.
The MNP model can be estimated by the method of simulated likelihood with
random sequences in order to overcome the multiple-dimension integration problem. The
estimated results are shown in Table 4.5. Notice that the variance-covariance matrix is
estimated in the bottom of Table 4.5. This is a four-choice situation. Since only utility
differences matter on which choice will be chosen, one choice must be set as the base
category, which is the KMT in our example. We have such a variance-covariance matrix:

(4-7)

⎛σ22 +σ11 − 2σ12 σ23 +σ11 −σ12 −σ13 σ24 +σ11 −σ12 −σ14 ⎞
⎜
⎟
Σ=⎜
.
σ33 +σ11 − 2σ13 σ34 +σ11 −σ13 −σ14 ⎟
⎜
⎟.
.
.
σ44 +σ11 − 2σ14 ⎠
⎝

147

Table 4.4 Bayesian Multinomial Logit Estimates, 2004 Taiwanese Legislative Election

Parameters
Total issue
distance
Party affection
Constant

Female

Education

Age

Taiwan identity

Gov’t satisfaction

Party
Contrast

DPP/KMT
PFP/KMT
TSU/KMT
DPP/KMT
PFP/KMT
TSU/KMT
DPP/KMT
PFP/KMT
TSU/KMT
DPP/KMT
PFP/KMT
TSU/KMT
DPP/KMT
PFP/KMT
TSU/KMT
DPP/KMT
PFP/KMT
TSU/KMT

Posterior
Mean
−0.708
0.564
−3.588
−0.774
−6.625
0.390
0.467
0.438
0.200
0.180
0.322
0.069
0.078
0.151
0.847
−0.338
1.165
4.779
−1.585
5.395

95% BCI
Lower
Upper
−1.130 −0.279
0.460
−5.839
−2.294
−9.983
−0.202
−0.031
−0.536
−0.059
−0.047
−0.048
−0.183
−0.163
−0.289
0.273
−0.969
−0.118
2.794
−2.916
2.385
15000
600

# of draws
# of observations
Source: TEDS2004LB.
Rhat: Gelman and Rubin’s convergence diagnostic.

148

0.674
−1.647
0.671
−3.505
0.969
0.995
1.347
0.487
0.406
0.691
0.319
0.340
0.588
1.390
0.224
2.744
7.207
−0.145
8.686

Rhat
1.01
1.01
1.02
1.02
1.00
1.03
1.00
1.10
1.02
1.02
1.00
1.01
1.01
1.00
1.03
1.00
1.05
1.01
1.03
1.02

Table 4.5 Bayesian Multinomial Probit Estimates, 2004 Taiwanese Legislative Election

Parameters
Total issue distance
Party affection
Constant

Female

Education

Age

Taiwan identity

Gov’t satisfaction

Party
Contrast

DPP/KMT
PFP/KMT
TSU/KMT
DPP/KMT
PFP/KMT
TSU/KMT
DPP/KMT
PFP/KMT
TSU/KMT
DPP/KMT
PFP/KMT
TSU/KMT
DPP/KMT
PFP/KMT
TSU/KMT
DPP/KMT
PFP/KMT
TSU/KMT

Posterior
Mean
−0.328
0.240
−1.034
−0.233
−1.707
0.114
0.200
−0.021
0.025
0.063
0.039
−0.038
0.003
−0.066
0.415
−0.155
0.301
1.699
−0.704
0.958
1.000
0.746
1.007
0.339
0.019
−0.101

95% BCI
Lower
Upper
−0.545 −0.119
0.171
0.301
−1.950 −0.124
−0.982
0.412
−2.962 −0.461
−0.176
0.401
−0.044
0.480
−0.551
0.445
−0.098
0.150
−0.035
0.182
−0.162
0.226
−0.174
0.094
−0.122
0.113
−0.278
0.123
0.091
0.744
−0.493
0.133
−0.254
0.929
0.803
2.647
−1.542
0.044
−0.205
2.084
1.000
1.000
0.247
1.998
0.322
2.438
−0.091
0.917
−0.606
0.597
−1.088
0.856
15000
600

σDPP-KMT ,DPP-KMT
σPFP-KMT ,PFP-KMT
σTSU-KMT ,TSU-KMT
σPFP-KMT ,DPP-KMT
σTSU-KMT ,DPP-KMT
σTSU-KMT ,PFP-KMT
# of draws
# of observations
Source: TEDS2004LB.
Rhat: Gelman and Rubin’s convergence diagnostic.

Rhat
1.01
1.01
1.02
1.02
1.00
1.03
1.00
1.10
1.02
1.02
1.00
1.01
1.01
1.00
1.03
1.00
1.05
1.01
1.03
1.02
1.02
1.01
1.03
1.01
1.03

Furthermore, the scale of utility function is unidentified. To make the model
identifiable, the first element of Equation (4-7) is set to 1. Hence, only five parameters in
the variance-covariance matrix can be estimated. Originally there are ten parameters of
variance-covariance matrix in a four-choice situation. However, five parameters can be

149

identified after the utility differencing and the constraint of the first variance component.
This is because only these five parameters determine the observable pattern of voting
choices (Train 2003, 104-110). The parameters of the estimated variance-covariance
matrix in MNP are not directly interpretable as usual covariance or correlation numbers
unless more assumptions are imposed on the matrix

Σ.

In Table 4.5, two covariance terms are statistically positive at the 0.95 confident
level. This evidence verifies the existence of a correlation among error terms among latent
utility functions. This gives us confidence that MNP does explain the voting choice in the
2004 Taiwanese legislative election better than MNL does. For the substantive
interpretation, we find that all conclusions by MNL stay the same except the influence of
satisfaction with the government on choosing between the KMT and the PFP. The
estimated coefficient becomes insignificant. Since the DPP is the government party and the
DPP belongs to pan-green camp different from pan-blue camp including the KMT and the
PFP. Therefore, the government’s performance should not have impacted voters’
consideration regarding the two opposition parties.

3.4 Substitution Patterns of Voter Choice
As stated previously, the substitution patterns are critical in examining whether the
IIA assumption holds at the individual level. When the IIA assumption does not hold, the
increase of voting probability with respect to one political party will attract
disproportionate vote share from other political parties. This situation is very possible in
the Taiwanese political environment because the political spectrum is essentially divided
into two pan-green and pan-blue camps. The research question of voting behavior in

150

Taiwan should not discard this contextual factor, or the model will not explain the
question of interest correctly.
The first difference of quantities of interest is computed in Table 4.6. For
individual-specific variables like Taiwanese identity and satisfaction with the government,
the substitution patterns are similar across different models. However, this is not the case
for two alternative-specific variables. As seen in Table 4.3, pan-green and pan-blue camps
roughly align themselves on two opposite sides of four issue dimensions. Hence two
political parties within the same camp have higher similarity than those in the other camp.
Therefore, if a voter’s ideal point is one unit further from his favorite party for whatever
reason, s/he should prefer the other party in the same camp over those in the other camp.
For example, a supporter of the PFP should have a higher probability to support the
KMT once s/he moves away from the PFP or the PFP adopts a more extreme policy
position. This scenario cannot be captured in the conditional model as seen in Table 4.6. If
the PFP’s policy position is one unit further away, in MNL the voting probability decreases
0.0532 with increases of 0.0019 to the TSU, 0.0280 to the DPP, and 0.0232 to the KMT.
Yet, in MNP the decreasing probability of voting for the PFP is 0.0697 which is composed
of only two increases of 0.0242 to the DPP and 0.0453 to the KMT. The reason that the
TSU does not get any benefits when the PFP moves away, is because there are two other
political parties closer to the original supporters of the PFP before moving.
Note also that in MNL, the increasing probability of the DPP, at 0.0280, is higher
than that of the KMT, at 0.0232. This seems unreasonable because the KMT and the PFP
belong to the same political camp. Why would a voter have a higher probability to vote for
the DPP rather than the KMT even though the PFP is not his/her favorite choice anymore?

151

The phenomenon comes from the IIA assumption because the DPP has a larger reported
vote share than the KMT.
Table 4 . 6 First Difference in the Voting Probabilities in 2004 Taiwanese Legislative
Election
Change
KMT
PFP
Model/Variable
TSU
DPP
Conditional Logit
Taiwanese identity 0 → 1 0.0191 0.1953 −0.1354 −0.0791
Satisfaction
ΔRange
0.0720 0.7723 −0.4949 −0.3494
KMT distance
Δ1
0.0074 0.1088 −0.1432
0.0270
DPP distance
Δ1
0.0094 −0.1580
0.1143 0.0343
PFP distance
Δ1
0.0019 0.0280 0.0232 −0.0532
TSU distance
Δ1
−0.1535
0.0074 0.0061 0.0018
KMT affection
Δ1
−0.0070 −0.1029
0.1355 −0.0255
DPP affection
Δ1
−0.0081
0.1360 −0.0984 −0.0295
PFP affection
Δ1
−0.0025 −0.0364 −0.0302
0.0691
TSU affection
Δ1
0.0221 −0.0107 −0.0088 −0.0026
Multinomial Probit
Taiwanese identity 0 → 1 0.0191 0.2064 −0.1383
Satisfaction
ΔRange
0.0850 0.7852 −0.5174
KMT distance
Δ1
0.0147 0.0739 −0.1628
DPP distance
Δ1
0.0073 −0.1271
0.0814
PFP distance
Δ1
0.0000 0.0242 0.0453
TSU distance
Δ1
−0.0143
0.0061 0.0097
KMT affection
Δ1
−0.0079 −0.0628
0.1108
DPP affection
Δ1
−0.0047
0.0894 −0.0605
PFP affection
Δ1
0.0000 −0.0321 −0.0554
TSU affection
Δ1
0.0172 −0.0066 −0.0113

−0.0889
−0.3537
0.0738
0.0384
−0.0697
0.0000
−0.0396
−0.0237
0.0877
0.0000

Bayesian MNP
Taiwanese identity 0 → 1
Satisfaction
ΔRange
KMT distance
Δ1
DPP distance
Δ1
PFP distance
Δ1
TSU distance
Δ1
KMT affection
Δ1
DPP affection
Δ1
PFP affection
Δ1
TSU affection
Δ1

−0.0793
−0.3023
0.0421
0.0304
−0.0602
−0.0014
−0.0325
−0.0228
0.0645
−0.0015

0.0117
0.0261
0.0171
0.0061
0.0005
−0.0021
−0.0122
−0.0019
−0.0043
0.0165

Source: TEDS2004LB.

152

0.1768
0.6175
0.0823
−0.1345
0.0191
−0.0069
−0.0757
0.0938
−0.0291
−0.0085

−0.1092
−0.3413
−0.1415
0.0980
0.0405
0.0104
0.1205
−0.0691
−0.0311
−0.0064

Because of the IIA assumption, the ratio between the DPP and the KMT must stay
the same when the voting probability for the PFP changes. But this is not the case for
predicting probability in MNP since the increasing probability of the DPP, at 0.0242, is
lower than that of the KMT, at 0.0453. The set of predicting probabilities by MNP makes
more sense because the voting probability for the TSU is lower and because the voting
probability for the DPP is lower than that for the KMT.
Compare a voter whose party affection for the KMT is one unit higher to the
average voter, with other variables controlled at their mean levels. In MNL, the increasing
voting probability for the KMT is 0.1355, consisting of 0.1029 from the DPP, 0.0255
from the PFP, and 0.0070 from the TSU. The ratio of decreasing probability between the
DPP and the PFP is about 4. Although the KMT can be considered as a moderate political
party because of its policy position roughly located in the middle between those of the DPP
and the PFP, the ratio of 4 is still higher according to the fact that the KMT and the DPP
do not belong to the same political camp. The picture in MNP is different again from that
in MNL. In MNP, the voting probability for the KMT boosts 0.1108 that comprises
0.0628 from the DPP, 0.0396 from the PFP, and 0.0079 from the TSU. The ratio of
decreasing voting probability between the DPP and the PFP is about 1.6. The contrasting
ratio of MNP is less than half of that of MNL. This explains the context of Taiwanese
politics better because of the existence of two political camps.
The other interesting point is about the discrete change of the TSU party affection.
In MNL, one unit increase of the TSU party affection augments the voting probability for
the TSU 0.0221 which includes decreasing 0.0107 from the DPP, 0.0088 from the KMT
and 0.0026 from the PFP. However, in MNP, the reducing probabilities of the DPP and

153

the KMT are reverse. The distribution of first difference in MNP is increasing 0.0172 for
the TSU, reducing 0.0066 from the DPP, and decreasing 0.0113 from the KMT. A possible
explanation is that the TSU used to be a faction within the KMT before it became an
independent party. Those voters who identify themselves with the TSU are used to be with
the KMT. Therefore, those supporters of the TSU now have more similar feeling to the
KMT than to the DPP.

4. Concluding Remarks
Electoral systems create the convergent and non-convergent electoral incentives with
substantial impacts on the position-taking strategy of political parties through mechanisms
of the electoral formula, and the district magnitude. The combined effects of the various
features in electoral systems induce the electoral threshold. Under SMD with a higher
threshold, political parties have incentives to converge toward the centrist position. Under
PR with a lower threshold, parties can move to a more extreme position to get elected.
This general pattern of divergence and convergence of political party positions is also
modified by the type of government and voter turnout rates depending on electoral systems.
These two aspects cause lower policy dependence under SMD and high under PR.
Voter choice is based on a random utility model. In order to measure the effects of
party position-taking strategies, the policy distance between political parties and voters is
incorporated into the representative component. The policy dependence among political
parties is manifested in the correlation in the error terms. While MNL imposes the IIA
assumption to make the error terms uncorrelated, MNP relaxes it. Therefore, MNL is
suitable for voter choice under SMD but MNP is more appropriate for voter choice in PR.

154

Furthermore, to compare the fit of the two statistical models (MNL and MNP), across
electoral systems, the statistical indicator of model comparison is a Bayes factor. Suppose
that Bayesian factor is calculated as MNP over MNL. The large positive means support for
a MNP voter choice model. As the electoral systems is coded from more divergent to more
convergent, such as ranked by PR to SMD, the correlation between a Bayes factor and the
coding of electoral systems is expected to be positive. The empirical analysis shows that the
average of Bayes factor of MNP over MNL is higher under PR than mixed and SMD
systems.
The evidence in the analysis of the 2004 Taiwan legislative election shows that the
policy dependence exists in political party issue positions. MNP shows that the error terms
are significantly correlated. The substitution pattern predicted by MNP model fit the
contextual background of Taiwanese politics.
While the research in Taiwan is quite compelling, the analysis is only under one kind of
electoral system, SNTV. The evidence needs to be found under other types of electoral
systems because the generalization should work also under SMD and PR. Moreover, the
mechanism of causing the policy dependence needs to be elaborated in more detail within
two types of electoral systems. This can be the direction of future research

155

CHAPTER 5
Conclusion
The focus of this project is the impacts of electoral institutions on political
representation from the view point of how voters decide in elections. The advantage of the
approach is to decipher the linkage between the voters’ preferences and policy outcomes
from the starting point of political participation. Since policy outcomes influence the
citizens’ welfare, they are the judgment of how well the citizens’ preferences are taken into
account: this is also the essence of democratic politics. Political participation is the first
step that voters make up their minds of whether or not to express their policy preferences.
From this forwarding-looking angle, how the citizen’s preferences are represented in the
policy outcomes, they are aggregated by the electoral system to select political agents who
have the power to bargain in the government. In other words, the expression of the
citizens’ preference is the cornerstone of political representation.
Electoral institutions organize the action of preference expression because the latter is
the result of the interaction between the citizens and politicians. By the insight of spatial
theory, citizens’ preferences can be viewed as a distribution and political agents pick their
policy positions to solicit the citizens’ support. Electoral systems frame how widespread
the policy positions of political agents are on a single issue spectrum. Then the citizens
decide whether or not to participate in elections and which political agent to vote for.
There are three aspects of political participation influenced by electoral institutions: voter
turnout, the biases of the citizens’ preferences, and voter choices. These three elements are
the focus of the project. The first element is how electoral systems affect higher or lower
turnout; the second is to explore if the citizens’ preferences is distorted by electoral systems;

156

the final is whether electoral institutions frame various types of political competition.
These three intertwined steps are about agents selections with concerns on the final results
of policy outcomes. In other words, these important steps shows how the agents are chosen
in the first place but they are related to the government policies. This project intends to
investigate that electoral systems have serious consequences on political representation
from the view point of voters’ behavior.
This first chapter tackles the micro-foundations of voting and addresses why PR
systems are associated with higher turnout than SMD systems. The micro-foundations are
built upon the calculus of voting and spatial theory. The central claim is that individual
evaluations of the B term in the calculus of voting are affected by spatial party competition
framed by electoral institutions. While SMD constrains the number of political parties and
creates large centripetal forces for party competition, it reduces individual perceptions of
the two components of the B term. In contrast, PR allows more political parties to survive
and does not generate many centripetal forces; thus, it helps voters acquire higher
estimates of the two counterparts of the B term.
The calculus of voting helps us understand why voting rates differ across countries.
The cost-benefit approach under a synthesized spatial theory facilitates explaining citizens’
voting behavior driven by electoral institutions. Since every election is specific based on the
constraints of political institutions, and country-level contextual factors, interactions
between political agents and electorates are centrally important in explaining individual
voting behavior.
The second chapter is to explore the question of how electoral institutions affect the
degree of political representation through the perspective of comparing the distribution of

157

voter preferences versus that of all electorate. The effects of electoral systems on political
representation are based upon voters’ response to party competition under spatial theory.
The main argument is that different types of electorate according to their relative locations
in the distribution of voter preferences have various incentives to voting. The moderate
type of electorate with location in the interquartile range has lower benefit evaluations for
voting across PR and SMD.

However, the extreme type of electorate with location

toward two ends of the issue spectrum has dissimilar profit schemes under PR and SMD.
The profit calculation for the extreme type is lower under SMD than PR because of
indifference and alienation for political parties’ policy position convergence toward the
median voter. Thus, due to inconsistent benefit evaluations among different types of
electorate, PR has a higher probability to induce disproportionality defined above.
The third chapter discusses how electoral institutions impact the pattern of political
competition with implication of the selection of statistical models. The single-member
district

and

proportional

representational

electoral

systems

have

institutional

consequences on interactions among political parties in the decision-making process in
parliament. SMD usually creates a mandate delegated to a single political party and PR has
a power-sharing system with more than one party. The policy implication is the degree of
dependence in the issue positions of political parties within electoral systems. When voters
ponder which political party to support, they can see whether or not there is policy
dependence among political parties under SMD or PR.
The concept of no policy dependence under SMD is equal to independence of
irrelevant alternatives related to multinomial logit. Another model which relaxes IIA is
multinomial probit which allows policy dependence in PR. To capture the effects of

158

electoral systems on vote choice, I examine whether MNL or MNP has a better model fit
under two electoral systems. Since two statistical models are non-nested, I conduct the
model fit comparison through Bayes factor with MNP over MNL. To test these hypotheses,
I compare the patterns of voter choice affected by electoral systems across countries. The
data are round 1 and round 2 of the Comparative Studies of Electoral Systems including
various types of electoral institutions. Furthermore, the case study of Taiwan 2004
legislative election proves that the substitution pattern among political parties derived
from MNP makes more sense conditional on the context of the real world.
Apart from mere analysis for representation typology, my research connects the effects
of electoral systems with the participation. Since the institutions of electoral systems are
inalienable in the process of democratic representation. Past research does not discuss how
electoral systems affect the expression of citizens’ preferences (Mansbridge 2003; Pitkin
1967; Young 2000). Even though the research of electoral systems has turned the attention
to citizens’ preferences, it does not care about how the preferences are derived from
participation (Blais and Bodet 2006; Budge and McDonald 2007; Golder and Stramski
2010; Huber and Powell 1994; McDonald and Budge 2005; McDonald et al. 2004; Powell
2000, 2006, 2009; Powell and Vanberg 2000). My research bridges the gaps in these two
lines of previous research.
What kinds of preferences are expressed is influenced by electoral systems in different
aspects. The major implication of my arguments is that electoral systems have positive and
negative effects on varied aspects of participation. PR has a positive effect motivating more
citizens to vote; PR has a higher possibility to induce a biased preference distribution than
SMD; Under PR, the vote choice is more difficult for citizens because of the policy

159

dependence requires more information to make correct selection of representatives,
meaning that the information cost is higher. This conclusion is not surprising because the
electoral systems have contradictory effects on participation and the linkage of citizens’
preferences and government policy is not a smooth process.
From a methodological perspective, the project has two contributions to the current
research of electoral institutions. The project is to emphasize the impacts of electoral
institutions at the micro level. The coherent argument of the three chapters is to explain the
voters’ decision-making process when facing the configuration of political agents’ policy
positions. This method promotes the understanding of how different institutions generate
various incentive structures to influence individual behavior. Furthermore, this project
adopts a unifying approach of spatial theory to develop the theoretical arguments. The
advantage is that the micro-foundation mechanisms can be extended beyond the country
borders and the comparison of the institutional effects across countries is plausible.
The micro-foundation mechanisms increase our understanding of how different kinds
of electoral systems work at different stages of political representation. Every type of
electoral systems has its own advantages and disadvantages in promoting or decreasing
political representation. Through this exercise, we can have more complete knowledge
about the good and bad of electoral institutions. In the future of institutional design, we
are able to adjust some parts of the institutions to achieve a better political representation.
For future research, there are several directions. First, to establish the validity of
proposed micro-foundation mechanisms in three chapters, they need to be tested by more
data collected both at macro and micro levels. To assure the reliability of corroboration,
macro- and micro- level data is necessary to gauge the effects of political institutions. These

160

hypotheses should be verified with new information to check if they still hold because
these mechanisms may evolve. We need to track the changes to understand the effects of
electoral systems more clearly. One way to do it is to expand the time period of the data
sets. Second, this project focuses only on the voters’ decision-making process. To have
more comprehensive knowledge of linking the citizens’ preferences to the policy outcomes,
the part of political parties can not be ignored. We need to have a more thorough theory of
party positioning strategies to know more about the interactions between voters and
politicians, influenced by electoral institutions. Finally, the forward-looking approach,
which is how the citizens’ preferences are represented in government policy, is only one
part of the meaning of political representation. The other standard is that political officials
are accountable to their constituents and the voters utilize elections as a tool to control
politicians. The feedback mechanisms are also important and should be integrated into the
voters’ decision-making process of political participation and voter choice. We need to
know how two kinds of mechanisms affect each other. These are possible directions for
more investigations to understand how the electoral process transforms the citizens’
preferences into the final policy outcomes.
As stated in the introduction chapter, the focus of policy preferences excludes other
properties of citizens’ preferences, such as gender, culture, economy, and ethnicity. There is
a significant amount of research women representation. For instance, see Rule (1994) and
Schwindt-Bayer (2010) for details. These attributes need to be operationalized for
advanced research on representation. Here are some of my conjectures. For the culture
attributes, it can be measured by a modernization index (Inglehart and Welzel 2005). Since
the data sets of World Value Survey are available for many countries, we already have the

161

citizens’ preferences in hand. The second step is to conduct the interview on the
representative counterpart. Then we can check this dimension of culture is representative
across electoral systems. In a similar vein, the economy representation can be measured by
matching the income distribution of citizens and that of representatives.
For the matter of generalizability hindered by issue voting, it is necessary to construct
a more exhaustive theory construction to accommodate two types of linkages: policy and
patronage. The building of such a unified theory will let us know how two linkages
interact with each other. Are they mutually exclusive? Or are they mutually reinforced?
What causes a country to have more one type of linkage, but not the other? Do they
depend on different stages of economic development? These are research questions worth
investigating in the future.

162

Appendices

163

Appendix Table A.1: Sixty-four Elections used in Chapter 1 Analysis (Part 1)
Year
Aggregate
Survey
Centripetal Polity2
Turnout
Turnout
Established
CSES1
1996
82.5
98.9
2
10
Australia
1997
56.2
78.3
2
10
Canada
2000
63.7
94.8
2
8
Mexico
1997
71.5
81.7
2
10
UK
1998
56.7
67.2
1
10
Hungary
1997
57.7
72.5
1
6
Mexico
2000
57.2
58.7
1
10
South Korea
1999
90.5
83.5
0
10
Belgium
76.3
88.3
0
10
Czech Republic 1996
1998
86.6
93
0
10
Denmark
1998
83.0
83.3
0
10
Germany
1999
84.1
83.3
0
10
Iceland
1998
73.4
89.9
0
10
Netherlands
1996
88.3
96.2
0
10
New Zealand
1997
78.0
85.7
0
10
Norway
1997
47.9
55.2
0
9
Poland
2002
62.8
62.0
0
10
Portugal
1996
78.0
78.1
0
10
Spain
2000
68.7
80.6
0
10
Spain
1998
81.4
87.0
0
10
Sweden
1999
43.4
58.8
0
10
Switzerland
CSES2
2004
94.8
97.9
2
10
Australia
2004
61.2
90.8
2
10
Canada
2002
71.6
79.3
2
9
France
2005
61.4
72.1
2
10
UK
2004
56.2
78.5
2
10
USA
2002
70.5
82.7
1
10
Hungary
2003
41.7
71.9
1
8
Mexico
2004
59.9
79.0
1
10
South Korea
58.0
73.9
0
10
Czech Republic 2002
2001
87.1
96.0
0
10
Denmark
2003
69.7
80.6
0
10
Finland
2002
79.1
91.3
0
10
Germany
2003
87.7
96.0
0
10
Iceland
2002
62.6
85.3
0
10
Ireland
2006
83.6
81.3
0
10
Italy

164

Appendix Table A.1: Sixty-four Elections used in Chapter 1 Analysis (Part 2, cont’d)
Year
Aggregate
Survey
Centripetal Polity2
Turnout
Turnout
CSES2
2002
77.0
83.8
0
10
New Zealand
2001
75.5
82.8
0
10
Norway
2001
46.3
58.1
0
10
Poland
2005
65.3
81.4
0
10
Portugal
2004
75.7
89.2
0
10
Spain
2002
80.1
88.4
0
10
Sweden
2003
45.4
74.0
0
10
Switzerland
Non-Established
CSES1
1997
70.7
90.0
2
10
Lithuania
2000
78.6
94.4
2
5
Peru
2001
78.6
95.4
2
9
Peru
1996
76.9
81.4
2
8
Taiwan
1996
78.2
82.0
1
8
Romania
1999
59.9
77.5
1
4
Russia
1998
68.1
69.0
1
7
Ukraine
1996
84.7
91.0
0
9
Israel
1996
75.7
75.8
0
10
Slovenia
CSES2
2002
82.3
87.9
2
8
Brazil
2005
87.1
95.8
2
9
Chile
2006
87.7
94.7
2
9
Peru
2004
77.1
86.5
2
8
Philippines
2004
64.4
78.8
2
7
Russia
2004
80.3
91.2
2
10
Taiwan
2005
48.7
91.5
1
9
Albania
2004
58.5
80.4
1
9
Romania
2001
66.2
82.4
1
9
Taiwan
2001
72.1
78.9
0
9
Bulgaria
2003
67.8
89.2
0
10
Israel
2004
60.7
77.4
0
10
Slovenia
*Aggregate turnout is defined as Vote /VAP according to IDEA, where VAP is
voting age population.

165

Appendix Table A.2 Replication of Table 2.2 Replacing Self-Judged Party Positions with
Average Party Positions (Part 1)
Coefficient Robust SD P-value
Fixed Part
-1.996

1.712

0.250

Compulsory1, γ0(1)

0.909

0.344

0.011

Compulsory2, γ0(2)

0.222

0.288

0.445

Compulsory3, γ0(3)

1.440

0.215

0.000

Closeness, γ0(4)

-0.764

0.410

0.068

ENP, γ0(5)

-0.091

0.044

0.047

District magnitude, γ0(6)

-0.002

0.002

0.425

Frequency, γ0(7)

-2.180

0.498

0.000

Concurrent, γ0(8)

0.416

0.217

0.061

Log District size, γ0(9)

-0.002

0.033

0.953

Politil Competition, γ0(10)

-0.014

0.007

0.064

GDP per capita, γ0(11)

0.169

0.140

0.233

Developing, γ0(12)

1.179

0.275

0.000

L_GDP Chang, γ0(13)

-0.029

0.024

0.234

L_GC_Developing, γ0(14)

-0.003

0.037

0.943

0.297

0.184

0.114

MIX, γ0(16)

-0.208

0.288

0.475

Female, β1

0.019

0.027

0.471

Education, β2

0.096

0.011

0.000

Income, β3

0.092

0.010

0.000

Inpower, β4

0.100

0.010

0.000

Makediff, β5

0.184

0.016

0.000

Partyid, β6

0.739

0.040

0.000

Age26_35, β7

0.279

0.035

0.000

Age36_45, β8

0.617

0.046

0.000

Age46 and above, β9

0.987

0.054

0.000

Intercept γ10(0)

0.006

0.002

0.001

PR, γ10(1)

0.008

0.003

0.021

Intercept of β0, γ0(0)

PR, γ0(15)

F slope, β10

166

Appendix Table A.2 Replication of Table 2.2 Replacing Self-Judged Party Positions with
Average Party Positions (Part 2, cont’d)
Coefficient Robust SD P-value
Fixed Part
H slope, β11
Intercept γ11(0)

0.031

0.006

0.000

PR, γ11(1)

0.015

0.007

0.041
P-value

1.81

χ2
3.29

σ u0

0.696

2372.21

0.000

σ u10

0.010

116.47

0.000

σ u11

0.022

88.28

0.016

Random Part
σ e (scale factor)

Std. Dev.

167

Appendix Table A.3: The Classifications of Sixty-Eight Elections Used in Analysis (Part 1)
Year

Established
CSES1
1997
Canada
1997
UK
+
1996
USA
1996
Australia
2000
Mexico
2000
Korea
1997
Mexico
1998
Hungary
New Zealand 1996
1998
Germany
1996
Spain
2000
Spain
1999
Iceland
1998
Netherlands
1997
Norway
2002
Portugal
1999
Switzerland
1999
Belgium
Czech Republic 1996
1998
Denmark
1997
Poland
1998
Sweden
CSES2
2004
Canada
2005
UK
2004
USA
2002
France
2004
Australia
2003
Mexico
2004
Korea
2002
Hungary
2006
Italy
2002
Germany
New Zealand 2002
2003
Belgium+
2002
Ireland
2004
Iceland
2003
Finland

Agg.
Survey SMD1 Mixed1 PR1 SMD2 MMM MMP PR2
Turnout Turnout

56.2
71.5
64.7
82.5
63.7
57.2
57.7
56.7
88.3
83.0
78.0
68.7
84.1
73.4
78.0
62.8
43.4
90.5
76.3
86.6
47.9
81.4

78.3
81.7
75.6
98.9
94.8
58.7
72.5
67.2
96.2
83.3
78.1
80.6
83.3
89.9
85.7
62
58.8
83.5
88.3
93
55.2
87

1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0

0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0

0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1

1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0

0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0

0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0

0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1

61.2
61.4
56.2
71.6
94.8
41.7
59.9
70.5
83.6
79.1
77.0
91.9
62.6
87.7
69.7

90.8
72.1
78.5
79.3
97.9
71.9
79
82.7
81.3
91.3
83.8
94.64
85.3
96
80.6

1
1
1
1
1
0
0
0
0
0
0
0
0
0
0

0
0
0
0
0
1
1
1
0
0
0
0
0
0
0

0
0
0
0
0
0
0
0
1
1
1
1
1
1
1

1
1
1
1
1
0
0
0
0
0
0
0
0
0
0

0
0
0
0
0
1
1
1
0
0
0
0
0
0
0

0
0
0
0
0
0
0
0
1
1
1
0
0
0
0

0
0
0
0
0
0
0
0
0
0
0
1
1
1
1

168

Appendix Table A.3: The Classifications of Sixty-Eight Elections Used in Analysis
(Part 2, cont’d)
Year

Established
CSES2
Netherlands+ 2002
2001
Norway
2001
Poland
2005
Portugal
2002
Sweden
2004
Spain
Czech Republic 2002
2001
Denmark
2003
Switzerland
Non-established
CSES1
Chile+
Israel
Lithuania
Peru
Peru
Romania
Russia
Slovenia
Taiwan
Ukraine
CSES2
Albania
Brazil
Bulgaria
Chile
Israel
Peru
Philippines
Romania
Russia
Slovenia
Taiwan
Taiwan

Agg.
Survey
SMD1 Mixed1 PR1 SMD2 MMM MMP PR2
Turnout Turnout

79.1
75.5
46.3
65.3
80.1
75.7
58.0
87.1
45.4

96.88
82.8
58.1
81.4
88.4
89.2
73.9
96
74

0
0
0
0
0
0
0
0
0

0
0
0
0
0
0
0
0
0

1
1
1
1
1
1
1
1
1

0
0
0
0
0
0
0
0
0

0
0
0
0
0
0
0
0
0

0
0
0
0
0
0
0
0
0

1
1
1
1
1
1
1
1
1

1996
1997
2000
2001
1996
1999
1996
1996
1998

72.8
84.7
70.7
78.6
78.6
78.2
59.9
75.7
76.9
68.1

84.2
91
90
94.4
95.4
82
77.5
75.8
81.4
69

1
0
1
1
1
0
0
0
1
0

0
0
0
0
0
1
1
0
0
1

0
1
0
0
0
0
0
1
0
0

1
0
1
1
1
0
0
0
1
0

0
0
0
0
0
1
1
0
0
1

0
0
0
0
0
0
0
0
0
0

0
1
0
0
0
0
0
1
0
0

2005
2002
2001
2005
2003
2006
2004
2004
2004
2004
2001
2004

48.7
82.3
72.1
87.1
67.8
87.7
77.1
58.5
64.4
60.7
66.2
80.3

91.5
87.9
78.9
95.8
89.2
94.7
86.5
80.4
78.8
77.4
82.4
91.2

0
1
0
1
0
1
1
0
1
0
0
1

1
0
0
0
0
0
0
1
0
0
1
0

0
0
1
0
1
0
0
0
0
1
0
0

0
1
0
1
0
1
1
0
1
0
0
1

1
0
0
0
0
0
0
1
0
0
1
0

0
0
0
0
0
0
0
0
0
0
0
0

0
0
1
0
1
0
0
0
0
1
0
0

1999

*

Aggregate turnout is defined as Vote /VAP according to IDEA, where VAP is voting age
population.
+
This indicates the case is excluded from multilevel analysis in Table 3.4 and Table 3.5
169

Appendix A.4: Codebook for MNL and MNP Models:
Dependent variable:
Lepavote: 1. Vote for KMT; 2. Vote for DPP; 3. Vote for PFP; 4. Vote for TSU;
others and no response are coded as missing.

Alternative-specific:
• Total issue distance: the square root of Euclidean distance of four issue
dimensions which are independence versus union, environmental protection
versus economic growth, non-welfare state versus welfare state, and reform
versus stability.
• Party affection: 0 to 10 to represent how much each respondent like each
political party.

Individual-specific:
• Female: 1. Female; 0. Male.
• Age: Age in groups. 1. 21-29; 2. 30-39; 3. 40-49; 4. 50-59; 5. 60 and above.
• Education: 1. elementary school and below; 2. junior school and below; 3. senior
high school and below; 4. professional school and below; 5. university and
above.
• Taiwanese identity: 1. those who thinks he is a Taiwanese or Taiwanese is a more
important identity than Chinese; 0. others.
• Satisfaction with Chen Shui-Bian’s Government: 0 to 1 with 0 indicating the least
satisfaction and 1 the most.

170

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