RATIONAL DECSSION MAKENG:
THREE MODELS

Thesis for the Degree of M. A.
.MlCE-flGAN STM‘E UNEVERSITY
Wayne A. Olin
1966

S

 

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ABSTRACT

RATIONAL DECISION MAKING:
THREE MODELS

by Wayne A. Olin

In this paper I describe what I consider to constitute
the conditions for rational decision making. I then
describe three models of decision making: the optimizing
and satisficing models as formulated by John T. Gullahorn
and Jeanne E. Gullahorn and the gain-loss model as formu-
lated by Santa F. Camilleri. I apply the gain-loss model
of rational decision making to some questionnaire data
collected by John T. Gullahorn, first to a two-alternative
situation and then to the three-alternative situation. I
conclude from these results that the gain-loss model of
rational decision making adequately explains the data from
the Gullahorn questionnaire in both the two-alternative and

the three-alternative situations.

RATIONAL DECISION MAKING:
THREE MODELS

by

Wayne A. Olin

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTEROFARTS
Department of Sociology

1966

ACKNWLEDGMENTS

I wish to express my gratitude to the chairman of my
committee, Dr. Santo 1'. Camilleri., and to the other members
of my comittee, Dr. Donald W. Olmsted and Dr. ‘Ihomas L.
Conner, for their many suggestions and aid with this paper.
1 would like to thank Dr. John '1'. Gullahorn and Dr. Jeanne
E. Gullahorn for their valuable ideas. I wish to thank
Nancy K. Hamond for proofreading this manuscript. I would
also like to thank my wife, Phyllis C. Olin, for her
patience in the typing of the entire manuscript.

ii

AMWLEDMNTS O O O O O O O O O O 0
us I OF TABLES O I O O O O O O O O 0
Introduction . . . . . . . . . . .

The Structure of Decision Making .

TABLE OF CONTENTS

Three Models of Rational Decision Making .

Empirical Application of the Gain-Loss Model:
Two Alternatives

Empirical Application of the Gain-Loss Mbdel:
Three Alternatives

conC1us1on3eeeeeeeeeeeeeeeee

LIST OF REFERENCES

iii

Page
ii
iv

17

37
49
52

LIST OF TABLES

Table Page

1 Union Stewardship 25. Employees' Club Office
Dilema: Frequency Distribution of
Responses . . . . . . . . . . . . . . . . . . l9

2 Reference Group Preferences, Percentages, and
Components for the Eight Situations: Two
Alternativeseeeeeeeeeeeeeeee26

Hypothesized Components and Their Definitions . 27

4 Predicted and Observed Percentages Compared:
NOAltCmtiveseeeeeeeeeeeeee35

5 Additional Hypothesized Components and Their
Definitionseeeeeeeeeeeeeeeee39

6 Reference Group Preferences, Percentages, and
Components for the Eight Situations: Three
Aththiveaeeeeeeeeeeeeeeee“

7 Predicted and Observed Percentages Compared:
MeeAltematives.............43

iv

RATIONAL DECISION MAKING: THREE MODELS

We

Hundreds of times every day, every individual is
confronted with the situation where more than one course
of action lies ahead of him and he can take only one of
the courses of action. Many times the individual does not
consciously choose one of the courses of action, but takes
a course of action because of factors other than conscious
choice. For example, the motorist confronted with a red
traffic light does not consciously consider the alternatives
of stopping or going through the intersection, but, because
of habit, training, or some other unconscious process, he
stops. Even though he may realize that not stopping is a
possible alternative, he does not say to himself, ”If I
don't stOp I may get involved in an accident or I may get a

ticket,“ He Just staps.

S s on

Many times , however, when the individual is confronted
with several alternatives, he does consciously consider the
consequences of each alternative and on this basis chooses
one of them. I will call this type of behavior decision
making. This decision making, as I define. it, involves
three components. First, the individual must realize that

l

there are at least two courses of action confronting him
and that he can only take one of them. Although there may
be many courses of action available to the individual, and
although he may be unaware of some of them, my definition
of decision making necessitates only that the individual

-5. .n’ ‘

be aware of at least two of the available roux-see of action.
Second, the individual must conscioust examine each of the
alternatives that he is aware of to determine what ”would
be expected of him andwhat he would, expect the consequences
to be. Third, the individual [met-use this conscious
(examination of the alternatives as the basis for selecting
one course of action in lieu of the other alternative courses.
The third criterion for decision making, that the
individual bases his decision on a conscious examination of
the alternatives, implies that in arriving at his decision
the individual uses some sort of reasoning process based on
his information about the alternatives. In other words, the a ‘
individul—etarts—fiflx‘M— information. dbmitthemltematives ,
Whrough some reasoning process, and arrives at a
' decision.

Ilhis raises several important questions about decision
making. Is this reasoning process roughly the same for all
people or is it peculiar to the individual? What is the form
that this reasoning process takes? Does the form of the
reasoning process vary from decision to decision, and, if so,

what are the determinants of the form; is- it the situation?

I would hypothesize that the answer to the question of
whether the reasoning process in decision making is roughly
the same for all peOple or whether it is peculiar to the
' ~individual. depends on the situation. In making decisions
’ that are relatively important to him and where the situation
appears to be relatively well structured, the individual
would use the same reasoning process as would another person
under the same conditions. Thus I hypothesize that people
making the same important decision in a structured situation
will use the same reasoning process, and each person's
decision will seem rational to all others under the same
conditions. I will call decision making under these con-
ditions rational decision making. In this paper, I will
assume that this hypothesis is correct and that situations
characterized by rational decision making are identifiable.

Many models of the form of the reasoning process in
rational decision making have been suggested. I will
present three models of the reasoning process, and I will
test one of these models. I would hypothesize that the
form of the reasoning process in rational decision making
is different for different decisions, and that the form is
a product of the importance of the decision and the degree
of the structuring of the situation.

A summary of some of what is known or suspected con-
cerning the process of rational decision making and the
reasoning process involved is given by Pestinger.

When a person is faced with a decision between
two alternatives, his behavior is largely oriented
toward making an objective and impartial evaluation
of the merits of the alternatives. This behavior
probably takes the form of collecting information
about the alternatives, evaluating this information
in relation to himself, and establishing a pref-
erence order between the alternatives. Establishing
a preference order does not immediately result in a
decision. The person probably continues to seek
new information and to re-evaluate old information
until he acquires sufficient confidence that his
preference order will not be upset and reversed
by subsequent information. This continued infor-
mation seeking and information evaluation remains,
however, objective and impartial.

when the required level of confidence is

reached, the person makes a decision. undoubtedly,
the closer together in attractiveness the alterna-
tives are, the more important the decision, and the
more variable the information about the alternatives,
the higher is the confidence that the person*will
'want before he.mdkes his decision. It is probably
this process of seeking and evaluating information.

that consumes time when a person must make a
decision.1 .

W
In this paper I will present three possible models of
the relationship between the final preference order of
the alternatives held by the person and his decision, i.e.,
the reasoning process of rational decision making. The
first two models, optimizing and satisficing, are discussed
by the Gullahorns.2 The third:model, gain-loss, is the

linen Futinsor. WWW
(Stanford: Stanford University Press, , pp. - 3.
2John T. Gullahorn and Jeanne E. Gullahorn, Compute;

sygglgtion of Role Conflict, System DeveIOpment Corporation
Paper No. SP- 1 Santa Monica, California: System

Development Corporation, 9 Nevember 1965), pp. 14-16.

 

product of S. P. Camilleri.3 I will discuss briefly the
first two models of rational decision making. I*will
examine in more detail the gain- loss model and will apply
it to some existing questionnaire data as a test of its
validity.

If the relationship between the preference order and
the decision of the person is optimizing, the person
"merely considers the rewards and costs of each alternative
and selects the one yielding the greatest profit."‘ Once
the person has a final preference order among the alterna-
tives, he chooses that alternative at the top of the list,
i.e., the one with highest preference.

The second model, that of satisficing, is attributed
'by the Gullahorns to Herbert Simon.‘ Whenindividuals
satisfice in decision making, they“look for’a course of
. action that is satisfactory or good enough.”5 According
to this.mode1 a person has a ”threshold of acceptability,“
and any alternative having a profit to the_person greater
than this threshold is “good enough” for the person. The

person considers the alternatives according to some order

 

3Santo r. Camilleri, 1 f 10 -
E;ghngg_§i£%§§igg,.A Paper Presented at the Midwest
Sociologica Association Meetings, Madison, Wisconsin,
April, 1966.

4Gullahorn and Gullahorn, p. 14.

5mm: a. sum, We: (New York:
Macmillan Co., 1957), p. xxv.

and the first one that exceeds the threshold is the one
he accepts. If none of the alternatives is chosen by this
satisficing procedure, the person selects one by the

optimizing procedure. The problem with this model comes
Sin.determining the order in which the person considers the
alternatives.

In a situation involving continuing social interaction,
it is reasonable to believe that of the possible courses of
action open to a person the first course of action that he
‘would consider in making a satisficing decision would be his

present course of action. In this regard, Homans says, "The!

evidence seems to be that the less their profit, the more
likely peeple are to change their behavior, and to change
it so as to increase their profit.”6 Homans' statement is
similar, but not equivalent, to the satisficing decision
model. Homans postulates no "threshold of acceptability."
He apparently postulates a probabilistic model; as the
profit of a person's present course of action decreases,
the probability increases that he will choose another, more
profitable, course of action.

The Gullahorns have compared the relative usefulness
of the optimizing and satisficing decision making models.
They have devised a representation of each of these models
in their computer simulation.model of role conflict

6George G. Romans. WW
222%3 (New York: Harcourt, Brace, and World, 1 ,
Pa 0

 

u~m~— _ ..- -..

resolution. They conclude that the computer simulation
model incorporating the satisficing decision.model more
nearly represents actual survey data concerning a decision
situation than does the computer simulation.model incorpor-
ating the optimizing decisionmodel.7 To this point, Simon
says, "However adaptive the behavior of organisms in
learning and choice situations, this adaptiveness falls
far short of the ideal of 'maximizing'. . . . Evidently,
organisms adapt well enough to ”satisfice'; they do not,
in general, ”Optimize.”8

As mentioned earlier, I would hypothesize that the form
of the reasoning process is dependent upon the importance of
the degigipn and the degree of the structuring of the
situation. In comparing the Optimizing and satisficing
models, I would say that the satisficing model would be more
applicable then.the Optimizing model to that rational decision
making characterized by less important decisions in less
structured situations; the Optimizingwmoddelwwoudld be more
flapplicable than the satisficing model to that rational
decision making characterized by more important decisions in
more structured situations. I would characterize the question-
naire that the Gullahorns dealt with as presenting a rational
decision making situation containing elements of both types.
All of the alternatives were specified, most of the expectations

 

7Gullahorn and Gullahorn, p. 16.

8am... A. Simon. W
(New York: John Wiley and Sons, 1 , p. 1.

of the individual and the consequences to him for each
alternative were indicated, but the decisions involved
could have been considered relatively unimportant to the
respondents since the decisions were hypothetical, not real-
life, decisions. WhQI-ngsmlwould ‘saywthant the“ satisficing
model; applies to the rational decision making situation of
log”; importance and low structuring and the optimizing model.
:aflpplies to therational decision making situation of high
importance and-high structuring ,‘ I wouch:ay that the gain-

loshsmmodel applies to rational decision mka of
low importance and high structuring:

.— .

This third decision model, the gain-loss model, is the
product of S. F. Camilleri. Camilleri postulates that for
two alternatives, A and B, the objective probabilities with
which each of the alternatives is chosen, denoted P01) and
P(B), are in the same ratio as the total gains from the
alternatives; that is

as = 9s

P B G B
where C(A) is the total gain to the person making the decision
from choosing alternative A, and 6(3) is the total gain to
the person from choosing the other alternative, alternative
8.9 mis model says that the higher the total gain to the
person of an alternativein relation to the total gain of
the other alternative, the higher will be the probability

that the person will choose that alternative.

 

9cm11ot1.

According to the Optimizing model, the person would
choose alternative A.with probability equal to l, i.e.,
with certainty, if the total gain from alternative A is
greater than the total gain from alternative B. The gain-
loss model differs from the satisficing model in that no
”threshold of acceptability" is hypothesized and no order
of consideration is hypothesized. Indeed, no order of con-
sideration would be logical in this situation. Unlike the
Homans situation where the person is faced with the decision
of whether to continue his present course of action or to
choose an alternative one, the Camilleri model applies to
the situation where the person is faced with a series of
independent decisions. Therefore the person has no reason
to tend to choose the same alternative each time; conse-
quently no one alternative would be expected to be considered
first.

As previously described, the gain-loss model of decision
making applies only to a two alternative situation. This
model can easily be extended to cover a multiple alternative
decision situation. For an n-alternative situation the
probability model would hypothesize the following relation-
ship between the probabilities of the person's choosing each
alternative and the total gain of each alternative to the

person.

{{l} = Pig; = {£3} = ... = Pin-l; = Pén;
G 1 G G . G n-l G n
This means that_the higher the total gain to the person of

an alternative in relation to the total gains of the other

10

alternatives, the higher will be the probability that the
person will choose that alternative. in Fastinger's termin-
ology, the higher an alternative is on a person's final
preference order, the higher will be the probability with
which he chooses that alternative.

In presenting the three models of decision making, I
have said that alternatives are compared on the basis of
their profit or total gain to the person. That is, the
individual in a rational decision.meking situation examines
an alternative to see what would be expected of him and
also what he could expect the consequences to himself to
be if he were to choose that alternative. The individual:
combines all these considerations figmehow into a single
indicator, profit or total gain, which is the value of that
alternative to him. These concepts of profit, as used by
the Gullahorns, and total gain, as used by Camilleri, are
not-equivalent.

According to Festinger an alternative may have favorable
characteristics and unfavorable characteristics. Festinger
says that when a person chooses between two alternatives,

A and B, the set of all the favorable characteristics of
alternative A.and of all the unfavorable characteristics

of alternative-B steer the person in the direction of
choosing alternative Am Similarly, the set of all the
favorable characteristics of alternative B and ofall the
unfavorable characteristics of alternative A steer the person

in the direction of choosing alternative B. The person is

11

pushed in two Opposite directions at once and is said to be

———_____~

in a state of conflict.10 Conflict isnot to be confused
';E£h dissonance; there is no dissonance in the pre-decision
process and therefore the person experiences no pressure to
reduce dissonance.

These ideas of Festinger's have been formalized by
Camilleri. Camilleri calls the favorable characteristics
of an alternative (as seen by the individual) the gains to
be expected from that alternative, and the unfavorable
characteristics of the alternative (as seen by the individual)
the losses to be expected from that alternative. Each gain
or loss (reward or punishment, having positive or negative
utility) may be subjectively certain or probabilistic.
Camilleri represents each gain or loss by a component which
is a positive or negative real number. If the gain or loss
is probabilistic, then the component representing it is the
numerical product of two quantities: the subjective prob-
ability that the gain or loss will be realized if that
alternative is chosen, and a positive or negative number
representing the gain or loss to the individual if that gain
or loss were certain and that alternative chosen. When the
gain or loss is subjectively certain, the component repre-
senting it is Just a positive or negative number representing
the gain or loss to the individual if that alternative were
chosen.11 .

1°Leon Festinser. AtJls5saLAuliausgflasfiilnsugagssa:
(Stanford: Stanford University Press, , p. .

IICamilleri.

 

12

Festinger's characteristics of an alternative are
represented by components which are positive or negative
numbers. Therefore the favorable characteristics of an
alternative are represented by a series of positive compon-
ents and the unfavorable characteristics by a series of
negative components. The favorableness or unfavorableness
of each characteristic determines the magnitude of the
component representing it. The set of all favorable char-
acteristics of an alternative is represented by the sum.of
the positive components of the alternative. likewise the
set of all unfavorable characteristics is represented by the
sum of the negative components. If we denote the sum of the
positive components of alternative A by A(+), the sum of the
negative components of A by A(-), the sum of the positive
components of alternative B by B(+), and the sum of the
negative components of alternative B by B(-), then the force
pushing the person toward alternative A is A(+) - B(~), and
the force pushing the person toward alternative B is B(+) -
A(-). Note that A(+) and B(+) are positive numbers while
A(-) and B(-) are negative numbers.

Camilleri calls the force pushing the person toward
alternative A the total gain to the person by choosing
alternative A, and denotes it by

60;) = A<+)-B(-)
He refers to the force pushing the person toward alternative
B as the total gain to the person by choosing alternative B,
and denotes it by

6(8) =- B(+)-A(-)

13

As given earlier, the basic postulate of the gain-loss model
of decision making is that the probabilities with.which a
person chooses each of two alternatives, P(A) and P(B), are
in a ratio equal to the ratio of the total gains to that
person of each of the alternatives, G(A) and G(B). This is
represented by the following equation.

W'hfi
Since P(A) and P(B) are probabilities, and since A.and B are
the only alternatives, it follows that P(A) + P(B) = l. The

following are the unique solutions to the two equations given

P(A)"GTE§AL('TA+GB' +-s- +B+-A-
3 a +- -
P(B) fiA-l-GQUB- A-+-B- +B+-A-

For three alternatives, the basic equation is

§8=€éfi=éfi

Since P(A), P(B), and 2(0) are probabilities and since A, B,

above.

and C are the only three alternatives, it follows that P(A)
+ P(B) + P(C) a l. The following are the unique equations
for the probability of each of the alternatives in a three-

alternative situation.

1"“ ‘ Where

a G
P(B) G<A)+G(B)+G(c)

= 9&0;
P(C) G A +0 B +G C

14

While the gain-loss model of decision making uses the
concept of total gain, which obviously is based on the ideas
of Festinger, the Optimizing and satisficing models use the
concept of profit which comes from Romans. Festinger states
that an alternative may have favorable characteristics and
it may have unfavorable characteristics. Thismeans that a
person contemplating a certain course of action expects that
that course of action will have desirable consequences as
well as undesirable consequences.

Humans deals with social interaction. mis means that
the alternatives of the person's that Romans deals with are
whether the person will engage in or terminate social inter-
action with this person, whether the person will engage in
or terminate social interaction with that person, and so
forth. Therefore the desirable and undesirable consequences
the person will expect from a contemplated course of social
interaction are the rewards and punishments that he expects
from the person with whom he is contemplating that particular
course of social interaction. Although Homans discusses the
situation where the other person emits puniMs to the
person, he does not incorporatmewthis situation inthg prOpo-
sitions of his theory of social interaction: l"ln the exchange
of hostilities only one side can win; the other runs away,
and it takes two to make social behavior.”2 For this reason
Romans does not incorporate the emission of punishments in

his theory of social interaction.

 

”Romans, p. 57.

15

Furthermore, the effect of a punishment is not as
predictable as the effect of a reward. The truth of Romans'
second preposition seems quite obvious: "The more often
within a given period of time a man's activity rewards the
activity of another, the more often the other will emit the
activity.”13 The consequences of punishment are not so
obvious. A person punished may withdraw from social inter-
action with the person emiting the punishment. If he remains
in social interaction, he may in turn try to punish.the other.
The frequency of that activity for which the person'was
punished.may increase or it may decrease. If it decreases,
there is no way of knowing what alternative activity, if any,
will take its place. To complicate matters even more,
people don't always seek to avoid punishment; through civil
disobedience a person.may actively seek punishment in order
to protest something he considers unjust.

If Homans' ideas are put in terms of Camilleri's
formalization, then it can be seen that Homans deals exclu-
sively with A(+) and B(+), the favorable characteristics,
desirable consequences, or rewards of A and B, the two
alternatives or courses of social interaction. He does not
use A(-) and B(-), the unfavorable characteristics, undesirable
consequences, or punishments of A and B, the two alternatives

or courses of social interaction.

 

131mm, p. 54.

16

Homans, however, does deal with punishment in the form
of cost. No matter which of mutually exclusive alternatives

a person chooses, he'willflnot receive the rewards from the

 

gfifigrgatives not chosen. These rewards that the person does
not receive are a punishment to him; but they are not the
result REWPP9$EQE§Et by any other person. The cost “of a
unit of a given activity is the value of the reward obtainable
through a unit of an alternative activity, forgone in emitting

the given one.”14

Egggit is defined as "the difference

between the value of the reward a man get by emitting a
particular unit-activity and the value of the reward obtain-
able by another unit-activity, forgone in emitting the first,"15
i.e., Profit = Reward - Cost. Again in terms of Camilleri's
formalization, the profit of alternative A, Profit (A), is
defined as:

Profit(A)

A(+) - B(+)
Similarly,

Profit(B) B(+) - A(+)
This is the profit used in the Optimizing and the satisficing
models of decision making to represent the value of an alter-
native to the person making the decision.

It is obvious that the profit used in the optimizing
and the satisficing models is not equivalent in definition

to the total gain.used in the gain-loss model of decision

 

“nun p. 60.
15m" p. 63-

17

making even though these two concepts are analagous. in
function, i.e., in their use as indicators of the value of

a course of action to the person contemplating that course
of action. Whether profit or total gain can better be used
to explain decision making behavior is an empirical question.
Each concept in its own model might predict equally well.

The gain-loss model of rational decision making has
been tested only minimally. In his paper, Camilleri applied
the gain-loss model to a two-person, game type, laboratory
situation where the participants were asked to make a
decision between two alternatives under varying conditional6
I will not discuss the experiment in detail, but will mention
just that the decision making situation was highly structured,
but the importance of the decisions to the participants was
probably low. According to the principles enunciated earlier,
the gain- loss model would be applicable to this rational
decision making situation. Although the number of subjects
in the experiment was small (six under one condition and
seven under another condition of the experiment), the results
were impressive. In order to further test the gain-loss
model of rational decision making, I will now apply it to

questionnaire data obtained from 148 respondents.

 

In a field study of social tensions in labor union
relationships, John T. Gullahorn gathered, among other

information, questionnaire data concerning a union

 

“Camilleri.

l8

stewardship 2;. employees' club office dilemma (see Table 1).17
Each of the respondents, 148 members and officers of a local
union, was presented the following hypothetical situation:
Assume you are an officer of the Employees' Club, which
is largely supported by the company. You believe strongly
in the union and attend meetings regularly. Your fellow
workers have chosen you to be their Chief Steward, and

you wonder whether you should resign from the club
office so you can devote your time to the job of Chief

Steward. 132 gm aven't gig 3:3 Q 2953 122; 221.1-

You feel responsible for the continued success of a

program which.you have started for the club, and at the

gtgsaifimiayou feel obligated to do a good job as Chief
In each of eight situations the respondent was asked to choose
one of three alternative courses of action.

Alternative Auwas to resign from club office.

Alternative B was to resign from.position of chief
steward.

Alternative C was to retain both positions.
In each of the eight situations the respondent was told that
each of three reference group preferred either that he retain
the club office or that he retain the position of chief
steward. Notice that the alternatives were phrased neg-
atively, i.e., which job, if any, to Eggign,‘While the
reference group pressures were phrased positively, i.e,,
which job to ggtgin. Therefore, reference group pressure

is either to not choose alternative A or to not choose

alternative B. For example in situation (1), all reference

 

“John 1'. Gullahorn, "Measuring Role Conflict,"
W52. 61 (January. 1956). pp- 299-303-

18Gullahorn and Gullahorn, p. 6.

19

Table 1. Union Stewardship v . Employees' Club Office Dilema:
Frequency D stribution of Responses

 

 

Asstme you are an officer of the Employees' Club, which is
largely supported by the company. You believe strongly in
the union and attend meetings regularly. Your fellow workers
have chosen.you to be their Chief Steward, and you‘wonder
whether you should resign from the club office so you can
devote your time to the job of Chief Steward. I23H£g§%11
gaven't time gg‘gg both jobg ggll. You feel responsib e

or the continued success 0 a program which you have started
for the club, and at the same time you feel obligated to do
a good job as Chief Steward.

 

I would be most likely to

In each of the following do the following

situations, please cheek

 

 

the appropriate space to Resign Retain Resign from
indicate the action you from.club both ‘ position of
would be most likely to office positions Chief Steward
take. (A) (B) (3)

W

W

MW

W

ent osition
5:2: if--

1. Both the union Exec-

'utiue Committee and the -

peeple you represent as 28 65 55
Chief Steward want you to

keep the club office.

2. The executive committee

wants you to keep the club

office--the pe0ple you 53 53 32
represent want you to ser-

ve as steward.

3. The executive committee

wants you to serve as

steward--the peeple you 43 57 43
represent want you to»keep

the club office.

4. Both the executive comp

mittee and the pe0ple you

represent want you to 90 35 22
serve as steward.

Table 1. Continued

20

 

 

I would be most likely to

do the following

 

Resign
from club
office

(A)

Retain
both

Resign from
position of
positions Chief Steward

 

You:r:2tk.ss.§hisf
fitgwggg will give 292

e to

fsxsssbl2_sbszies

h fo e a ement

will the club offigg.
What if--

5. Both the executive comp
mitten and the people you
represent want you to keep
the club office.

6. The executive committee
wants you to keep the club
office-~the pe0ple you
represent want you to ser-
ve as steward.

7. The executive committee
wants you to serve as
steward--the peOple you
represent want you to keep
the club office.

8. Both the executive comp
mittee and the people you
represent want you to
serve as steward.

45

81

57

105

(c) (B)
59 44
48 19
53 33
32 11

 

N=l

group pressure is for the respondent not to choose alternative
A. The eight different situations were the 23 or eight combin-
ations of the three binary reference group pressures.

Reference group X was the management.

Reference group Y was the union executive committee.

21

Reference group Z was the persons represented, i.e. ,

the persons the respondent represented in his
hypothetical position as chief steward.

Each of the eight hypothetical situations presented by
the questionnaire is highly structured and the decisions
asked for are probably not too important to the respondents
since the situations are hypothetical and not real-life p
situations. According to the criteria mentioned earlier,
the gain-loss decision model would be applicable to these
rational decision making situations.

Before dealing with all three alternatives, I'will first
apply the gain-loss model of rational decision making to two
of the alternatives, A and B. There are two reasons for
doing this. If a simple situation is dealt with first, it
should be easier for the reader to understand how the gain-
loss model is applied to a decision making situation. Also,
alternative C presents certain problems which should be faced
only after fully understanding the gain-loss model. Therefore,
for those respondents who chose either alternative A or B for
a particular situation, I will apply the gain-loss model to
explain their choosing between alternatives A and B. In this
first application of the model, no attempt will be made to
explain why the respondents chose A or B over alternative C,
but rather why they chose A instead of B or B instead of A.
Before doing this, it must first be shown that it is mathemat-
ically correct to apply the gain-loss model to two alternatives
of a three alternative rational decision making situation.

22

In considering only two (A and B) of the three alter-
natives (A, B, and C) we are looking only at those respondents
who choose either A or B. Thus any probability statement
about the choice of A.or the choice of B would be a con-
ditional probability statement. we are interested in the
conditional probabilities, P(A, A.or B) and P(B, A or B),
i.e., the probability that A‘will be chosen or that B will
be chosen given that either A or B was chosen. These con-

ditional probabilities are evaluated as follows.

P(A’A°”B)=WPAoz-B“ “(flax-LTPA
31““ P(A)=GA+GB +GC

and P(A or B) =P(A) +P(B) =GA 4.6:; +BG

then P(A, A or B) = P

g B
Similarly, P(B, A or B) G A + G B

Thus, the conditional probabilities, in regard to the total

 

gains, for two alternatives in a three alternative situation
are the same as the absolute probabilities for the two alter-
natives in a two alternative situation.

Although there is no difference in the probability
equations in regard to the total gains, there is a difference
in the definition of the total gains. According to the gain-
loss.model, the total gain that a person would expect to
receive by choosing a particular alternative is, in Festinger's

terminology, the sum.of the favorable characteristics of the

23

alternative chosen and the unfavorable characteristics of
the alternatives rejected. Thus for the three alternative
situation, A(+), B(+), and C(+) are each the sum of the
components representing the favorable characteristics of
alternatives A, B, and C, respectively; and A(-), B(-), and
C(-) are each the sum.of the components representing the
unfavorable characteristics of alternatives A, B, and C,
respectively, and are negative quantities. Then C(A), 6(3),
and C(C), the expected total gains from alternatives A, B,
and C, respectively, are given by the following equations.

G(A) = A(+)-B(-)-C(-)

5(3) = B(*)-A(-)-C(-)

6(6) = C(+)-A(-)-B(-)

The conditional probabilities are

$-8-
pcA.aorB>=rra'—‘+s‘:§=-xt+-—Hmn

= B+-A--
P(B, A.or B) A * + B + _ A _ -

I310
II

(110
ll

Therefore in dealing‘with.only two alternatives of a three
alternative situation, the only components of the third
alternative that are involved are its negative components,
i.e., C(-). The components making up A(+), B(+). A(-).
B(-), and C(-) must be specified for each of the eight
decision: posed by the Gullahorn questionnaire. Before
doing this, the characteristics of the components must be
elaborated on.

The gain-loss model postulates that the ratio of the
probabilities with which each alternative is chosen is equal

to the ratio of the total gains of those alternatives.

24

Mathematically, this means that the hypothesized components
lie on a ratio scale with an unspecified unit, i.e., only

the ratio of each component with the other components enters
into the equations. The numerical value used for each com-
ponent is meaningless; only the ratio of the numerical values
used has meaning in the gain-loss model.

Assuming a situation to be characterized by a rational
decision making process means that the hypothesized component
structure applies to all those making decisions in the situa-
tion. However, this does not imply that the ratios of the
components are the same for each decision maker in the
situation; they may be unique for each person. In order to
apply the gain-loss model to data from.a number of different
individuals, as in the Gullahorn questionnaire data, where
only the frequency distribution of choices is known. we
must assume that the ratios of the components are the same
for all respondents. Note that without this assumption, the‘
gain-loss model cannot be applied to collective data.

Furthermore, it is assumed that the eight decisions
asked for in the Gullahorn questionnaire are independent of
one another. Of course, two decisions may be considered not
independent insofar as the decisions are similar; What is
assumed, therefore, is that the act of a person choosing one
alternative does not affect the alternative he chooses in
his next decision. NOnetheless, we still assume that the
reasoning process used by the individual is the same for all

eight situations. Indeed, we assume that the ratios of the

25

components involved in the decisions remain the same for all
eight situations.

It is hypothesized that the component structure, i.e.,
the components representing the desirable and undesirable
characteristics of alternatives A and B, for each of the
eight situations, are as given in Table 2. These components
are defined in Table 3. Since I am assuming that the question-
naire presents eight rational decision making situations, i.e.,
all respondents use the same reasoning process, my hypothesized
component structure applies for all respondents. It should
be noted that the five components a, b, x, y, and 2 used to
represent alternatives A and B are all gains, i.e., I assume
that in the hypothetical situation presented in the question-
naire a person would not expect either alternative A.or B to
result in undesirable consequences in any of the eight sit-
uations. Therefore for all eight situations,

M4=Bo>=o
and A(+) and B(+) are the sums of the respective hypothesized
components of alternatives A and 8 given in Table 2.

As indicated in Table 2, l hypothesize that for alter-
native C the undesirable consequences, i.e., C(-), are'the
same for all eight alternatives and are represented by the
negative component -d. Therefore since A(-) = B(-) a O and
C(-) = -d, the equations for the total gains of alternatives
‘A and B can be reduced to the following:

so) = A(+) - B(-) - 00") = A(+) +d
6(3) = B(+) - A(-) - c(-) = 3(+) +d

26

n canes see one .ee>auecueua<_vne eureka euneueuem mo ecoauacauee new use» eem

.uusocooaoo no enoauasauev new

«0902

.eueueaeueo ecu evesauee on use: ones_eao«uosude noon emery;

 

 

 

 

can u. n ‘ m.o u+a¥u¥¢ m.oo one any
om e- u+n n.0m asses «.mo «me have
can u. syn o.u~ u+u¥c o.em n<m Aev
am e- u+a¥n «.me as. e.on <<m any;
«an e- x¥n e.oe u+avu e.om mn< nee
as e- u+x¥n e.~m new n.ee <n< “nee
me e- ayusn e.nn u+u n.eo m<< have
no u. u+a¥u¥n n.oe u e.nn <44 “do
n no <_uo Auvo no musesodaoo unsouem nudesodaoo uneunem nax roguesudm
museaoenh usesooaou vaudeenuoohm nebueeno venueenuonhm ve>ueeoc ”ozone
rename eucououom
unuoaax nan-eugsmum guano cannon avenge page cannon an eouoofiom
n < O>du§ud<
no>auucuoue<

 

 

 

 

 

 

eebauenueua< 938

«eaoduenuam

unwau ecu you eucecooaoo use .eoweuceouem .eosoueueum ozone eocoueuem

.N oases

 

.......

27

Table 3. Hypothesized Components and Their Definitions

 

 

the gain expected by the individual from retaining the
position of chief steward (he believes strongly in
the union, attends meetings regularly, and was
elected chief steward his fellow workers and
feels obligated to them .

6
II

the gain expected by the individual from retaining the
club office (he feels responsible for the continued
success of a program which he started for the club).

-d a the loss to self and the negative sanction from.the
three reference groups expected by the individual
for not being able to do both jobs well if he retains
both positions (he hasn't time to do both jobs well).

x a the gain expected by the individual from.retaining the
position preferred by the management (reference
group X).

y = the gain expected by the individual from retaining the
position preferred by the union executive committee
(reference group Y).

the gain expected by the individual from retaining the
position preferred by the peoPle he represents
(reference group Z).

 

j

Thus the total gain for alternative A for each situation is
the sum.of the hypothesized components of alternative A for
that situation (as given in Table 2) plus d. Likewise the
total gain for alternative B for each situation is the son
of the hypothesized components of alternative B for that
situation (as given in Table 2) plus d. For example, the
total gain to the person choosing alternative B in situation
(1) where all three reference groups do not reject alter-
native B is
G(B, 1) . b+dtxfy+z
The equations expressing the conditional probabilities

for alternatives A and B are as follows.
9

 

III | [I]! III l‘ I ii 4' ll‘I-[l ll‘ 1' III! III. ‘I [I l l

28

a +
P(A, A or B) A + 1+3 + Ii
- B +

Notice that the denominators of the conditional probability
equations are the same for all eight situations, x;2.,

A(+) +B(+) = a+d+b+d+x+y+z
and the numberators are the entries in Table 2 plus d. There-
fore the sum.of all the components of a particular alternative
in a particular situation (as given in Table 2) plus d div-
ided by a+d+b+dixfy+z is the probability predicted by the
gain-loss model of that alternative's being chosen in that
situation. For example, the predicted conditional probability
with which a person will choose alternative B in situation
(1) where all three reference groups do not reject alternative

B is

P(B,1,Aors)=m

Since there are two conditional probability equations
for each situation, one for alternative A and one for alter-
native B, and there are eight situations, we now have l6
equations, each utilizing the six components a, b, d, x, y,
and 2, which specify, according to the gain-loss model of
rational decision making, for each of the eight situations,
the predicted conditional probability'with‘which a person
who did not choose alternative C will choose alternative A
or alternative B. Note that for all 16 equations a never

occurs without d and similarly b never occurs without d.

29

Therefore, it is mathematically impossible in these eight
situations to arrive at the numerical values of the ratios
for all three components a, b, and d. These components will
have to be dealt with as only two parameters, a-I-d and b+d,
even though they are three separate components. All we need
now are the numerical values of the ratios of the five
parameters, a-I-d, b-t-d, x, y, and 2. Since the values of the
ratios of these parameters are not based on theoretical con-
siderations, the only possible source of estimates of these
ratios is empirical data. It would be possible to administer
questionnaires to a sample from the same papulation that
Gullahorn's respondents were sampled from, m. , members and
officers of local unions. These data then could be used to
estimate the ratios of the parameters. However, this infor-
mation is more readily available in the results of Gullahorn's
questionnaire survey dealt with here.

The probability equations predicted by the gain- loss
model of decision making specify a relationship between the
ratios of the parameters and the probabilities with which
an alternative will be chosen. Obviously, if the mmerical
values of the ratios of the parameters are known, the equa-
tions can be solved for the mmerical values of the prob-
abilities. Similarly, but not so obviously, if the numerical
values of probabilities are known, the equations can be solved
for the numerical values of the ratios of the parameters.

We can use a set of the 16 probability equations with their
accompanying observed frequencies to get the values of the

I’lllillllil .l n A

30

five parameters and then use these parameters in the remain-
ing probability equations to derive a set of predicted prob-
abilities which can be compared with the observed frequencies
as a test of the gain-loss:model of decision making.

Table 1 presents the frequencies with.which each alter-
native in each situation was chosen by the 148 respondents.19
Since the gain-loss model deals in probabilities and not
frequencies and since in this application of the model‘we
are using only two of the three alternatives, 1 will use the
conditional percentages given in Table 2. These conditional
percentages are, for each of the eight situations, the per-
centage of subjects responding with alternative A.and the
percentage of the subjects responding with alternative B
based on the total number of subjects responding with either
alternative A.or alternative B.

It is a mathematical theorem that in order to solve a
set of equations for the numberical values of the ratios of
n unknowns we need a set of n-l linearly independent equa-
tions; for five unknowns we need four linearly independent
equations. We have 16 equations, but they are not all
linearly independent, since P(A) = l-P(B); i.e., if we know
P(A), we can find P(B). Therefore we are left with only
eight different equations, one for each situation. This
means that we can test the predicted probabilities in four

of the situations.

 

l-9Gullahorn, p. 303.

31

Our problem is which four of the eight situations to
use to estimate the parameters since there are many such
sets of four which we could use. Although there are eight
different equations, there are at most only four of these
that are consistent, because the model does not fit the
data exactly. If it did, we would have at most four linearly
independent equations and all of these would be consistent.

There are many criteria which could be used to select
the four situations whose four linearly independent and
consistent equations can be used to estimate the values of
the ratios of the five parameters. The criterion that will
be used here will be that of choosing those situations where
the frequencies for alternatives A and B are most equal,
i.e. , where the conditional percentages in Table 2 are
closest to 50%. This criterion will be used to avoid what
has been called the ceiling effect. those situations which
do not result in a large number of choices of alternative A
or alternative B will be used to estimate the parameters.
Thus, in effect, information from the middle ranges will be
used to predict the more extreme points. It can be seen
that these situations are, in order, (5), (3), (7), and (l)
and (2), the latter two being equally close to 50%. Since
the conditional probability equation for (l) is not consis-
tent with those for (3), (5), and (7), the equation for
(2) will be used. Thus situations (2), (3), (5), and (7)
will be used to estimate the parameters, which will then be

32

used to predict percentages for the four other situations,
(1), (4), (6), and (8).

Since it is easier to deal with the parameters if they
are given numerical. values rather than if their ratios are,
I will arbitrarily determine a unit for their ratio scale
by letting

a+d+b+d+xfy+z = 100
Since this is the denominator of the fraction side of all
the probability equations, the numerators of the fraction
side of the probability equations (the sum of the hypothesized
components given in Table 2 for a particular alternative of
a situation plus d) equal the observed percentages (the
fraction.choosing an alternative times 100). For example,

for situation (2), alternative A, the model predicts that

.___£:2£i___.
P(A’ 2’ A °r B) .____ a+d+b+d+x+y+z

Since we let the denominator equal 100, this equation becomes
100 ' P(A, 2, A or B) = a+d+z
This equation illustrates a point that I made earlier. The
equations predicted by the gain-loss model of rational
decision making can be used in either of two ways: to
predict probabilities or to estimate (predict the values of)
parameters. If we already had an estimate of a+d+z, where
we assume that a+d+b+d+xfy+z = 100, we could predict
P(A, 2, A or B). If we already had the observed percent-
ages we could use them to get the value of 100 ‘ P(A, 2, A
or B) and therefore an estimate of a+d+z, where we assume

that a+d+b+d+xty+z = 100. I will use this equation from

33

situation (2) to estimate the parameters. Note that 100
times P(A, 2, A or B) is the percentage of the times that
alternative A is chosen in situation (2). Therefore using
Table 2 we get the prediction that
100 - P(A, 2, A or B) = 66.3 = a+d+z
and we have the following estimate of the sum of two of our
parameters a+d and z.
a+d+z = 66.3
By using the probability equations for alternative A
in situations (2), (3), (5), and (7) and by using the obser-
ved percentages given in Table 2 and by setting the denominator
equal to 100 in order to fix the unit of the ratios of the
parameters, we have the following five equations.
100 ' P(A, 2, A or B) = 66.3 = a+d+z
100 ° P(A, 3, A or B) = 47.3 = a+dfy
100 ° P(A, 5, A or B) = 50.6 = a+d+x

100 ’ P(A, 7, A or B) 63.3 = a+dtxfy
a+d+b+d+xfy+z = 100
Solving these equations, we obtain the following estimates

of the five parameters.

a+d = 34.6
b+d = 5.0
x = 16.0
y = 12.7
= 31.7

We should remember that these numerical values of the
five parameters are based on an arbitrary and meaningless

unit and therefore the numerical values of the parameters

34

are meaningless and are not unique, e.g., the set of

numbers (69.2, 10.0, 32.0, 25.4, 63.4) could be used.

Only the ratios of the values for the five parameters are
unique and have meaning. For example, the following four
ratios have meaning and their mimerical values are uniquely

determined by the four probability equations used.

£31 =
b+d 6.92
2111: .31
x
é = 1.26
y
I. = .40
2

To simplify computations, the denominator will be set equal
to 100 and the numerical values for the five parameters
given previously will be used. 'Now that we have numerical
values for the five parameters, we can predict the condi-
tional percentages with which each alternative is chosen

in the four remaining situations, xi;., (1), (4), (6), and
(8). Making use of the fact that the predicted percentages,
Bred%, of an alternative equals 100 times the predicted
probability, we obtain the following predictions for sit-
uations (l), (4), (6), and (8) respectively.

Pred%(A, 1, A or a; = 1000?“, 1, A or B) = a+d = 34.6
Pred%(B, l, A or B = 100'B(B, l, A or B) = b+dixfy+z = 65.4
Pred%(A, 4, A.or B) = 100°P(A, 4, A or B) = a+dfy+z = 79.0
Pred%(B, 4, A or B) = 100'P(B, 4, A or B) = b+d£x = 21.0
Pred%(A, 6, A or B; = lOO'P(A, 6, A or B; = a+d+x+z = 82.3
Pred%(B, 6, A.or B = 100-P(B, 6, A or B = b+dfy = 17.7

35

Pred%(A, 8, A or B;

100‘P(A, 8, A or B; = a+d+xfy+z = 95.0
Pred%(B, 8, A or B

1oo-P(B, 8, A or B = b+d ; 5.0

These predicted conditional percentages along with the obser-
ved percentages (from.Tab1e 2) are repeated in Table 4 for

purposes of comparison.

 

Table 4. Predicted and Observed Percentages Compared: Two
Alternatives

 

 

Alternative:

 

 

A B
Predicted Observed Predicted Observed Differ-
Situation Percent Percent Percent Percent ence
(1) 34.6 33.7 65.4 66.3 .9
(4) 79.0 80.4 21.0 19.6 1.4
(6) 82.3 81.0 17.7 19.0 1.3
(8) 1 95.0 90.5 5.0 9.5 4.5

 

 

 

 

It should be noted that since
Pred%(A, A or B) = lOO-Pred%(B, A or B)

only four predictions are made (one for each situation) and
not eight (as it might appear). For this same reason, the
differences between observed and predicted percentages are
of the same magnitude for both alternatives for each of the
four situations. These differences are given in Table 4.

It appears from the size of the differences that the
four predictions are indeed quite accurate; they range from
.9 to 4.5 with a mean of 2.0 percentage points. Since the

distribution of the observed conditional percentages for

36

each alternative of each situation is not known and since
there is no basis for assuming that it is any particular
distribution, no statistical test of the significance of
the differences between the predicted and the observed
percentages will be performed. In lieu of a statistical
test of significance, I conclude that the predictions
look very good.

In arriving at these predictions, situations (2), (3),
(5), and (7) were used to estimate the parameters. These
situations were selected on the basis of the criterion of
using those situations where the frequencies of alternatives
A and B were most equal. Other criteria could be used. As
a result, different situations might be used to estimate the
parameters and also a different accuracy of prediction might
be obtained. For example, the criterion of selecting those
situations where the largest number of respondents chose
either Alternative A or alternative B could have been used.
As can be seen from Table 2, using this criterion would
result in selecting situations (3), (4), (6), and (8) to
predict for situations (1), (2), (5), and (7). The con-
ditional probability equation for situation (2) is not con-
sistent with those of situations (4), (6), and (8). Therefore,
situation (3) would be used, since it is the next situation
specified by the criterion. Using this criterion would result
in differences between predicted and observed percentages of
4.1, 4.6, 2.7 and 5.9 for situations (1), (2), (5), and (7),

respectively. The average of these differences is 4.3

37

percentage points. Although the predictions obtained by
using the second criterion are not as accurate as those .
obtained by using the first criterion, they are still quite
good.

There are probably other criteria that could be used
and certainly many other sets of four situations (54 to be
exact) that have consistent conditional probability equa-
tions. The accuracy of the predictions based on these 54
other sets of situations will not be determined. However,
it should be reported that situations (1), (4), (6), and
(8) give errors for situations (2), (3), (5), and (7) of
4.6, 4.1, 6.8, and 10.1, respectively, with a mean differ-
ence of 6.4 percentage points. Although these predictions
are still less accurate than those obtained by using the
first criterion, they are still good. It appears to me that
the predictions resulting from this last set of criterion
are less accurate than those resulting from any of the other
possible sets of situations.

I conclude from these results that, using the component
structure hypothesized, the gain- loss model of rational
decision making adequately explains the Gullahorn question.
naire data for two of the three alternatives.

2w ._t '3 ~ r; .2." val.
'- ;;j_‘.fi—1L€ s .

We now turn to the problems posed by alternative 0 and
and also of applying the gain-loss model to all three alter-
natives, i.e., predicting for each person making a decision

l|||.|l.|| ‘
tl II.

 

1"“ :
'I‘l‘llllull‘
AI‘I‘IIIIII'I
‘Ill

38

in one of the situations of the Gullahorn questionnaire
whether he will choose alternative A.or alternative B or
alternative 0.

In all eight situations the respondent is told that each
of the three reference groups prefers that he retain either
the club office or the position of chief steward, but never
that it prefers both.20 For example, the respondent is not
told that reference group x.prefers alternative A, but that
it does not prefer (i.e., rejects) alternative B; therefore,
we would infer that reference group X prefers either alter-
native A.or O. This means that in genera1.whether a refer-
ence group rejects alternative A or rejects alternative B
doesn't matter with regard to alternative 0; it always prefers
alternative C (along with another alternative).

It is hypothesized that the gain expected by the indivb
idual from retaining both positions (alternative C) is not
the sum of the gain expected by the individual from retaining
the position of chief steward and the gain expected by the
individual from retaining the club office. It is hypoth-
esized that the gain from retaining both positions is greater
than the sum of the gains from.retaining either position.

The additional gain to the individual comes from.having
avoided a conflict situation. He gains by retaining both
positions in not having to choose which position to resign.
Therefore we hypothesize that a seventh component is invol-
ved in the eight decisions asked for in the Gullahorn
questionnaire, gig,, component c as defined in Table 5.

 

20Gullahorn and Gullahorn, p. 6.

39

Table 5. Additional Hypothesized Components and Their
Definitions

 

 

D
II

the gain expected by the individual from not having to
choose which position to resign.

u = the gain expected by the individual from the management
(reference group x) for retaining both positions when
the management wants him to retain the club office.

v = the gain expected by the individual from the executive
committee (reference group Y) for retaining both
positions when the executive committee wants him to
retain the club office.

w = the gain expected by the individual from the people he
represents (reference group Z) for retaining both
positions when the peeple he represents want him to
retain the club office.

 

As with the parameters a+d and b+d, the components a, b, and
c cannot be mathematically separated. Therefore their sum,
a+b+c, will be dealt with as one parameter.

As mentioned above, we might logically assume that the
person would expect to receive a gain from a reference group
by choosing alternative 0 no matter which alternative the
reference group rejected, i.e., regardless of the situation.
For this reason we might hypothesize that the components
of alternative C would be the same for all eight situations,
mu

a+b+c+x+y+z
Since there are no negative components in either of the
other alternatives for each of the eight situations, the
following would be true for all eight situations.
6(0) = c(+) = a+b+cjx+y+z
The gain- loss model hypothesizes that the probability

4.0

with which alternative 0 would be chosen from among the

three alternatives A, B, and C is

“‘3’ ' Was

It was shown earlier that

G(A)+G(B) B a+d+b+d+x+y+z
for each of the eight situations. Therefore, for each of
the eight situations and according to the above hypoth-
esized component structure for alternative C, the prob-

ability equation for alternative C would be

a+d+b+dfl+y+z+e+bic+x+y+z

Thus the gain-loss model would predict that the probability
with which alternative C is chosen is the same for all
eight alternatives. By looking at the observed frequencies
with which alternative C was chosen in the Gullahorn survey
as given in Table 1, you can readily see that this prediction
is false. The frequencies range from 32 to 65 for 148
respondents.

There are three possible explanations for the failure
of the gain-loss model in this case; the gain-loss model is
not a true model of reality; or incorrect component struc-
tures were hypothesized due to a faulty analysis of the
situations; or the data were imprOperly interpreted.

In regard to the second possible explanation, the
Gullahorns point out the following.

In terms of Homans' theory we reasoned that in a situ-
ation involving cross-pressures from highly valued

41

reference groups, the personal cost of forgoing the

expected rewards from incumbancy in either position

might be so high as to preclude the respondent's

realizing a profit from favoring one role at the

expense of the other. In such a case we predicted

that the respondent would choose what we considered

a desperation alternative-~that is, he would retain

both positiins though aware that he could not do both

jobs well.
This would mean that alternative C should include an additional
positive component in those situations where there were cross-
pressures from.reference groups. Doing this, however, would
not account for the fact that the frequency of choosing alter-
native C was highest in situation (I) where there were no
cross-pressures at all.

Instead, I think the third explanation, that the data
were imprOperly interpreted, is the actual one. Looking
at the observed frequencies for alternatives B and C in
Table I, one notices that they are highly correlated. In
fact, the Spearman rank order correlation coefficient for
alternatives B and C over the eight situations is +.90. We
could interpret this to mean that alternatives B and C were
‘viewed by the respondents as having the same types of favor-
able characteristics. Although this is not a perfect explanp
ation, it is a reasonable one. If it is true, then the
failure of the model is due to causes other than the model.
The first explanation, that the gain-loss model is not a true
model of reality, is not necessary and the probabilistic

model of decision.making is not proved false.

 

2‘12L9p. P- 5-

42

One may well ask why would alternatives B and C be
viewed as equivalent sources of favorable characteristics.

I would hypothesize that since the re8pondents were union
members and officers, they would value being chief steward
‘much.more than.holding the company club office. When the
reference group pressure was to remain as chief steward,
they readily rejected the club office. When the reference
group pressure was to retain the club office, many respond-
ents, rather than give up the position as chief steward
elected to retain both positions.

But all is not rosy. Based on the total frequencies
with which either alternative B or C was chosen, a smaller
percentage (54%) chose to retain both positions (alternative
C) when all the reference group pressure was toward retaining
the club office (situation (1)) than the percentage (76%)'who
chose to retain both positions (alternative C) when all the
reference group pressure was toward retaining the position
of chief steward (situation (8)). These variations in
alternative C could be explained by noting that frequencies
for alternative C are less variable than those for alter-
native B. This would imply that alternative C is composed
of a relatively large constant component (a+b+c) plus compon-
ents analagous to those for alternative B for the situation.
Thus three additional components u, v, and w are hypothesized
as defined in Table 5. Using these components, the components
of alternative C for situation (I) are

a-I-b-I-c 'HJ'I'VW- d

43

and for situation (2) they are

a+b+c+u+v-d
and so forth. For the eight situations, the components of
alternative C are given in Table 6 which also repeats the
components of alternative A and alternative B from.Table 3.
When the model‘was applied to the two alternatives, all the
components for alternatives.A and B were positive, i.e.,
A(-) = B(-) a 0. This is also the case when.the model is
applied to all three alternatives. Therefore, the total
gain from alternative C is the sum of the components for that
alternative as given in Table 6. The numerator of the prob-
ability equation for alternative C for a particular situation
is the sum of the positive components for that alternative
of that situation as given in Table 6. The denominator is
the sum of all the total gains for all three alternatives
of that situation. For example, the probability equation of
alternative C of situation (I) is

+b+c
P(c’ 1) ' a+d+b+d+x+y+z+a+b+cm+v4w

and the probability equation of alternative C of situation
(2) is

”gnu-w
“0’ 2) ‘3 a+d+b+d+x+y+z+a+b+c+u+v

 

Notice that the denominator is not the same for all situations
as it was in the two-alternative case. The numerators of

the probability equations for alternatives A.and B are the
same as for the two alternative conditional probability equa-
tions. The denominator is the sum of the total gains for all

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45

three alternatives for that particular situation. For
example, the probability equations for alternatives A and
B of situation (I) are

P(A, l) =

 

 

m
a+d+b+d4x+y+z+a+b4c4u+v+w

 

W
P (3’ 1) ’ a+d+b+d+x4y4¢+a+b+c+uw+w

We now have 24 probability equations. Since
NC) = lam-2(a)
eight of the equations are not independent of the other 16
equations. But we do have 16 independent equations. We
also have nine parameters, a+d, b+d, a+b+c, x, y, z, u, v,
and w. If we use a set of eight independent equations of
four of the situations and their associated observed frequen-
cies and fix the unit of their ratio scale by specifying that
a+d+b+d+x+y+z a 100

we can then get non-unique estimates of the nine parameters.

Again we are faced with the problem of selecting the
situations whose probability equations will be used to estimate
the parameters. A criterion similar to the one used before
will be used here. These four situations where the frequency
of the least chosen alternative and the frequency of the most
chosen alternative are closest together will be used. In this.
way the extremes will be avoided in estimating the parameters.
The four situations meeting this criterion are situations
(2), (3), (5), and (7), the four used for this purpose before.
Using the probability equations for these situations, I
obtained the following estimates of the parameters.

46

a+d = 34.6 x = 16.0 u 5 0.0
b+d = 5.0 y a 12.7 'v = 1.9
a+b+c = 53.8 2 = 31.7 w = 10.7

Several points should be made about these nonpunique
estimates of the nine parameters. Since the same situations
were used here as earlier and the unit was fixed by the same
equation, the estimates of a+d, b+d, x, y, and z are the
same here as earlier. In solving the equations, the actual
value of u.that was obtained was -l.9, which is contrary to
the model and the hypothesized component structure since u
represents a gain. There are two explanations of this
unexpected negative quantity. First, the hypothesized comp
ponent structure does not adequately represent the favorable
and unfavorable characteristics of the three alternatives in
each situation. Perhaps the gain represented by c should be
a function of the reference group pressure instead of a
constant as it is now. The second explanation is that the
negative quantity results because the model does not fit the
data exactly. As mentioned earlier, different estimates are
obtained.when a different set of situations is used. Possibly
u is quite small and the looseness with.which the model fits
the data resulted in a negative component. This second
exaplanation is further supported by the fact that when
situations (4), (6), (7), and (8) are used to estimate the
parameters, u.has a small positive value. This second explan-
ation will be considered as true and u'will be set equal to

261:0.

47

Although the values of a, b, c, and d'were not obtained
(another situation would have to be used, thus reducing the
number of situations for which to predict the results of
the decisions), their ranges can be. It can be shown that a
is in the range (29.6 to 34.6), b is in the range (0.0 to 5.0),
c is in the range (14.2 to 24.2), and d is in the range (0.0
to 5.0). This would indicate that the individual expects to
receive much.more gain by retaining the chief stewardship and
resigning the club office than by retaining the club office
and resigning the chief stewardship. The expected loss from
not doing both jobs well is low. And the expected gain from
not having to choose which position to resign is large.

Using these estimates of the nine parameters, I derived
the predicted probabilities of each of the three alternatives
for situations (1), (4), (6), and (8). The predicted percen-
tages along with the observed percentages are reported in
Table 7.

The predictions given in Table 7 look quite good. The
differences between observed and predicted percentages range
from 1.3 to 13.4 percentage points with an average of 5.2
percentage points. Again, since the distribution of the
responses is unknown, no statistical tests will be performed
on the predicted and observed percentages. I conclude from
these results that the gain-loss model of rational decision
making adequately explains the data from the Gullahorn
questionnaire when applied to all three alternatives. Thus
further support is given to the validity of the gain-loss model

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49

as a model of rational decision making. If other situa-
tions were used to estimate the parameters, different pre-
diction accuracy would be obtained, e.g., using situations
(4), (6), (7), and (8) to estimate the parameters, the
errors in the predictions (to one significant figure) range
from O to 6 with an average of 3.3 percentage points.
However, no attempt was made to examine the other 54 sets of
four situations to get a range of the prediction accuracy

of the gain-loss model applied to the Gullahorn questionnaire.

922214121223
The predictions of the model would not have been.valid

if I had used the component structure of alternative 0 as
originally conceived. Only after including the components
u, v, and w did the model give valid results. Thus the gain-
loss model can.be heuristic in the finding of additional,
important components of an alternative. However, this can
be carried too far. If enough parameters are used almost
any mathematical model will “fit" any data. Care should be
taken that all parameters used have a sound theoretical
basis for their use.

It appears that the parameters used in the application
of the probabilistic model to this three-alternative case

have a relatively high degree of theoretical soundness.

It also appears that the gain-loss model itself has a rel-
atively high degree of validity when applied to these data
and possibly for a large class of decision making situations.
What does this all mean?

50

It means that there is a class of rational decision
making situations, as typified by those in the Gullahorn
questionnaire,'Which can be adequately explained by the gain-
loss model. And it means that the validity of the assumptions
of the gain-loss model is supported for this class of rational
decision.meking situations. The assumptions of the gain-loss
model are that the individual making a decision (1) analyzes
the favorable and unfavorable characteristics of each alter:
native, (2) treats a gain foregone as a loss and a loss
.avoided as a gain, and (3) chooses each alternative with a
probability preportional to its total gain (the sum of the
favorablelcharacteristics of the alternative and the unfavor-
able characteristics of the other alternatives). And the:
gain-loss model also assumes that (4) the ratios of the comp
ponents used to represent these favorable and unfavorable
characteristics are constant over very similar rational decision
{making situations. Thus, the validity of these four assumptions
is given support.

Several questions are raised by this analysis. What are
the characteristics of the class of rational decision making
situations for which the gain-loss model is applicable? Are
they characterized, as I have hypothesized, by a high degree
of structuring and a low degree of importance? Is rational
decision making ever a deterministic process? For different
individuals in the same decision making situation, is the
decision process ever probabilistic for some, but determin-

istic for others? And if so, what principles of individual

51

psychology and group dynamics lead to probabilistic and
deterministic decision making processes? Many decisions
are made by groups of people; can the probabilistic model
be extended to this situation? Further extension and
application of the probabilistic model might answer these
and other questions concerning the basic process underlying
all social organization and such of individual psychology,
decision making.

52

List of References

Camilleri, Santo F. A Model of Qegigign—Mgkigg in an
Exchange Situatiog. A Paper Presented at the Midwest

Sociological Association Meetings, Madison, Wisconsin,

Festinger, Leon. 0 0 Co n sso .
Stanford: Stanford University Press, 1 .

. C t c io d son c .. Stanford:
Stanford University Press, 1 .

Gullahorn, John T. "Measuring Role Conflict," éfl§59£§%
Journal of Sociolo , 61 (January, 1956), pp. - 3.

Gullahorn, John T. and Gullahorn, Jeanne E. 22322222
Simulation of Role Conflict Resolution, System.Develop-
ment Corporation Paper No. SP- 1. Santa Monica,
Cgééfornia: system Development Corporation, 9 November
1 .

Homans, George. Soc Be vio ° E em t Po 8.
New York: Harcourt, Brace and World, 1 1.

Simon, Herbert A. dmi at t e v o . New Yotk:
Macmillan Co., 1 .

. Med 8 of ° S c l o 1. New York:
John Wiley and Sons, 1 .

lull!
l

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73