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MANAGING A PROSECUTOR’S OFFICE DOMESTIC
VIOLENCE CASELOAD TO INCREASE ASSAILANT l
ACCOUNTABILITY: A SYSTEM DYNAMICS APPROACH

presented by

PETER SVEND HOVMAND

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MANAGING A PROSECUTOR’S OFFICE DOMESTIC VIOLENCE
CASELOAD TO INCREASE ASSAILANTIACCOUNTABILITY:
A SYSTEM DYNAMICS APPROACH

By

Peter Svend Hovmand

A DISSERTATION

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

DOCTOR OF PHILOSOPHY

School of Social Work

2003

ABSTRACT

MANAGING A PROSECUTOR’S OFFICE DOMESTIC VIOLENCE
CASELOAD TO INCREASE ASSAILANT ACCOUNTABILITY:
A SYSTEM DYNAMICS APPROACH

By

Peter Svend Hovmand

Domestic violence is a major social problem. Many communities have ad0pted a
coordinated approach to increasing victim safety and assailant accountability. Most
communities continue to rely on the criminal justice system as the primary means of
holding assailants accountable. Criminal justice system reforms such as mandatory
arrest policies have increased the number of arrests and increased the role of the
prosecutor’s office in holding assailants accountable for their actions. This research
considered the question of how the domestic violence caseload of a prosecutor’s office
was dynamically related to holding assailants accountable.

The research used a single case design of a prosecutor’s office from 1998 to
2001 with a system dynamics approach, which is a method that uses analysis of
computer models to understand the relationships between the structure and behavior
of complex systems in terms of nonlinear feedback 100ps. Data sources for the model
building included numerical time series and key informant interviews. A major
challenge for this study was the problem of modeling sparse time series associated
with small p0pulations. The problem was solved by evaluating the realism of the
models’ responses to a family of smoothed numerical time series. A series of models
were built and tested. The resulting baseline model was formulated mainly in terms

of caseflows, which included arrests, review of warrants, prosecution of cases, and

the allocation of prosecutor resources between review of warrants and prosecution
of cases.

The results found general support for the hypothesis that case dispositions are
affected by caseloads. The baseline model did a reasonable job of reproducing the
general trends, but it did not capture the dynamics of dismissals of repeat arrests.
Analysis of the baseline model showed that reductions in prosecutor resources to
domestic violence caused warrant reviews to be dominated by caseload pressures
as Opposed to case attributes. The baseline model also showed that if there were
sufficient resources for prosecuting domestic violence cases, then the prosecutor’s
office could handle large increases in new cases without affecting prosecution dy-
namics. Analysis of the feedback loops revealed that when caseloads were stable,
accountability and caseloads were both controlled by the allocation of resources to
reviewing warrants. Analysis of arrests led to the identification of a potential posi-
tive feedback loop from first time arrests of male assailants to subsequent arrest of
female victims. That is, arresting some types of assailants led to an increased risk
of victims being arrested as assailants learned police officers’ criteria for a domestic
assault and subsequently used that knowledge to get victims arrested. Separate anal-
yses and key informant interviews supported this finding. This would represent an
unintended consequence of mandatory arrest laws for domestic violence. Key infor-
mants suggested a time-critical counteracting feedback mechanism, namely, victim
interviews within a week of the arrest. Other findings included indications that the
prosecutor’s office resource allocation problem was dynamic, and that trials play a
significant role in determining the outcomes of all case dispositions." System dynam-
ics showed great potential for studying the prosecution of assailants and community

responses to domestic violence.

COpyright by
PETER SVEND HOVMAND
2003

ACKNOWLEDGMENTS

This dissertation was by no means an individual achievement. Many pe0ple
supported the effort in one or more ways. The faculty and staff of the Michigan
State University School of Social Work provided a unique environment for pur-
suing doctoral research on domestic violence using a system dynamics approach.
Diane Levande, my chair, enthusiastically supported the research and intellectual
excursions from beginning to end. She shared a passion for understanding and
confronting violence against women, systems thinking, and phiIOSOphy. Cynthia
J ackson-Elmoore brought a keen objectivity through her focused questions and
insights. Marilyn Frye helped me develop a more critical ear for the language,
metaphors, and politics that have shaped the philos0phy underlying this disserta-
tion. Ralph Levine provided numerous opportunities for learning the basics of sys-
tem dynamics in the classroom, gaining modeling experience on research projects,
and challenged me with more advanced concepts. Cris Sullivan helped me put on
the page what I had learned from working in the community.

Leslie Hagen provided early opportunities for me to see the potential of this
research. Cressida Heyes provided a. solid foundation in her political philosophy
seminar for thinking about power and posed early questions about the nature of
system dynamics for social science research. David Garvin introduced me to no-
tion of obfuscation, Mike Jackson showed me the practice of accountability, and
James Nelson helped me deve10p these ideas phiIOSOphically his Wittgenstein semi-
nar. David Lounsbury introduced me to Ralph Levine and system dynamics. Jack
Homer impressed upon me the importance of grounding reference modes in real
numerical time series. David Ford provided an invaluable Opportunity to learn how
to model resource allocation problems and answered my questions about feedback

loop dominance.

Lori Post, Chris Maxwell, and Ellen Hayes generously supported this work by
allowing me to use their data and provided access to 'key informants. This research
was partially supported through research on various grants by the Centers Disease
Control and Michigan Department of Community Health.

MSU Safe Place funded the majority of my doctoral studies through graduate
assistantships and kept me in touch with the immediate issues facing communities.
Holly Rosen has been an inspiration in her work as a community activist, leader in
the battered women’s movement, and social worker.

Stephen Jefferson, Bev Henrichsen, Peg Whalen, and Melissa White were amaz-
ing throughout the process. They read countless drafts and heard numerous pre-
sentations at the earliest and most confusing stages, as did my parents, Beverly and
Svend Hovmand, and brother, Lars Hovmand, who asked me questions along the
way that made the rest easy. Charlene Warner and Eyvind Hovrnand Warner were
always there. They felt the ups and downs, the twist and turns, as much as me.

None of this would have been possible, however, without the generosity of the
participants I interviewed and their dedication to help victims of domestic violence
and hold assailants accountable. They took time out of their hectic schedules, even

on a Friday evening, to talk about their experiences.

vi

Contents

1 Introduction 1
1.1 Research question ............................. 3
1.2 System dynamics ............................. 4
1.3 Overview .................................. 5

2 Review of research literature 7
2.1 Overview ......................... ‘ ......... 7
2.2 Domestic violence ............................. 8
2.3 Operational definition of accountability ................. 10
2.4 The criminal justice response ...................... 11

2.4.1 Police and deterrence effects from arrest ............ 14
2.4.2 Batterer intervention and treatment effects ........... 16
2.4.3 Prosecution ............................ 18
2.4.3.1 Charging decision .................... 19

2.4.3.2 Decision to prosecute .................. 21

2.4.3.3 Plea-bargaining decisions ............... 24

2.4.3.4 Effects of case disposition decision .......... 29

2.5 Discussion ................................. 30
2.5.1 Caseload pressure and caseload management .......... 31

vii

4

2.5.2 Structure of prosecutor decision making ............ 33

2.6 Conclusion .................. ' ............... 35
Methods - 36
3.1 Overview .................................. 36
3.2 Single case study design ......................... 37
3.3 Studying dynamic systems ........................ 37
3.4 System dynamics ............................. 39
3.5 Case selection ............................... 41
3.6 Violence against women database .................... 43
3.7 Estimating rates and times for state transitions ............ 45

3.7.1 Modeling state transitions .................... 47

3.7.2 S-language implementation of finite state machines ...... 48
3.8 Battering tactics .................... . ......... 48
3.9 Numerical time series ........................... 51

3.9.1 Illustration of sparse time series ................. 52

3.9.2 Conventional approaches to handling noisy data ........ 58

3.9.3 Solution to the sparse time series problem ........... 59

3.9.4 Rates and stocks numeric time series .............. 60
3.10 Building system dynamics models .................... 62
3.11 Key informant interviews ......................... 66
3.12 Conclusion ................................. 67
Results 68
4.1 Overview .................................. 68
4.2 Demographics ............................... 69
4.3 Case attributes .............................. 73

viii

4.4
4.5
4.6
4.7

4.8
4.9

Case dispositions ............................. 76

Time series statistics ........................... 79
Descriptive models ............................ 80
Baseline model .............................. 90
4.7.1 Arrest submodel ......................... 92
4.7.2 Warrant processing submodel .................. 97
4.7.3 Case processing submodel .................... 104
4.7.4 Allocation submodel ....................... 108
4.7.5 Behavior of baseline model .................... 112

4.7.5.1 Behavior of simulated time series ........... 113
4.7.6 Sensitivity analysis ........................ 115

4.7.6.1 Sensitivity to the number of new cases ........ 118

4.7.6.2 Hequency response ................... 119

4.7.6.3 Sensitivity to number of prosecutors I ......... 125

4.7.6.4 Sensitivity to smoothing parameter .......... 125
4.7.7 Dynamic behavior of feedback 100ps ............... 136

4.7.7.1 Dynamics of managing prosecution caseloads . 140

4.7.7.2 Dynamics of accountability .............. 145
4.7.8 Summary of baseline model ................... 149
First versus repeat offenses ........................ 149
Key informant interviews ......................... 157
4.9.1 Victim arrests ........................... 158
4.9.2 Batterer intervention programs ................. 159
4.9.3 Trends ............................... 159
4.9.4 Victim advocacy ......................... 159
4.9.5 Prosecution ............................ 160

4.9.6 Resource issues .......................... 161

4.9.7 Rural issues ...... ° ....... ' ............... 162

4.10 Revised model ............................... 162
4.11 Conclusion ................................. 166

5 Conclusion 171
5.1 Overview .................................. 171
5.2 Major findings and discussion ...................... 171
5.3 Limitations of study ........................... 175
5.3.1 Community racial / ethnic demographics ............. 175

5.3.2 Lack of replication ........................ 176

5.3.3 Sparse time series ......................... 176

5.3.4 Validity of identifying first time arrests ............. 178

5.3.5 Stakeholders ................... , ......... 178

5.4 Policy implications ............................ 179
5.5 Directions for future research ...................... 180
5.6 Conclusion ................................. 181
References 183

List of Tables

3.1

3.2
3.3
3.4
3.5
3.6

4.1

4.2

4.3

4.4
4.5

4.6
4.7

Distribution of Records by Year and Type of File in Violence Against

Women (VAW) Database ......................... 44
Variables in the Individual Data Matrix (I DM AT) .......... 46
Finite State Machine Example ...................... 49
Major Categories of Battering Tactics .................. 50
Times Used to Generate Caseload Statistics .............. 61
Entry and Exit Times for Caseload or Stock Variables ......... 61

Distribution of Sex by Suspects and Victims Across Subsets of Vio-
lence Against Women Database ..................... 71
Distribution of Race / Ethnicity by Suspects and Victims Across Sub-
sets of Violence Against Women Database ............... 72
Distribution of Age by Suspects and Victims Across Subsets of Vio-
lence Against Women Database ..................... 74
Arrest Charges Across Subsets of Violence Against Women Database 76
Type of Relationship Between Victim and Suspect Across Subsets of
Violence Against Women Database. ................... 77
Dispositions Across Subsets of Violence Against Women Database . . 77
Distribution of Reasons Given by Prosecutor for Denial or Dismissal

Across Subsets of Violence Against Women Database ......... 78

4.8 Distribution of Consequences from Prosecution Across Subsets of Vi-
olence Against Women Database ..... ‘ ............... 79
4.9 Distribution of Counseling Referrals Across Subsets of Violence Against

Women Database ............................. 79
4.10 Statistics for Raw Time Series of Rate Variables ............ 80
4.11 Statistics for Raw Time Series of Stock Variables ........... 81
4.12 Variables in Arrest Submodel ...................... 96
4.13 Constants in Arrest Submodel ...................... 97
4.14 Summary of Arrest Submodel Fit .................... 98
4.15 Variables in Warrant Processing Submodel ............... 102
4.16 Constants in Warrant Processing Submodels .............. 102
4.17 Summary of Warrant Submodel Fit ................... 103
4.18 Variables in Case Processing Submodel ................. 107
4.19 Constants in Case Processing Submodel . . . . . . ......... 107
4.20 Summary Case Processing Submodel Fit ................ 111
4.21 Variables in Allocation Submodel .................... 112
4.22 Summary of Baseline Model Fit ..................... 118
4.23 Sensitivity of Authorizations to Smoothing Delays ........... 134
4.24 Sensitivity of Denials to Smoothing Delays ............... 134
4.25 Sensitivity of Dismissals to Smoothing Delays ............. 135
4.26 Sensitivity of Plea Offers Accepted to Smoothing Delays .- ...... 135
4.27 Sensitivity of Prosecutions to Smoothing Delays ............ 136
4.28 Major Feedback Loops in Baseline Model ................ 138

4.29 Dominance of Arrests Feedback L00ps on Prosecutions Across Phases
of Loop Dominance ............................ 145
4.30 Dispositions by SuSpect / Victim Sex ................... 154

xii

4.31 Test of Association Between Disposition Suspect / Victim Sex ..... 155
4.32 Dispositions by Suspect / Victim Sex for Adult Domestic Violence Cases 155
4.33 Test of Association Between Disposition Suspect / Victim Sex for Adult

Domestic Violence Cases ......................... 156
4.34 Suspects by Previous State and Sex of Individual ........... 157
4.35 Suspects by Previous State and Sex of Individual for Adult DV . . . 157

xiii

List of Figures

2.1
2.2

3.1
3.2
3.3
3.4
3.5
3.6

4.1
4.2

4.3

4.4
4.5

4.6

Criminal Justice Response to Domestic Violence ............ 12
Prosecution of Domestic Violence Cases ................. 32
Finite State Machine ........................... 47
Original Expected Rate of Cases per Day ................ 53
Noisy Time Series ............................. 54
Quarterly Aggregated Time Series .................... 56
Monthly Aggregated Time Series . . . . . . . . . . ......... 57
Comparisons of Warrant Request Time Series ............. 63
Subsets of Violence Against Women Database ............. 70
Smoothed Time Series of Warrant Requests Generated from Violence

Against Women Database ........................ 83
Descriptive Model with Dispositions as a Function of Caseload Pres-

sure, PACM120 .............................. 84
Simulated Results from PACM120 .................... 87
Descriptive Model with Dispositions as a Function of Case Attributes

and Caseload Pressure, PACM131 .................... 88
Simulated Results from PACM131 .................... 89

4.7 Descriptive Model with Dispositions as a Emotion of Case Attributes,

PACM141 ................... ' .............. 90
4.8 Simulated Results from PACM142 .................... 91
4.9 Trends in First Time Arrests Versus Repeat Arrests .......... 93
4.10 Arrest Submodel ............................. 94
4.11 Simulated Results from Arrest Submodel ................ 97
4.12 Warrant Processing Submodel ...................... 99
4.13 Simulated Results from Warrant Processing Submodel ........ 103
4.14 Case Processing Submodel ....................... 105
4.15 Simulated Results from Case Processing Submodel .......... 109
4.16 Allocation Submodel ........................... 110
4.17 Overview of Baseline Model ....................... 114
4.18 Simulated Results of Arrests from Baseline Model ........... 115
4.19 Simulated Results of Warrants from Baseline Model . . ........ 116
4.20 Simulated Results of Prosecutions from Baseline Model ........ 117

4.21 Sensitivity of Authorizations to Increase in Number of New Cases . . 119
4.22 Sensitivity of Denials to Increase in Number of New Cases ...... 120
4.23 Sensitivity of Prosecution Caseload to Increase in Number of New Cases 121
4.24 Sensitivity of Plea Offers Being Accepted to Increase in Number of

New Cases ................................. 122
4.25 Sensitivity of Dismissals to Increase in Number of New Cases ..... 123
4.26 Oscillations Used for Studying Frequency Sensitivity of Baseline Mode1124
4.27 Sensitivity of Arrests and Warrants to Frequency ........... 126
4.28 Sensitivity of Prosecutions to Hequency ................ 127
4.29 Sensitivity of Authorizations to Decrease in Number of Prosecutors . 128

4.30 Sensitivity of Denials to Decrease in Number of Prosecutors ..... 129

XV

4.31 Sensitivity of Prosecution Caseload to Decrease in Number of Prose-

4.32 Sensitivity of Plea Offers Being Accepted to Decrease in Number of
Prosecutors ................................ 131
4.33 Sensitivity of Dismissals to Decrease in Number of Prosecutors . . . . 132
4.34 Reference Atomic Behavior Pattern Index (ABPI) for First Arrest
Prosecutions ................................ 141
4.35 Reference Atomic Behavior Pattern Index (ABPI) for Repeat Arrest
Prosecutions ................................ 144

4.36 Reference Atomic Behavior Pattern Index (ABPI) of Percent Held

Accountable ................................ 146
4.37 Warrant Requests by Type of Relationship and Year ......... 151
4.38 Warrant Requests by Suspect /Victim Sex and Year .......... 153
4.39 Finite State Machine to Test Paths of Suspects by Sex I ........ 156
4.40 Safety Planning in Revised Model .................... 164
4.41 Community Awareness in Revised Model ................ 164
4.42 Resource Allocation in Revised Model .................. 165
4.43 “Going Rate” in Revised Model ..................... 167
4.44 Prosecutor Meetings with Victims in Revised Model .......... 168
4.45 Overview of Revised Model ....................... 169

xvi

Chapter 1

Introduction

This dissertation is about improving the effectiveness of prosecution of batterers
in cases of domestic violence. There are many ways that one might think about
domestic violence, but it is foremost a facet of sexism—the Oppression of women by
men. Domestic violence names a category of practices used by men in an effort
to domesticate women into compulsory heterosexual, monogamous, and patriarchal
relationships through the use or threat of violence.1 To say that these practices are
used in an effort to domesticate women means that the effects on women are neither
uniform, total, nor universal. Domestic violence is coercive at both the individual
and macro level. And to say that these practices are used by men means that men
as a social group2 benefit from the individual batterer who abuses by drawing on the

specter of the abusive relationship to structure the relationships of women to men.

 

1This does not presuppose that women cannot be abusive, men cannot be victims of domestic
violence, or that same—sex domestic violence does not happen. Nor does it mean that “other" kinds
of cases are uninformative in the analysis of sexism and the oppression of women.

2The notion of a social group is a macro or structural concept. Social groups are socially
constructed categories, a part of social reality, and refer in the sense of Iris Young (1990, pp. 42-
47) to the classes that structure the relationship between oppressor and oppressed. These classes
are populated by individuals who’s membership varies or might not even fit the category term. So
theoretically, being male does not mean that one is a man. But, it raises the question about the
extent that males might be able to meaningfully separate from membership or association with
the men as a social category.

Domestic violence includes practices such as a batterer verbally abusing a woman,
isolating her from friends and family, preventing her from getting or keeping a job,
making threats of violence, and beating, raping, or killing her.

Legislators and local agencies have responded incrementally to increased public
pressure by funding domestic violence domestic programs, providing civil reme-
dies like personal protection orders, criminalizing batterer behavior, and reforming
procedures for handling cases of domestic violence. In terms of holding assailants
accountable, most reforms have focused narrowly on domestic violence as a crim-
inal behavior. Some of the promoted changes to the criminal justice system have
included adOption of pro or mandatory arrest policies, mandatory referral Of do-
mestic assault police reports to the prosecutor’s office, implementation Of special
prosecution units, and court mandated referrals to batterer intervention programs.
(Pro-arrest policies encourage police Officers to make warrantless arrests in cases
Of misdemeanor domestic violence whereas mandatory arrest policies require police
Oflicers to make a warrantless arrest in cases of misdemeanor domestic violence.)
However, jurisdictions have varied considerably in their actual implementation.

Reforrners have tended to explain resistance to change in terms of attitudes since
individuals working in the criminal justice system have frequently blamed the vic-
tim, minimized the abuse, or colluded with the assailant. Appointing a police chief
or electing a prosecutor or judge who understands the dynamics of domestic vio—
lence does make a difference, but this approach is limited to the extent that reforms
are not institutionalized. Moreover, institutionalizing reforms through changes in
organizational policies does not by any means guarantee their effectiveness, espe-
cially when the changes ignore the real working conditions of practitioners. Some in
the battered women’s movement like Ellen Pence (1999) have similarly reconsidered

their approach to understanding the criminal justice system:

In the past, we might have asked, ‘Why did this practitioner take this
action?’ Now we ask, ‘How was this practitioner institutionally organized
to take this action?’ Instead of seeing actions as the result of what goes
on in the head Of a judge or probation Officer or police Officer, we see it

as the result of what is going on in the work practices. (pp. 37-38)

Reforms that pay attention to how practices are structured are more likely to lead
to organizational changes that are sustainable, and hence last long enough for the

results to accumulate and impact assailant accountability.

1. 1 Research question

One obvious way to consider how practitioners are institutionally organized in the
criminal justice system is to look at the structure of their work-flows. This has
become increasingly important as more communities have adOpted mandatory ar-
rest policies, which have effectively restricted police Officers’ discretion, moved more
cases into the prosecutor’s Office, and thus displaced discretion in the criminal justice
system from police Officers to prosecutors. Hence, many communities are noticing
increases in the number Of domestic violence cases where warrants are denied or
cases are dismissed, potentially undermining the benefits of mandatory arrest and
prosecution. That is, there appears to be a relationship between the caseloads of
prosecutor’s offices and dispositions that affects the extent to which communities
can hold assailants accountable via the criminal justice system. Thus, the general re-
search question for this study is: how does a prosecutor’s office dynamically manage

its domestic violence caseload?

1.2 System dynamics

Understanding how a prosecutor’s office manages its domestic violence caseload can
be conceptualized in a variety of ways. In this study, it is understood in terms of
feedback control mechanisms or feedback lOOps. A system dynamics approach is
used to identify and understand the feedback how in terms of patterns of feedback
IOOp dominance. The notion of feedback loop dominance is relevant to complex
systems where the dynamic behavior of the system is being understood in terms
Of the structure Of feedback loops, where the set of feedback lOOps generating the
system’s behavior over time also changes over time.

System dynamics is a method for modeling and evaluating complex systems of
feedback loops, which are formulated as systems of coupled nonlinear ordinary dif-
ferential equations. Such systems of equations are generally impossible to solve
analytically. SO system dynamics modeling relies heavily on numerical methods and
computer simulation to solve this system Of differential equations. The purpose of
model building in system dynamics is to understand and solve problems in terms
of feedback loops. The interest in studying how a prosecutor’s Office manages its
domestic violence caseload is to increase assailant accountability. SO the question
for this study in terms of system dynamics becomes one of understanding the re-
lationship between the (a) mechanisms regulating the caseload in a prosecutor’s
offices, and (b) the mechanisms regulating the prosecutor’s office holding batterers
accountable. This can be understood as identifying the feedback loops (if any) that
dominate both some measure of accountability and the prosecutor’s office caseload

during a particular phase of dynamic behavior.

1.3 Overview

Chapter 2 provides the broad theoretical framework for this study and a review of the
existing literature on domestic violence arrests, prosecution research, and batterer
intervention programs, reviewing several lines of domestic violence and prosecution
related research. Included is a summary of the research on deterrence from arrest,
evaluations of batterer intervention programs, and review Of prosecution research
including the prosecution Of domestic violence cases and plea bargaining.

Chapter 3 covers the methods. One of the main goals for this study is to deve10p
methods for studying community responses to domestic violence with particular at-
tention paid to modeling small populations. The chapter describes the use of a single
case study design, use Of the main database for generating the numerical time series
from the prosecutor’s Office violence against women (VAW) data base, methods for
handling the resulting sparse time series associated with small pOpulations, and the
development of a finite state machine approach to studying the transition patterns
of individuals within the database.

Chapter 4 describes the results, starting with descriptive statistics Of the VAW
database and comparisons against census demographic graphics. The results from
testing three descriptive models are then discussed. These models simply test to
what extent (a) simple systems Of differential equations can reproduce the general
behavior pattern of the numerical time series, and (b) to what extent dispositions can
be formulated as functions Of caseload relative to other formulations. This is followed
by discussion of the development and testing Of the baseline model, which begins
with each submodel and concludes with an analysis of the integrated baseline model.
A variety of tests are conducted on the baseline model, including sensitivity to

various parameters, frequency response, and smoothing parameters used in handling

the sparse time series. The relationship between the behavior of the baseline model
and structure of the feedback lOOps is then analyzed in. terms of identifying patterns
of feedback lOOp dominance. The next major section Of Chapter 4 covers follow-up
analysis examining the disaggregation of arrests by type of relationship and sex Of
suspect. The chapter concludes with a summary of the key informant interviews,
which were based on questions developed during the development and testing Of the
baseline model, and proposed inclusion of additional feedback loops for a revised
model.

Chapter 5 is the conclusion. This chapter summarizes the major findings of the

study, major limitations, policy implications, and directions for future research.

Chapter 2

Review Of research literature

2.1 Overview

This chapter introduces the problem Of domestic violence as a major social prob-
lem and argues that we need to better understand how prosecutors manage their
domestic violence caseloads in order to improve and assess the limits of the crim-
inal justice system response. The chapter summarizes the previous modeling and
simulation work on the criminal justice system response to domestic violence, which
points to a need to better understand the linkage between arrests and batterer in-
tervention programs. This is followed with a review Of the literature covering the
three main aspects Of the criminal justice system response: police and deterrence
effects from arrest, batterer intervention programs and their treatment effects, and
prosecutors and their decision making. The chapter concludes with a discussion of
how prosecutor decision making can be understood as a dynamic problem of how

prosecutors manage their domestic violence caseloads.

2.2 Domestic violence

With 25% Of women reported having been raped or physically assaulted by an inti-
mate partner during their lifetime (Tjaden & Thoennes, 1998), woman abuse con-
tinues to be a major social problem in the United States. Battering involves a con-
stellation of tactics, including emotional abuse, isolating the victim from resources,
preventing her from getting or keeping a job, coercion and threats Of violence, rape,
and murder. “Battering is far more than a single event, even for the woman who is
hit once, because it teaches a profound lesson about who controls a relationship and
how that control will be exercised” (Schechter, 1982, p. 17). In order to make the
distinction between the single event and pattern within this dissertation, abuse will
refer to a specific behavior including physical abuse, sexual abuse, emotional abuse,
economic abuse, destruction Of property, coercion, and threats; battering refers tO a
pattern of abusive behaviors; domestic violence includes both abuse and battering;
and men who batter refers to men who use tactics of abuse and battering against
their intimate partners (Pennsylvania Coalition Against Domestic Assault, 1992,
Section K. Definitions). Hence, the terms ‘male batterers’, ‘batterers’, ‘abusers’,
and ‘assailant’ will be used interchangeably to refer to adult men (ages 18 and over)
who batter women.

Abusers use battering tactics to keep or delay a woman from leaving an abu-
sive relationship, with violence continuing and often escalating after she leaves. In a
Michigan study, 37.4% Of the women with one or more violent partners said that the
violence continued after separation and 45.6% indicated that the violence increased
(Largo, Smith, Thrush, McCrOhan, & Rafferty, 1999). Adding to the assailant’s be-
haviors are economic, social, and institutional barriers such as no alternative hous-

ing, lack of support from friends or family, difficulty finding a job and coordinating

childcare, and risk Of losing child custody to the assailant.

Before the modern battered women’s movement, the State colluded with as-
sailants by failing to extend the criminal law to domestic violence (Fagen, 1996;
Mullender, 1996; Schechter, 1982). Police used their discretion to avoid making
arrests and prosecutors did not pursue cases where the victim-Offender had an inti-
mate relationship. With no legal protection and no shelters until the 1970’s, many
women who did leave had no Option but to return to the abuser. Police, social
workers, and other professionals judged a woman’s decision to return to the abuser
as an indication that she did not really want to leave. It was a “laissez-fair approach
that dominated police and court response” (Pence, 1999, p. 14). Feminists pio-
neered the battered women shelters as a way to increase victim safety and initiated
system reform efforts focused on the criminal justice system’s response to domestic
violence and holding the assailant accountable. Today, many communities have im-
plemented a coordinated response to responding to domestic violence (Mullender,
1996; Pence, 1999). People working to end domestic violence Often speak Of reform
in terms of enhancing victim safety and increasing assailant accountability. “De
terrnining whether the coordinated community response enhances victim safety and
increases Offender accountability is central to the impact evaluation of a community
intervention project” (Shepared, 1999, p. 183).

The long-term goal of this research is increasing assailant accountability. Com-
munities rely primarily on the criminal justice system to hold assailants accountable
through arrest, prosecution, probation monitoring, and referral to court mandated
batterer intervention programs. “The main challenge appears to be in making the
existing components of interventions work together more decisively and consistently.

They need to hold men accountable for their behavior” (Gondolf, 2002, p. 218).

2.3 Operational definition Of accountability

With respect to the criminal justice system and the prosecutor’s Office, the most
visible aspect of a accountability1 is the verdict of guilty, either through a trial
or guilty plea. Perhaps the simplest operational definition for accountability as
a practice for the prosecutor’s Office is then the proportion of cases that result
in a verdict of guilty. While this simple definition is in many ways convenient,
it is flawed in the sense that it depends on cases actually flowing through (or at
least into) the criminal justice system. For example, a prosecutor’s Office might
have a high proportion of its cases resulting in a guilty verdict, but this would not
represent accountability as a practice if police officers were not arresting abusers
because the prosecutor’s office refused to prosecute most cases. And in contrast,
a prosecutor’s Office might not have prosecuted any cases while still representing
accountability as practice if, in some future history, the practice of battering was
extinct. To get at the notion Of accountability as practice, one must look not at
the frequencies Of dispositions, but at the structures that explain those frequencies.
That is, accountability as practice is the structuring of dispositions. In terms of
system dynamics, this can be defined as follows: accountability as practice is the
structure of feedback loops that determine the prOportion of dispositions resulting
in a guilty verdict.

 

1The term ‘accountability’ has several conflicting uses in popular discourse, particularly when
one is talking about patterns of behaviors in the context of oppression, where one social group
tends to obfuscates abuses as a tactic for maintaining power and control over another social group.
However, a thorough philosophical analysis of accountability is beyond the scope of this dissertation
and a topic for future research.

10

2.4 The criminal justice response

An idealized stock-and-flow picture of the criminal justice response to domestic vi-
olence is shown in Figure 2.1. Text within boxes represent stocks of individuals,
whereas text with no surrounding box represent flows of individuals between stocks.
Stocks represent the number of individuals in a given state. Individuals can, theo-
retically, remain in a given state indefinitely.

New assailants at risk Of arrest come into the community’s stock of Assailants,
which represents individuals committing behaviors that fit the criteria for criminal
domestic violence. Note that individuals move into and out of Assailants with
changes in criminal law, that is, a change in the boundary of a category. For example,
the criminalization Of domestic violence will increase the number of individuals at
risk of an arrest.

Some assailants might be arrested and move via Arrests into the prosecutor’s
Office caseload, Prosecutions, others might stop committing criminal domestic vi-
olence and leave the community’s stock of Assailants before they are arrested via
Cessation, and the rest will remain in the stock of Assailants (perhaps indefinitely).
Cessation includes assailants that no longer abuse their intimate partners (a change
in behavior or death) and assailants who moved to non-criminal battering tactics
(either by changing their own behavior or by changes in the enforcement of criminal
law). Some Of the cases being prosecuted will be denied or dismissed, and return
to the stock of assailants via Dismissals, while others will move into the stock Of
cases with Sanctions, either through informal agreements or formal guilty pleas. Of
those that are sanctioned, some will discontinue committing criminal domestic vi-
olence and leave the system of assailants via Cessation, while others will return to

Assailants.

11

Figure 2.1: Criminal Justice Reaponse to Domestic Violence

Cessation Cessation

I I

v '

New ts—D Assailants I-IDArrests-ID ProsecutionSI-—> Sanctions

II I
|

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Understanding how this simple model of the criminal justice response functions
to hold assailants accountable is essential for both improving the current system and
understanding its limits. The criminal justice system is, however, a complex system
of interacting subsystems. Developing a scientific understanding of how such systems
work is challenging because they entail sets of feedback loops that are inherently
difficult to identify and assess using traditional statistical methods that rely on the
classic linear cause-effect relationship. Research into complex systems has therefore
been mostly theoretical in the sense of social theory or mathematical modeling and
computer simulation. Computer models and simulations have been used tO study a
variety of social phenomena, but only recently has the approach been applied to the
problem of domestic violence. The major challenge for these early efforts has been
conceptual, that is, how to represent the problem and prevailing theories in terms

Of quantified variables and their relationships.

12

Previous modeling work on the criminal justice response to domestic violence
(see Figure 2.1) focused on understanding the specific problem Of batterer interven-
tion programs not appearing to have any measurable effect at the community level
despite increases in court mandated referrals (Hovmand, 2000). One explanation by
service providers for the lack Of impact was that as referrals increased, more agencies
entered the batterer intervention market, which increased competition and lowered
standards Of accountability. Specifically, programs with large groups could afford to
hold participants accountable and risk losing a group member whereas small groups
could not. The model assumed that all batterer intervention programs had a positive
effect size and that every arrest resulted in some type of intervention. Analysis of
the model indicated that the problem was not caused by market competition or de-
teriorating standards, but policies where the chances of being referred to a batterer
intervention program after an arrest were pr0portional to the severity of criminal
behavior. Specifically, the intervention programs were most effective when the least
criminally severe assailants had the highest chances of being arrested and referred
to the batterer intervention program, for two reasons. First, removing assailants at
the lowest levels of criminal behavior reduced the number who would escalate to
higher levels of criminal behavior. Second, assailants at the lowest level of crimi-
nal behavior were also closest to the desired state of not battering and hence had
a better chance of stOpping violence, versus just reducing the severity of violence.
The key finding was that the effectiveness Of the criminal justice system response to
assailants was sensitive to how the probability of an arrest and mandated referral
varied by the severity of criminal behavior, that is, the link between Assailants and
Sanctions in Figure 2.1, the prosecutor’s office.

While the police response and batterer intervention programs have been exten-

sively researched, relatively few studies have looked at the prosecution of domestic

13

violence cases. The next three sections review the research relevant to the crimi-
nal justice system response to domestic violence: police and deterrence effects from
arrest, batterer intervention programs and their treatment effects, and prosecutors
and their decision making. The basic argument is that while there is little evidence
of deterrence effects from arrests, batterer intervention programs are showing some
tentative indications of being able to reduce recidivism. Hence, the limitation of
community responses is currently the link between arrests and batterer intervention
programs, that is, the prosecutor’s Office.

Prosecutors play a major role in the flow Of misdemeanor criminal cases, from
authorizing the arrest warrants to plea bargaining. Prosecutors decide whether there
was enough evidence to establish probable cause for the domestic assault arrest.
Contrary to popular perception, most criminal cases resulting in guilty dispositions
are settled through plea agreements. This is true for both felonies and misdemeanors.
In plea agreements, prosecutors and defense attorneys might negotiate the charge,
the sanction, or both. When an agreement has been reached between the prosecutor
and defendant, the agreement is presented in front of the judge for final approval.
While judges have the final say on sentences, their Options are ultimately limited to

what the prosecutor presents in court.

2.4.1 Police and deterrence effects from arrest

The police response to domestic violence has several facets, including reporting
domestic violence (Coulter, 1999) and decisions to arrest (Rigakos, 1997; Robinson,
2000). In the discourse on reducing domestic violence, the major focus of police
response has been whether there is a deterrence effect from arrest on the future
behavior of assailants. Interestingly, most of the domestic violence legal reforms

have not questioned the deterrence theory behind legal intervention (Fagen, 1996).

14

Deterrence theory presupposes a rational choice model Of behavior where the “pain”
of sanction is weighed against the “pleasure” of illegal behaviors and individuals
refrain when the pain outweighs the pleasure (Maxwell, 2000). There are several
ways in which this rational choice model is wrong. Rational decisions about what to
do are often framed by our imagination and expectations in a given situation. Some
behaviors “make sense” when one considers a perspective on a situation that has no
other viable alternatives. Moreover, we rarely have complete information, but have
to try and balance various degrees Of uncertainty. Nonetheless, deterrence theory
has played a major role in research on domestic violence arrests and their effects.

Sherman and Berk (1984) found support for a specific deterrence effect from
arrest with batterers in the widely publicized Minneapolis Experiment. The study
provided empirical support for the benefits Of arresting assailants in domestic vio-
lence cases, which together with several large lawsuits and pressure from advocacy
groups, led states to pass pro or mandatory arrest statues (Davis, Smith, & Nick-
les, 1998). Michigan, for example, passed legislation taking effect on July 1, 1994
(PA 62) that required all police departments to implement pro or mandatory arrest
policies. Pro-arrest policies allow police Officers to make a warrantless arrest with-
out having actually witnessed the assault. Mandatory arrest policies require police
Officers tO make the arrest in such circumstances.

As a follow-up to the original Minneapolis Experiment, the Spouse Abuse Repli-
cation Project (SARP) tried to replicate the original study. The researchers were
mixed in their analysis about whether arrest deterred assaults (Zorza & Woods,
1994). Analyzing data from Milwaukee, Sherman et al. (1992) did not find support
for an overall deterrence effect, but they did find support for a deterrence effect for
white, Hispanic, and employed abusers and an escalation effect for abusers who were

Black or unemployed. Sherman et al. (1992) interpreted the result as supporting the

15

claim that there is a deterrence effect with abusers who have a stake in conformity
while those who do not have a stake in conformity retaliate against their victims
because they have less to lose.

The replication studies contained some serious flaws and the results should be
read as inconclusive (Garner, Fagan, & Maxwell, 1995). Zorza and Woods (1994, p.
66) point to some of the issues, including not considering the escalation of domestic
violence, Officers’ statements, misclassifying assailants and their risk, including self-
defense cases, problems with censored data, and failing to consider the impact of
the courts and prosecutors’ responses to domestic violence. While some have called
for more studies, others have raised concerns about the continuance Of mandatory
arrest laws, given the absence of an overall effect, since they might disempower vic-
tims or result in less reporting and seeking of medical help (Smith, 2000). There are,
however, a number of other reasons for favoring mandatory arrest. Arrest temporar-
ily separates the assailant from the victim, providing a window of Opportunity for
her to seek shelter or make other arrangements, and sends a message to her family
and community that domestic violence is illegal, which might ultimately reduce the
intergenerational transmission of domestic violence (Zorza & Woods, 1994). Arrest
also provides the principal pathway Of moving assailants from the community into

the batterer intervention program.

2.4.2 Batterer intervention and treatment effects

While there is no conclusive evidence that mandatory arrest or prosecution have
an overall deterrence effect on abusers, there is evidence that supports a cautious
Optimism that batterer treatment programs do lower recidivism rates for at least
some assailants. There have always been some “therapeutic” interventions with

men who batter, but the 1980’s represented a period of development and growth

16

for batterer intervention programs. Policy changes like pro or mandatory arrest
increased the referrals and demand for court mandated. batterer intervention services
(Sonkin, 1988). By the late 90’s, approximately 80% of the batterer intervention
programs’ referrals were court-mandated (Healey, Smith, & O’Sullivan, 1998).

A group approach for men who batter is now the preferred method over individ-
ual, couples, Or family treatment (Tolman & Edleson, 1989). In couples and family
therapy, the clinician is to remain neutral with respect to each individual and avoid
taking sides. Such a stance risks the victim feeling blamed for the abuse and in-
creases the likelihood that victim will be silenced in the sessions by the batterer’s
threats outside the Office (Kaufman, 1992; Tolman & Edleson, 1989). In addition,
Tolman points out that many batterers will seek treatment only when the woman
is about to leave. After being assured that she is not going to leave, he continues
abusing. This deepens the cycle Of abuse, leaving the victim feeling betrayed by
the therapists and professionals, and making subsequent efforts to leave even more
difficult. Despite these Observations and concerns by advocates, many couples and
family therapists feel they are successful in treating family violence.

From a national survey, Gondolf (1990) identified three different treatment the-
ories or modalities for court-mandated batterer programs: therapeutic, psycho—
educational, and didactic-confrontational. Therapeutic approaches focus on treating
one or more emotional problems. Psycho-educational approaches stress cognitive
restructuring and development Of social skills. Didactic-confrontational modalities
emphasize consciousness raising and taking responsibility for abuse. Programs dif-
fer not only theoretically, but also in their implementation. As a result of the wide
variation in programs, many states have now implemented minimum standards for
court mandated batterer intervention programs (Bennett & Piet, 1999). It remains

to be seen whether having the standards improves the quality of the interventions

17

and if that improvement leads to a decline in recidivism. But without the standards,
nearly any program would qualify as a batterer intervention program, and this could
place the lives of victims at even greater risk.

Problems with methodology in evaluating batterer intervention programs have
Often hindered firm conclusions from being made about reductions of battering
(Eisikovits & Edleson, 1989; Fagen, 1996; Petrik, Gildersleeve—High, McEllistrem,
& Subotnik, 1994). Issues include: high attrition rates, variability in consequences
for not attending or drOpping out, delays between the original incident and the first
session, availability of culturally specific groups, no standard follow-up measures or
intervals, few control groups, and low survey response rates (Davis & Taylor, 1999;
DeHart, Kennerly, Burke, & Follingstad, 1999). However, more recent research is
beginning to suggest that some programs do contribute to decrease in rearrest, at
least with some men (Davis & Taylor, 1999; Gondolf, 1995, 1999; Taylor, Davis, &
Maxwell, 2001).

2.4.3 Prosecution

The increase in arrests has moved more assailants into the prosecution casefiow, but
relatively few studies have focused on the prosecution of domestic violence (Cahn,
1992). This should be alarming for two reasons. First, the prosecution casefiow has
consistently been found tO have a large attrition rate or “sieve effect” attributed to
the exercise Of prosecutor discretion (Moyer, 1982). Prosecutors use their discretion
to make decisions about the number and kinds of charges, whether to prosecute,
what to Offer and negotiate in plea bargaining, and what tO recommend for a sen-
tence. The second reason is that it is unclear what happens when there is an increase
in domestic violence cases referred to the prosecutor’s Office. Presumably, there is

an increase in convictions and referrals, but what about the number of cases denied

18

for prosecution, dismissed, or diverted to something other than batterer intervention
programs?

The next four sections review some of the existing research on prosecutor decision-
making: charging decisions, decision to prosecute, plea bargaining, and effect of case
deposition on future behavior. While discussed separately, these decisions and their
effects are not necessarily distinct. For example, plea bargaining can easily include
decisions to reduce charges. The decision to prosecute might rely on information
about the effectiveness Of prosecution on a given type of case. And charging deci-
sions might be made expecting a subsequent reduction of charges during the plea

bargaining.

2.4.3.1 Charging decision

The first decision prosecutors normally make is whether or not to charge the defen-
dant and on which charge(s). Prosecutors can decide to not charge a defendant at
all, nolle prosequi, or add to, remove, or change the charge at arrest. Charging de-
cisions typically determine the court that the case will be heard in and prosecutors
might lower the charges in order to get a more favorable judge or avoid constraints
on sentencing or plea agreements.

Schmidt and Steury(1989) found that prosecutors were more likely to issue crim-
inal charges when the victim was injured, a weapon was used, defendant failed to
appear at the charging conference or had a prior record. But, prosecutors were
less likely to file charges when the victim and defendant continued to have a sexual
relationship, were living together, the defendant was employed, and there were no
indications of alcohol or drugs at the incident.

There are major problems in terms of both the reliability and validity of domes-

tic violence suspects’ prior records. First, indicators Of whether or not a suspect

19

has prior domestic violence Offenses are notoriously unreliable. Criminal history
databases are Often incomplete with respect to misdemeanor arrests and convictions,
and assailants will often move from one jurisdiction to another to avoid accumulat-
ing a record. Second, domestic violence related Offenses can include a wide range
Of criminal behaviors, from stalking to destruction of prOperty and disturbing the
peace. Most criminal records do not, at this point, record whether or not a crime is
related to domestic violence. Some record keeping systems now make it possible to
indicate whether or not any crime is domestic violence, but their implementation is
slow.

While Schmidt and Steury’s (1989) study has been the only one focusing on
charging decisions in domestic violence cases, other researchers have looked at pros-
ecutorial discretion for other types of crime. Albonetti (1992), for example, consid-
ered prosecutorial discretion to reduce burglary and robbery charges, finding that
seriousness of the case and indicators of the defendant’s character (having a prior
record, young, habitual Offender) lowered the chances of charges being reduced. Al-
bonetti tested and did not find race or gender to be factors in the decision to reduce
charges, which might be due to reliance on regression models. Logistic regression
models estimate the probability of an outcome from a set of explanatory variables.
One major limitation of such approaches is the risk of oversimplifying into cause-
effect models complex decisions processes that involve feedback 100ps.

For example, prosecutors Often negotiate the charge with the possible sentences
in mind. Hence, the charging and sentencing decision are not independent, but in-
teract across time. Prosecutors might also charge cases as misdemeanors or felonies
as a way to get a judge considered more favorable for the prosecution. Similarly,
mandatory sentencing guidelines and other constraints on criminal behavior for cer-

tain types of crimes may influence prosecutors’ charging decisions. For example,

20

McCoy (1984) argued that Califomia’s Determinant Sentencing Law, which was
intended to reduce judges’ sentencing discretion, resulted in prosecutors reducing
their initial charges in order to avoid the constraints on plea bargaining in felony
cases. And in a more recent analysis, Taha (2001) found that the impact of Sentenc-
ing Reform Act of 1984 on federal prosecutors was an increase in more precharge
bargaining which resulted in defendants pleading guilty faster and to lesser charges.

There has also been some suggestion that organizational factors between police
and prosecutors play a role in charge decisions. For example, police agencies monitor
prosecutor’s charging decisions as a guide for determining standards for a viable
criminal case (Schmidt & Steury, 1989). And McCoy (1984) described other effects
in the context of a hydraulic theory of discretion in the criminal justice system,
whereby efforts to limit discretion in one part Of the system resulted in increases in
another part. That is, instead of limiting discretion, discretion was simply displaced
from one part Of the criminal justice system’s response to anOther. Her point is
important in the context of domestic violence because as communities limit police
discretion to arrest and restrict judicial discretion, an unintended consequence might

be the displacement and concentration of discretion in the prosecutor’s office.

2.4.3.2 Decision to prosecute

Once charges have been filed, the prosecutor can decide whether to go forward or
delay prosecution, usually for up to a year with misdemeanor cases. Albonetti (1987)
considered the effects of uncertainty on prosecutor discretion, looking at variables
such as the types of evidence, defendant-victim relationship, defendant arrested at
scene, gender, race, defendant’s prior record, offense type, use of weapon, type of
victim, victim provocation, and statutory severity. Albonetti hypothesized that

a prosecutor’s uncertainty about winning a case would decrease the likelihood of

21

prosecuting the case. Albonetti found support for and concluded that uncertainty
about winning a case at initial stages of prosecution guided the decision to prosecute.
Albonetti also noted that warrantless arrests were less likely to be prosecuted. Most
misdemeanor domestic violence cases involve warrantless arrests. In warrantless
arrest, police Officers make the initial decision, and prosecutors review that decision
with the result of either authorizing or denying the arrest warrant. In contrast,
prosecutors are more likely to prosecute cases when they make the initial screening
decision.

Prosecutors do make decisions based on the strength of a case. And, stronger
cases are more winnable by definition. But, it is unclear how Albonetti’s sense Of
uncertainty differs from the notion of the strength Of a case. If one wants to say that
the strength of the case is the same thing as the uncertainty of winning a case, then
Albonetti’s findings are much less interesting. One might be tempted to simply say
that uncertainty of winning and the strength of the case are the same thing. But
there are differences between the two concepts, especially in cases involving violence
between intimate partners.

A prosecutor can have a strong case in terms of evidence, victim credibility, use
Of a weapon, and so on and still be uncertain as to whether or not a jury would find
the batterer guilty if the case went to trial. The prosecutor and defense attorney’s
assessments of what would happen if a case went to trial, and their certainty in that
assessment, is likely to have a significant influence over the plea bargaining process
and the decision to prosecute. Thus, the uncertainty lies not in the strength of the
case, but in assessing the “going rate” for a case with a given set Of attributes. The
going rate is a state variable and subject to both mis—perception and adjustment
as the outcomes Of similar cases change over time. For example, if the prosecutor

offers pleas below the going rate, the going rate will eventually drOp. Likewise, if the

22

prosecutor manages to secure convictions above the going rate, the going rate will
gradually increase. But what the real going rate is at any point in time is uncertain.
If there is an argument to be made about the relationship between uncertainty and
prosecutor decision making, then it is in the prosecutor’s estimation of the going
rate for a particular case.

Martin (1994) looked specifically at the decision to prosecute domestic violence
cases and found that prosecution was more likely when defendants committed more
serious ofl'enses, had prior arrests for domestic violence, if the charge was criminal
trespassing or harassment, or either victim or defendant was using alcohol or other
drugs during the incident. Martin did not find that victim injury predicted pros—
ecution. In contrast to Martin (1994), Hirschel and Hutchinson (2001) could only
find two explanatory variables that were significant in their model of the decision to
prosecute: victim injury and the victim arguing with police against a citation / arrest.
And, Dawson and Dinovitzer’s (2001) model Of the decision to prosecute contained
only one statistically significant explanatory variable, namely, a victim’s willingness
to COOperate.

Albonetti and Hepburn (1996) looked at the decision to defer prosecution in
felony drug possession cases and found that Older males with prior arrest records or
multiple charges were less likely to have prosecution deferred in lieu of drug treat-
ment, while defendants arrested for marijuana possession were more likely. Albonetti
and Hepburn did not find support for a direct relationship between the defendant’s
minority status and the prosecutor’s diversion decision, but they did find support
for a more complicated interaction between prior record, age, and minority status.
Specifically, Albonetti and Hepburn ( 1996) argued that (a) defendants with prior
contact with the criminal justice system were more likely to know how to negotiate

a deferred prosecution, and (b) defendants with minority status were more likely to

23

have increased contact with the criminal justice system, which would be the direct
consequence of such practices as racial profiling.

This last argument is significant because it points to an unintended consequence
of a suspect’s contact with the criminal justice system that has an impact on fu-
ture dispositions. Specifically, one usually thinks of criminal history as something
that accumulates. As suspects accumulate prior convictions, subsequent sentences
are enhanced. But Albonetti and Hepbum’s (1996) argument points to a second,
compensating mechanism, whereby increased contact with the criminal justice sys-
tem contributes to the accumulation of experience manipulating the system, and
might as Albonetti and Hepburn point out, actually lead to lessening of sanctions
relative to the arrest charge. The possibility of this second mechanism has major
implications in the context of domestic violence and arrest policies. If there is such
a mechanism, then it means that an unintended consequence of pro and mandatory
arrest will be batterers who become more sophisticated in manipulating the criminal
justice system and controlling victims. This is similar to the concern that some have
with batterer intervention programs, namely, that these groups effectively provide
batterers with an Opportunity to share battering tactics and become more effective

at manipulating victims and services providers.

2.4.3.3 Plea-bargaining decisions

Plea bargaining is a loose term for negotiations between the prosecutor and defense
attorney, and can include everything from how the defendant will be charged to
sentencing, pretrial release, and victim restitution (Dawson, Smith, & DeErances,
1993). For the prosecutor, the main advantage of plea agreements is having the guilty
verdict without having to invest the resources needed to prepare a case for trial.

For the defense attorney, plea agreements can obviously result in more favorable

24

sanctions, but not always. Hollander-Blumoff (1997) argues, for example, that the
private defense attorney is likely to pursue the interests Of their client, but a public
defender or court appointed attorney might have other interests in mind since they
are repeat players in their negotiations with the prosecutor. Consequently, public
defenders might encourage their client to accept a guilty plea at least in part as a
way to build credit with the prosecutor for another case.

Plea agreements are controversial from a victim’s rights perspective because ad—
vocates and the public tend to see the results as the criminal justice system being
soft on crime (McCoy, 1993). Independent of how one feels about plea agreements
they have become an essential part of the business of diaposing cases in a timely
manner with limited resources. Even small reductions in the number of plea agree-
ments can result in large increases in the number Of cases going to trial. This has
led to the popular hypothesis that prosecutors seek guilty pleas in an effort to re
duce the caseload pressure, i.e. their decisions are governed by. the economics of a
disposition assembly line (for a discussion of this, see McCoy, 1993). The caseload
pressure hypothesis is unappealing in the sense that justice might vary for reasons
outside the principles of justice. In contrast, the professional norms hypothesis states
that decisions to seek a guilty plea are better understood as a function of shared
professional norms about fairness, legal standards, and punishment (McCoy, 1993).
McCoy (1993) argues that prosecutors and defense attorneys share common views
about the “going rate” for a “normal crime” and plea bargaining becomes simply
an efficient way of handling cases with predictable outcomes. Cases are expedited
without compromising the principles of justice.

In one of the earliest studies, Heuman (1975) considered the impact of caseload
pressure on plea bargaining by studying trial dispositions from 1880 through 1954

in Connecticut Superior Courts. Heuman was responding to criticisms of plea bar-

25

gaining that argued that its use was a recent phenomenon brought on by expanding
caseloads. Heuman found that trial verdicts represented between 10 and 20% Of all
dispositions from 1880 through 1954, and hence plea bargains had always been a
part of the criminal justice process and remained relatively stable.2 Heuman (1975)
then compared dispositions and caseloads between low and high volume superior
courts and found no evidence for a direct relationship between caseload pressure
and plea bargaining, but qualified the results, saying that caseload pressure might

have indirect effects, namely:

The prosecutor may nolle3 the marginal case which he might have pur-
sued for a plea earlier. He may offer to reduce more charges and recom-
mend lighter sentences, or he may simply demand more severe sentences

after trial. (p. 527)

Rhodes (1976) considered the impact of caseload pressure in terms Of delays and
applied William Landes’s model of plea bargaining as a market transaction. In this

model,

the plea bargaining process, which is of central importance to modern
jurisprudence, can be characterized as a market transaction in which
the prosecutor “buys” guilty pleas in exchange for promises Of sentence

leniency (Rhodes, 1976, p. 311).

Rhodes (1976) assumed that prosecutors would be interested in maximizing the

total mean number of years in punishment and derived an expression that Optimized

 

2Heuman’s conclusion about the existence and stability of plea bargaining in the criminal justice
system is popular, but not without disagreement. For example, Alschuler (1979) argues that plea
bargaining was infrequent and discouraged, and only started during the 1920’s with the expansion of
prosecutor offices and bureaucratization, reaching its present form during the due process revolution
of the 1950’s and 1960’s.

3For a prosecutor’s ofice to nolle or nolle prosequi a case is to abandon the lawsuit.

26

years in punishment with prosecutor resources. His results suggested that (a) the
rate that prosecutors use plea bargaining could be understood as a combination of
legal strengths of the case and court delay, and (b) plea bargaining was essentially
a market clearing mechanism.

McDonald (1985) took a more comprehensive view with interviews and hype
thetical cases, and found caseloads to be general determinants Of the need to plea
bargain, but did not actually predict which cases were plead or the terms of the plea
agreement. McDonald did find that with greater caseloads, less attention was given
to less serious crimes, increasing the likelihood that plea-bargains for less serious
cases would become more generous. In ranking prosecutors’ information cues to a
range of hypothetical cases, McDonald Observed that the participants did not pay
much attention to court caseload in their plea bargaining decision. Instead, they
focused on the strength of the case, seriousness of the offender, and seriousness Of
the Offense. I

These studies relating caseload to prosecutor decision making (Heuman, 1975;
McDonald, 1985; Rhodes, 1976) all suffer from two problems. First, they focused
on felony cases. Most criminal domestic violence cases are misdemeanors, and
misdemeanors are generally considered less serious Offenses. The second major
problem with these studies is that they focused on court caseloads, not prosecu-
tor caseloads. Court caseloads and prosecutor caseloads are arguably related, but
prosecutor caseloads are more likely to have a direct impact on the prosecutors day-
to-day decision making. This impact could either be direct if prosecutors decided to
deny warrants or dismiss cases based on their current caseload. Or there could be
indirect effects as higher caseloads might mean less time to investigate and prepare
cases, which might lead to more dismissals.

McAllister and Bregrnan (1986) also studied plea bargaining and found that as

27

the probability of conviction and length of sentence increased, prosecutors were less
willing to Offer plea agreements while defense attorneys were more willing to accept
plea agreements. McAllister and Bregrnan concluded that there was no evidence of
a bias by prosecutors and defense attorneys toward plea bargains. However, there
were two major problems in McAllister and Bregman’s experimental design. First,
they essentially assumed that prosecutors and defense attorneys would be trying to
Optimize some utility function, specifically, the difference between (a) current plea
offer, and (b) the product of the likelihood of conviction and sentence if convicted
at trial. If the chances of a conviction were 50% and the average sentence 2 years,
defense attorneys would be looking for a plea Offer of 1 year or less while prosecutors
would be looking for a plea offer Of 1 year or more. But, this is essentially a rational
model of decision making with full information. One might Object to this criticism
by pointing out that there are still guesses involved. For example, that participants
were only provided with the probability Of conviction or the average sentence. But,
knowing the probability of conviction or average sentence is to know a real parameter
value, not an estimate Of it. In reality, we can only statistically estimate parameter
values. The real decisions that prosecutors face is one with uncertain information,
which is what Albonetti (1987) was trying to get at.

The second major problem in McAllister and Bregman’s (1986) study is their use
Of hypothetical situations to draw inferences about real-world decision making. Such
studies have been successful at showing that decision making frequently does not
conform to the classical model of rational choice. But, these types of experiments
simply need to demonStrate that peOple do not follow the rational choice model
in some situations. If, for example, peOple generally followed the rational choice
model in making decisions, then one would expect people to use that model in

both real situations and hypothetical situations. And a corollary, if peOple do not

28

follow the rational choice model in hypothetical situations, then it is unlikely that
they follow the rational choice model in real situations. There has been much
experimental research showing that people do not follow the rational choice model
in hypothetical situations. But having shown that people do not follow a particular
decision model in a hypothetical situation is not the same as showing what they
actually do in real situations. Specifically, generalizing claims about prosecutor and
attorney decision making from hypothetical situations into the real world introduces
a major external validity problem, especially if one considers the role of heuristics
in the theory Of bounded rationality. Ebbesen and Konecni (1980) conducted an
experiment illustrating this external validity problem. They compared the results
of judges’ sentencing decisions in hypothetical cases and real court cases. While
they were able to identify a model of the information cues used in judges’ decisions
in both situations, they found that the models differed. That is, the associations
between information cues and sentencing decisions from hypothetical decisions did
not correspond to what they actually observed the same judges to be doing in the
courtroom with real cases. Ebbesen and Konecni’s (1980) point is that one would

not know this unless one Observed and tested decision models in real situations.

2.4.3.4 Effects Of case disposition decision

One reason for even wanting to understand prosecutor decision making is the per-
ceived impact of these decisions on defendants’ future behavior. Two studies have
considered the effect of prosecuting domestic violence cases on defendants’ rearrest
rates. Ford and Regoli (1992) evaluated no—drOp versus drOp permitted prosecution
policies. In no—drOp policies, victims are not allowed to drOp the charges and the
prosecutor pursues the case seeking a finding of guilty, Often using other forms of

evidence such as photos, medical reports, police reports, 911 transcripts, and other

29

witnesses. Ford and Regoli did not find an overall difl'erence between nO—drop versus
drop permitted prosecution in terms of subsequent reports of abuse. However, they
did find that women in the drOp-permitted group who elected to proceed with pros-
ecution were less likely to report subsequent abuse than women assigned no—drop
prosecution, whereas women in the drop-permitted group who dropped charges were
the most likely to report subsequent violence. Ford and Regoli called for more stud-
ies to understand these results, but speculated that one explanation might be that
victims were empowered by a combination of their ability to drOp charges and al-
liance with the criminal justice agencies. Davis et al. (1998) also studied the effect
of court disposition (dismissal, probation with treatment, and jail) on six-month re
arrest rates. Davis et al. did not find evidence Of a deterrence effect from prosecutor

outcomes.

2.5 Discussion

The current research on prosecutor decision-making does not address the general
issue of how prosecutor discretion with domestic violence cases is affected by the
prosecutor’s caseload size. The published studies each have one or more of the
following shortcomings. First, many studies on prosecutor’s decision making simply
did not consider the prosecutor’s caseload size as a factor. Second, the studies that
did consider the relationship between caseload size and decision making focused on
felony cases and studied the court’s caseload, not the prosecutor’s. The vast majority
of criminal domestic violence cases are charged as misdemeanors, not felonies. A
large portion of these cases are simply not prosecuted and handled informally outside
the court’s docket. SO it is likely that the caseloads of prosecutors and courts

differ in size and that court caseloads are not a good proxy for prosecutor caseloads

30

when it comes to studying decision behavior. Third, while a number of studies
suggested that there might be a more complicated and indirect relationship between
prosecutor caseload size and decision making, most simply treated each decision as
statistically independent of previous decisions. However, both the caseload pressure
hypothesis and professional norms hypothesis suggest feedback mechanisms that
involve information about previous decisions. In the caseload pressure hypothesis,
for example, previous decisions to file criminal charges would increase the caseload
and in turn discourage charges being filed in new cases. And in the professional
norms hypothesis, defense attorneys and prosecutors would be using previous case
dispositions to determine the likely outcome or going rate for a current case. In
both hypotheses, the determinants Of the current decision facing a prosecutor would
include state variables indicating outcomes of previous decisions. Both caseloads and
the going rate are likely to vary over time, making the determinants Of prosecutor

decision'making dynamic and not static.

2.5.1 Caseload pressure and caseload management

The question about whether caseload size affects prosecutor decision making is es-
sentially equivalent to asking whether prosecutors have ways of managing the size
of their caseload. Prosecutor decisions affect their caseload. Arrests contribute to
the caseload while dispositions remove cases from the caseload. The net effect of re-
ferrals and dispositions depends on how fast prosecutors dispose of cases relative to
the arrest rate. Denying prosecutions will have an immediate effect on the caseload,
whereas taking a case to trial will delay the disposition. If the prosecutor’s caseload
size affects prosecutor disposition decisions, then caseload size and decision making
will exist within a feedback IOOp, specifically, a caseload adjustment mechanism.

Conversely, if prosecutors try to manage their caseload, they will have to monitor

31

the size Of their caseload and use that information in the decisions that affect the
caseload. Thus the prosecutions depicted in Figure 2.1 On page 12 should be ex-
tended to include the relationships between the prosecutor’s caseloads and decisions

that affect case dispositions (see Figure 2.2)

Figure 2.2: Prosecution of Domestic Violence Cases

 

 

Arrests-I) Prosecutions—ID Sanctions

 

 

 

 

 

 

Dismissals

The major consequence Of this extension is that considering caseload as a po-
tential determinant of prosecutor decision making implies the existence of one or
more feedback loops. Feedback how are generally difficult to identify and under-
stand using linear methods like regression. The relationship between Prosecutions
and Prosecution decisions in Figure 2.2 is reciprocal in that one variable affects the
other and visa versa. Linear methods estimate parameters by fitting some observed
data to a hypothesized model, which is generally assumed to be Open loop in nature
in order to satisfy the mathematics for finding a solution. Reciprocal relationships
violate this assumption and result in misleading estimates. Methods like regression
and structural equation modeling do have ways of representing time variant, non-
linear variables, usually through the creation Of dummy variables, but they simply

represent descriptions of the time variant behavior, not the underlying mechanisms

32

generating that behavior (HedstrOm & Swedberg, 1998). By analogy, it would be
like modeling a plant’s growth over time curve instead Of the things that affect its
growth. While potentially helpful, one is not using a quantitative model tO specify
and test hypotheses about growth, but instead using a model to simply describe
the observations. What is needed is an account of how the underlying feedback
mechanisms generate the observed behavior. The problem Of understanding the
link between Arrests and Sanctions in Figure 2.1 on page 12 posed at the beginning
of this chapter can thus be re-conceptualized in terms of identifying the underlying

mechanisms regulating and adjusting Prosecutions.

2.5.2 Structure Of prosecutor decision making

Until now, most of the discussion on prosecutors and their caseloads has been at
the individual level. Individuals do display patterns in decision making, but what
is often of more interest is the structuring of that decision making. That is, there
is clearly some variation in how individual prosecutors make decisions. For exam-
ple, some prosecutors refuse to prosecute cases unless the victim OOOperates while
others take a much more aggressive stance against domestic violence and proceed
with evidence based prosecutions that do not rely on the victim’s COOperation in the
process. But, understanding the structure that constrains all prosecutors in their
decision making, whether they take domestic violence seriously or not, is just as
important because it ultimately represents the main limiting condition on develop-
ing an effective criminal justice system response for holding assailants accountable.
The structure of individual prosecutor decision making is arguably at the level the
prosecutor’s office, where one or more assistant prosecuting attorneys are involved in
criminal domestic violence cases. So the question becomes, how does a prosecutor’s

office manage its domestic violence caseloads?

33

Thinking of the prosecutor’s Office response to domestic violence in terms of
a caseload management problem has several advantages. First, it has immediate
relevance to prosecutor’s Office in terms Of day-to-day Operations, which both moti-
vates individual participation in a study and is likely lead to real-world application.
Second, understanding the problem in terms of caseload management helps us un-
derstand not only how to improve the criminal justice response, but also understand
its limits, i.e. what are the theoretical potentials of various caseflow management
policies? It might turn out, for example, that there is only a marginal potential
for improving the criminal justice response to domestic violence in terms of holding
assailants accountable. This would suggest (1) that communities should find alter-
native ways of holding the majority of assailants accountable, and (2) resources for
improving the criminal justice system should be focused more on improving victim
safety as Opposed to increasing assailant accountability.

Finally, viewing the prosecutor’s role in terms of caseload management helps
relate the issue to a class of more general problems in social science. For ex-
ample, caseload management problems are really a subset Of resource allocation
problems. In the context of service delivery systems, a resource allocation prob—
lem concerns how one allocates resources to provide services. When resources are
fixed, the resource allocation problem reduces to a caseload management problem
because caseload is the only variable that can be manipulated to balance resources
with services. But this poses a question: What if prosecutor’s Office resources are
increased, for example, through a grant to fund a domestic violence prosecution
unit? Will the increase improve the response? The answer depends on the nature
Of the resource allocation problem. If services are prOportional to resources, then
the answer is probably yes. But if the resource allocation problem is dynamic, more

resources might actually create new demands that cancel any potential benefits.

34

Highway construction in a congested metropolitan area is a classic example of a
dynamic resource allocation problem. Roads are built to alleviate traffic congestion.
But, reduced traffic congestion in a busy metropolitan area has the unintended con-
sequence Of increasing construction of commercial and housing real-estate, which
in turn increases traffic congestion to the original or higher levels. Understanding
the nature Of the resource allocation problem (and hence the caseload management
problem) helps identify and explain the unintended consequences of various policies
that a prosecutor’s Office might have with respect to prosecuting domestic violence

cases.

2.6 Conclusion

This chapter reviewed the social science research on the criminal justice systems,
covering deterrence eflects from arresting abusers, batterer intervention programs,
and prosecutions. It was then argued that changing practices of holding abusers
accountable involved, at least as presently implemented in the criminal justice sys-
tem response, a better understanding of the flow of cases from the arrest of abusers
under pro or mandatory arrest laws to the prosecution and referral of abusers to
batterer intervention programs. This led to the main question for this study: how

do prosecutors dynamically manage their misdemeanor domestic violence caseloads?

35

Chapter 3

Methods

3. 1 Overview

The previous chapter argued that to better understand the link between arrests
and referrals to batterer intervention programs, we need a better understanding of
how prosecutors manage their domestic violence caseloads. Previous research on
prosecutor decision making relied on methods that are best suited for studying lin-
ear causeefl'ect relationships. However, the effects of caseloads on case dispositions
and referrals arguably entails one or more adjustment mechanisms, that is feed-
back IOOps. This chapter describes the main methods that were used to generate
and analyze the numeric time series and study the feedback loops that structure
the complex relationships between how a prosecutor’s Office manages its domestic

violence caseload and case dispositions.

36

3.2 Single case study design

Though most prosecutor’s offices Operate under the same legal system within a state,
the Offices are largely autonomous with respect tO state oversight and the demands Of
their jurisdictions vary significantly from small rural counties to large metrOpOlitan
areas. Thus it is likely that prosecutor’s offices vary in how they balance the demands
of their communities with their available resources and priorities. Mechanisms that
prosecutors use to dynamically manage their caseloads are therefore likely to vary
significantly from Office to Office. The only way that one might assess the extent
Of variation is to consider each Office as an independent case, from which one can
later abstract commonalties and try to identify generic structures. Prior to making
any comparisons, however, one must have a reliable and generalizable method for
identifying and assessing hypotheses about how a prosecutor’s Office manages its
domestic violence caseload. Therefore, this study focused on deveIOping a robust
method for identifying and assessing hypotheses on caseload dynamics using a single

case study research design (Yin, 1994) Of a single prosecutor’s Office.

3.3 Studying dynamic systems

There are any number Of ways that one might go about studying and analyzing data
on the dynamics of a prosecutor’s office domestic violence caseload, from qualitative
studies to statistical analysis of numerical time series. There are, however, major
epistemological challenges tO consider when studying the dynamics of complex social
systems.

The first epistemological challenge is the misperception Of feedback in complex
dynamic systems. PeOple Often invoke event—based, Open-100p views of causality

that ignore feedback mechanisms and fail to appreciate the significance of delays,

37

nonlinearities, and the distinction between stocks and flows (Sterman, 2000, p. 27).
The tendency is to think of causation in terms Of physical action involving human

agency that stems from our prototypical metaphor of causation:

At the heart of causation is its most fundamental case: the manipulation
Of objects by force, the volitional use of bodily force tO change something
physically by direct contact in one’s immediate environment. It is con-
scious volitional human agency acting via direct physical force that is at

the center of our concept of causation. (Lakoff & Johnson, 1999, p. 177)

The further one moves away from the prototypical of manipulating Objects, the more
figurative the application of causation becomes. The effect of this tendency to see
physical action as prototypical causation is to grossly misperceive the relationship
between structures Of feedback 100ps and dynamic behavior, even when people have
full and complete information about the underlying structure Of feedback lOOps
(Moxnes, 2000). That is, one might have a good idea of what the structure is, but
not why or how it generates the dynamic behavior of interest.

One might try and meet this challenge by more formally specifying the rela-
tionships between variables in terms of quantitative relationships. But such an
approach comes with its own problems, which raises the second major epistemologi-
cal challenge when studying complex social systems: quantitative models Of complex
systems are inherently under-determined, meaning that they rarely have a solution
to a given set of equations and data. Or put differently, there are too many variables

for too few independent equations.

In the quantitative realm, engineers and econometricians have long strug-
gled with the problem of uniquely identifying the structure and pararn-

eters of a system from its Observed behavior. Elegant and SOphisticated

38

theory exists to delimit the conditions in which one can identify a system
from its behavior alone. In practice the data are too Scarce and the plau-
sible alternative specifications are too numerous for statistical methods
to discriminate among competing theories. The same data Often support
wildly divergent models equally well, and the conclusions based on such

models are not robust. (Sterman, 2000, p. 26)

This emphasis on uniquely identifying the structure and parameters dominates sta-
tistical thinkingl. It is arguably driven by what Lakoff (1987) calls the traditional
view Of Objectivism, part Of which is the idea that words, numbers, mental represen-
tations and so on, get their meaning from a correspondence with the external world.
Wittgenstein discusses this view as the picture theory of meaning (1921/1974). But,
this emphasis on correspondence is impossible to satisfy when it comes to complex

dynamic systems because such systems are generally under-determined.

3.4 System dynamics

System dynamics (Forrester, 1961/1999, 1971; Richardson, 1991; Richardson &
Pugh, 1986) takes an approach to studying complex system that differs from the
emphasis on identifying the structure and parameters of a system from behavior
alone. Part of the system dynamics paradigm is that numerical data represent only
a small fraction of our knowledge of complex systems (Forrester, 1980). PeOple ex-
perienced with some aspect of a system can Often have accurate mental models Of
specific parts Of a system, usually in terms of simple linear cause-effect relationships.
When their understanding of that part of the system is realistic, it is because they

are close to that part Of the system. System dynamics uses that “local” informa-

 

1For example, see Suppes and Zinnes’ (1963) work on measurement theory.

39

tion to simplify and deve10p the structure of feedback loops that might account for
dynamic behavior along with available numerical data, and then tests that hypoth-
esis that a given structure can account for the Observed dynamic behavior using
computer simulation. Knowledge about complex systems is not acquired through
trying to identify the structure or estimate parameters, but understanding which
structures are capable of explaining the dynamic behavior and why (in terms Of
explicitly formulated feedback mechanisms).

System dynamics modeling has been successfully used to study complex sys-
tems in case study designs. The term ‘system dynamics’ Often refers to a variety
Of theories and approaches to research on systems, but in this study, it means
the method pioneered by Jay W. Forrester in the 1960’s as industrial dynamics
(Forrester, 1961 /1999, 1971; Richardson, 1991; Richardson & Pugh, 1986). Sys-
tem dynamics is a method “for understanding certain kinds of complex problems,”
specifically dynamic problems where quantities change over time and involve the
notion of feedback (Richardson & Pugh, 1986, p. 1). Within system dynamics it-
self, approaches vary in their emphasis on quantification Of variables and reliance
on computer simulation for model analysis (Lane, 2001). The approach used in this
study emphasizes the role of computer simulation in the building and testing of a
system dynamics model.

The main purpose in system dynamics is to understand the relationships be-
tween the structure of feedback Mom and behavior over time. That is, how does
a particular structure of feedback loops reproduce a specific pattern of behavior—
Only being able to reproduce the behavior is not enough. In system dynamics, the
relationship between the structure of feedback bow and behavior can be formally
describe in terms Of feedback IOOp dominance (Ford, 1999). The general notion is
that the behavior of a variable is controlled by one or more feedback lOOps. The

40

feedback how that dominate a given variable at a given point in time are called the
dominant feedback lOOps. Complex behavior patterns emerge as the dominance of
feedback loops with respect to a given variable change over time. That is, feedback
dominance over a variable often shifts from one feedback IOOp to another. These
' shifts in feedback loop dominance are largely insensitive to variations in parameters
(Richardson, 1991). The dominance of a feedback IOOp can also be hidden by other
feedback IOOps. That is, the control that a feedback loop might exert on variable
might be masked by another feedback lOOp, called a shadow feedback IOOp. And to
complicate matters some more, shadow feedback lOOps can be nested. Intuitively,
the effect is that one might not notice the effects of a dominant feedback loop upon a
variable until one actively identifies and disables the shadow feedback lOOps. Thus,
system dynamics is usually used to understand the relationship between structure
and behavior in terms of feedback loop dominance as Opposed tO the more conven-

tional approach in statistics of parameter estimation.

3.5 Case selection

The prosecutor’s office selected for this study had several attractive features. First
and foremost, the Office was participating in a larger multi year evaluation study
Of coordinated community responses to domestic violence. Researchers at Michigan
State University had already established strong collaborative relationships with the
coordinating council, local shelter, prosecutor’s Office, and law enforcement. Strong
collaborative relationships with stakeholders would be critical to gaining access to
key informants and numerical data. Second, researchers were already collecting,
cleaning, and analyzing substantial amounts of secondary data from various agen-

cies, including shelters, law enforcement, and the prosecutor’s Office. That meant

41

potentially having several measures of the same variable from which one could assess
the reliability. Having access to multiple data sets also meant having more informa-
tion to use for calibration and testing of models. This would lessen the amount of
speculation required for certain trends and model parameters.

A third feature of this prosecutor’s office was that it served a rural county with
approximately 60,000 peOple. That might at first seem an undesirable trait in a
study, but it provided an Opportunity tO solve the main barrier to conducting future
multiple case study designs using system dynamics and involving small pOpulations.
In the context of time series analysis, the small sample sizes of rural counties and
other small pOpulation phenomena (e.g. rare diseases) imposes a major limitation
on the number of data points available for statistical analysis. Specifically, in small
populations events happen much'less frequently than with larger populations. SO
one generally has to aggregate over larger periods of time than larger populations
in order to attain adequate sample sizes for statistical analysis. One might, for
example, be forced to aggregate the arrests over years instead Of months or weeks.
Aggregating over larger periods of time reduces the number of data points one has
across time. This is not a problem if the phenomenon under study is stable over
time, but if one is interested in the dynamics over time, then aggregating over larger
time intervals smooths out changes. And if the time intervals are too long rela-
tive to how fast a quantity is changing in time, one might not see indications of
the phenomenon at all. One might try to avoid this problem by aggregating data
from several small communities. But such an approach would essentially presup-
pose that their aggregated representation reflected a common underlying structure.
There are many ways that small populations can vary, from economic conditions to
culture and geography. This problem of small pOpulations is major methodological
challenge facing any future multiple case study design that tries to look at struc-

42

tural differences of responding to domestic violence between various communities
and pOpulations. Solving this problem would make it much easier to demonstrate
the feasibility of such a multiple case study design and work with more diverse com-
munities, including both rural and metrOpOlitan communities, as well as smaller

suprpulations.

3.6 Violence against women database

The prosecutor’s office violence against women (VAW) database was the main source
of case data for demographic comparisons and construction of numerical time series.
The prosecutor’s Office maintained the VAW database in Microsoft Access, which
was imported into R for data manipulation and statistical analysis. Text variables
were coded and dates were converted to POSIXlt representations. Some variables,
like the reason for denial or dismissal, contained text descriptions along with dates
of when cases were denied or dismissed. Such text descriptions were parsed for date
formats, and converted into POSIXlt representations.2 POSIXlt dates had to be
corrected for Y2K. Ages Of victims and suspects were calculated as the difference
between the date of Offense and date Of birth.

The VAW database (n=6358) contained a subset of the prosecutor’s Office cases,
including records of personal protection orders (n=1029), 91 1 calls involving violence
against women for the county (n=2821), warrant requests (n=1993), and 48-hour
reports by police departments (n=474) covering offenses from approximately Jan-
uary 1, 1994 through June 10, 2002. However frequency distributions of types of

cases by year suggested a pattern of inconsistent data entry before January 1, 1998.

 

2POSDth is a specific way of representing dates and times as a long named list of vectors
representing seconds, minutes, hours, days of month, months Of the year, years, day of week, day
of year, and daylight savings flag.

43

The primary focus on this research was on the prosecution of assailants, all of which
started as warrant requests. Thus the initial subset (n=1’457) included warrant re-
quests with valid dates Of ofiense on or between January 1, 1998 and December 31,
2001.

Table 3.1: Distribution of Records by Year and Type of File in Violence Against
Women (VAW) Database

 

 

Year 48HR 911 PPO1 WARRANT
< 1995 0 o 0 2

1995 0 444 o 168

1996 0 535 0 46

1997 5 257 2 33

1998 113 0 152 229

1999 85 994 193 235

2000 123 588 162 240

2001 95 0 121 200
20022 49 0 63 82

 

1Based on date that PPO was authorized.
2Limited to records through June 10, 2002.

The VAW database contained first names, last names, and middle initials along
with sex, date Of birth, and address for both suspects and victims. A unique list of
individuals was generated by first generating a unique sorted list of concatenated
string of the name and date Of birth for both suspects and victims with each row
being assigned a unique personal identification (PID) number. Since the list was
sorted by string names and dates of birth, it was relatively easy to identify multiple
rows that appeared to refer to the same unique individual. In such cases, string rep-
resentations of the individual were assigned the first PID number of the matching

string representation. Victim and suspect names were then replaced with corre

44

sponding PID numbers (n=2050 for 1457 records of warrant requests). Two records
were eliminated because names were missing (leaving a total of 1455 records Of war-
rants). Another 17 records were drOpped from the analysis because their dates were
obviously invalid, for example, a record having a dismissal date that came after the
date that a plea Offer was accepted. The main variables of the resulting individual
data matrix, I DM AT (n=1438), is shown in Table 3.2. Basic descriptive statistics

were run on I DM AT for the all warrants and selected subsets.

3.7 Estimating rates and times for state transitions

Each record in I DM AT represented one warrant request. An individual who was
arrested for a probation violation would appear again as another warrant request.
Using the PID numbers, it was possible to estimate the number of times individuals
appeared in the database as well as the number of days between their appearances.
Such statistics could be used to estimate recidivism rates, re—victimization rates,
commutative hazard functions, and mean times to failure. For example, some indi-
viduals were recorded as victims in some records and suSpects in others. Rearrest
rates might also depend on the type of sanction. At first, each set of transition statis-
tics was calculated manually. Each set of transition statistics usually led to more
questions about alternative explanations for the observed frequencies and transition
times, which in turn led to writing another calculation. It quickly became apparent
that transition patterns of individuals through the prosecutor’s Office could be fairly
complex in their own right. To facilitate a exploration of the possible patterns, a

more general approach was required.

45

Table 3.2: Variables in the Individual Data Matrix (I DM AT)

 

 

Variable Description

File/Type Type of file

DateOFF Date of offense

Charge Arrest charge

PolDept Police department
Prosecutor Prosecutor

SPID Suspect’s PID number
SDOB Suspect’s date of birth
SAGE Suspect’s age

SRace Suspect’s race/ethnicity
SSex Suspect’s sex

Rel'I‘ype Victim-suspect relationship
VPID Victim’s PID number
VDOB Victim’s date of birth
VAGE Victim’s age

VRace Victim’s race/ethnicity
VSex Victim’s sex

A.B’I‘ype Type of assault
DatePOA Date plea offer accepted
’Iiial'Iyp Type of trial

Judge Judge

Dispo Disposition
Dismissal.Denial.Reason Reason for denial/ dismissal
Probmnth Months of probation
DOSmnth Months of delay of sentence
CGroup Counseling group referral
DateTRL Trial date

DateDenied Date denied
DateDismissed Date dismissed
DateAUTH Date warrant authorized
Date.VMeet Date met with victim

J aildys Jail days

 

46

3.7 .1 Modeling state transitions

The solution was to model individuals’ state transitions with a finite state machine
(FSM), which is essentially an abstract way to describe a system with a finite number
Of states and finite number of transitions from one state to another state. Figure
3.1 shows a diagram of a simple FSM with three states (So, 01, and 0,.) and one
condition (a) that triggers transitions from the initial state So to 01, and from Olto

0n, and then from 0,, to 0".

Figure 3.1: Finite State Machine

a a

O O O a

Finite state machines, automata, and Turing machines are typically used in com-
putation theory and such applications as computer language compiler design (Lewis
& Papdimitriou, 1981). Finite state machines have also been developed and recently
applied in various engineering applications for modeling and diagnosing system fail-
ures (Ozveren & Willsky, 1990; Sampath, Sengupta, Lafortune, Sinnamohideen, 8!.
Teneketzis, 1995; Sampath, Raja, Lafortune, Sinnamohideen, & Teneketzis, 1996;
Rczé & Cordier, 2002). Table 3.3 shows a simple description of a finite state ma-
chine corresponding to Figure 3.1 that was used for calculating the state transitions
associated with assailants’ rearrest. Three states are specified: an initial state So
that all individuals start out in by default, the state 01that individuals end up in

after their first appearance as a suSpect, and the state Onwhich move into after

47

subsequent Offenses. Transitions from one state to another state are triggered by a
condition being satisfied. In Table 3.3, individuals move from one state to another
state when the individual’s PID number is equal to the suspect’s PID number for a

given record.

3.7 .2 S—language implementation Of finite state machines

Functions were then written in R, a variant of the S programming language (Becker,
Chambers, & Wilks, 1988; Venables & Ripley, 2000), which took a description such
as that in Table 3.3 and applied it to a subset of I DM AT to generate a table of
transitions along with their transition times. The output could be used to calculate
statistics on transition times and construct transition matrices. FSMs were used
for calculations of first Offense-repeat offense transitions, which could be further
analyzed by the type of sanction imposed and type of referral to a counseling group.
The FSM depicted in Figure 3.1 and Table 3.3 was used to identify cases that
were first Ofl'enses and repeat Offenses I DM AT. FSMs were also used to calculate
the transitions from one type of victim-offender relationship to another type of
relationship, transitions from one type of offense to another type, and test for the

reliability of demographic variables such as sex and race/ ethnicity.

3.8 Battering tactics

The A.BType variable in I DM AT contained a text description of the types of
battering tactics used during the assault. Initial inspection of frequency distributions
suggested that there might be differences in the types of tactics reported. Many
descriptions included multiple tactics, typically separated by a forward slash (“/”).

These tactics were parsed into a sorted list Of tactics, with each row corresponding

48

Table 3.3: Finite State Machine Example

Element Example

 

States SO: 01: 0n

 

Condition Expression

 

Conditions
a PID==SPID

 

S.- Condition Si+1

 

'IYansition table

 

to one tactic. This list was then cleaned to remove Obvious duplicates. For example,
“Threw Object” and “threw object” were both recoded as “THREW OBJECT”. The
result was a list of 279 unique descriptions, 15 of which appeared to name more
general categories (see Table 3.4).

Several methods were considered for coding the battering tactics in hOpe of
finding some differences between either warrants involving female suspects and male
suspects or differences between first Offense suspects and repeat Offense suspects.
One approach would be to manually recode each description in terms of an existing
scale or published frequency distribution, but this would arguably have made it
difficult to assess what the resulting distributions represented since many records
contained descriptions that did not easily fit into existing coding schemes. Instead, a
single large indicator matrix Of tactics was constructed with each row corresponding
to a record in I DM AT and each column corresponding to one of the 279 unique

descriptions resulting in TACM AT (6358 rows by 279 columns). One could then

49

Table 3.4: Major Categories of Battering Tactics

 

 

Category % of all cases
ARGUED 5
BIT 22
CHOKED 12
SEXUAL ASSAULT 9
GRABBED 10
KICKED 16
PULLED 2
PUNCHED 19
PUSHED 34
SLAPPED 27
STALKED 4
THREATEN ED 16
THREW DOWN 1
THREW OBJECT 5
USED A WEAPON 1

 

use TACM AT in a cluster analysis to generate an atheoretical set of classifications
that might identify combinations of tactics that corresponded to different types
of suspects (e.g. victims versus assailants, first offenders versus repeat offenders).
Or, one could use an existing theory and recode records from TACM AT. While
simulations demonstrated the computational feasibility Of running a cluster analysis
on TACM AT, the results were disappointing because police Officers had already
coded their police reports in terms of legal criteria for an arrest. That is, instead
of describing what happened in terms of the specific battering tactics, the fields
appeared to contain labels that corresponded to the legal criteria that police officers
might have used to justify an arrest decision. For example, while there were some
descriptions Of battering tactics that made distinctions about the type of object

thrown, most simply labeled such behavior as “threw Object.”

50

3.9 Numerical time series

I DM AT was a case or individual level data matrix that included dates of certain
critical events. These dates could be aggregated over time intervals to produce
numerical time series of rates (e.g. number of events per unit time). Preliminary
inspection of the I DM AT suggested that aggregating events (arrests, warrant au-
thorizations, denials, dismissals, etc.) over months would be sufficient for identifying
and representing the time variant behaviors involved with how a prosecutor’s office
manages its domestic violence caseload. This was based on the assumption that the
shortest time constants of interest would be on the order of 30 days since the mean
number of days from the date of the offense for a warrant being approved was ini-
tially estimated to be 31 days with the mean number of days from authorization to
plea offer being accepted and dismissed being 53 days and 96 days respectively. Ag-
gregating events on months would have allowed a sufficient sample size to avoid the
problems associated with sparse time series. However, using the median as a more
robust estimate of the central tendency and plotting the cumulative distributions
over days from ofl'ense led to a starkly different and more realistic picture. Over
50% of the warrants were being authorized within a day, 50% of cases were being
plead in 29 days or less after the arrest, and 50% of dismissals were happening in 70
days or less after arrest. With less than one warrant request per day, aggregating on
days would mean having to deal with sparse time series (Figure 3.3c is a simulated
example of sparse time series) as the number of cases per day jumped randomly
between values of 0 and 8. Aggregating on weeks would avoid the problem of having
zeros as discontinuities, but still suffer from not having enough cases. Specifically, as
the rates (number of events per unit time) that one would be aggregating on became

smaller, the totals per unit time would become increasingly sensitive to both the

51

size of the aggregating bins and their origin of the aggregating bins (Hiirdle, 1990).

3.9.1 Illustration Of sparse time series

The impact of smaller rates on the sensitivity of aggregations to bin size and their
origin can be seen through a series of simulations where the expected number of
events per unit time decreases. Figure 3.2 shows three simulated time series of the
rate or expected number of cases per day with respective overall means of 100, 10,
and 1 (note that, going from left to right, the vertical scaling decreases by a factor
of ten for each graph). In the case of IDMAT, the actual mean number of arrests
was on the order of one case per day.

The number of events per unit time is always an integer value equal to or greater
than zero. This is typically modeled as a Poisson distribution. One can generate a
simulated time series of observations by randomly sampling one case per unit time
from a Poisson distribution with the expected rates corresponding to the time series
shown in Figure 3.2. Specifically, 0m(t) = P(Am(t)) where, 0m(t) is the observed
value at time t, P(/\,,,(t)) is a random value sampled from the Poisson distribution
with a rate of A",(t). The rate Am(t) is a function of time and the mean expected
value m such that Am(t) = m+ 0.1 -m ~sin(t - 21r/ 1461), where m is the overall mean
(i.e., 100, 10, or 1)

The resulting noisy time series are shown in Figure 3.3. As m gets smaller, the
effects of the distribution being bounded at zero become more pronounced. Figure
3.3a would typically be seen as a noisy but continuous time series. But as m gets
smaller, the result is something that looks much more discrete with quite a few days
with zero cases. Figure 3.3c would be a good example of a sparse time series.

When the number of events per unit time is relatively high, aggregating the

noisy time series over quarters results in a reasonable approximation of the original

52

Figure 3.2: Original Expected Rate of Cases per Day

 

 

 

 

 

 

 

 

 

 

 

 

.531 E
In In
.9: 2
>~
5 s
is 3.8.
a s.
8:. , , , . as: . . . .
1998 1999 2000 2001 2002 1998 1999 2000 2001 2002
Tine Tine
(a) Mean = 100 (b) Mean = 10
$2.
3.
5‘
is.
I.
an
0
SI
°19'98 1999 2000 2001 2662
Time
(c)Mean=1

53

Cases per day
140

so

120

100

Figure 3.3: Noisy Time Series

 

 

 

 

   

 

 

I a.
Em-
E ..
8
g 531
0
IO‘
Lf—T—lé—fi_ WV
1998 1999 2000 2001 2002 1998 1999 2000 2001 2002
This Time
(a) Mean = 100 (b) Mean = 10

 

Cases per day
2 3 4 5 6

1

  

 

 

o-
1998 1999 2000 2001 2002

(c) Mean = 1

54

expected values, but not so for sparse time series. Figure 3.4 shows the result Of
aggregating the counts over quarters. The thick solid line Shows the original expected
values, the thin solid line shows the aggregated counts over quarters (divided by the
number of days per quarter to standardize the values), and the thin dashed line
shows the effect of offsetting the origin of the bins by as little as nine days.3 Figure
3.4a illustrates how aggregating the number of cases per day on quarters results in a
reasonable approximation of the original expected values and is insensitive to minor
variations in the origin of the aggregating bins. However, as m gets smaller, the
aggregated time series does a worse job of approximating the original time series
and becomes more sensitive to variations in the origin of the bins. Figure3.4b might
still be a reasonable approximation, but one would be hard pressed to identify the
original time series in Figure 3.4c. Figure 3.4c also shows how even a small change
in the origin of the bins of only nine days can affect quarterly totals, especially the
first, second, and third quarters of 2000. I

The effects of small tirne series on aggregated values get worse as the size of the
aggregating bins get smaller. Figure 3.5 shows the results Of aggregating the num-
ber Of cases over months which are, again, divided by the width of the aggregating
bin to standardize the values. While Figure 3.5a still appears to be a reasonable
approximation of the original time series, Figure 3.5b is starting to become ques-
tionable and showing more effects from varying the origin of the bin size. Figure

3.5c is unrecognizable.

 

3The choice Of offsetting the origin by nine days is arbitrary. The main point is that the Offset
is small relative to the width of the bins.

55

Figure 3.4: Quarterly Aggregated Time Series

 

 

 

 

 

 

 

 

 

 

m. -4
° F

2* °-.

584 .' s“? .
L- is

is I?
8d Q

., sI

°’ 1998 1999 2000 2001 1998 1999 2600 20K
Tim Time
(a) Mean = 100 (b) Mean = 10

 

 

 

 

 

56

110

l

Memmmporday
100 105

95

Figure 3.5: Monthly Aggregated Time Series

 

 

12

11

Moancasesperday
10

9

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

t.. 0‘
1998 1999 2600 2601 2002 1998 1999 2000 2001 2002
Time Time
(a) Mean = 100 (b) Mean = 10
x.
n.
5'94.
85,.
is.
ice.
0
34
vs.
0
1958 1699 2600 2601 2602
Time
(c)Mean=1

57

3.9.2 Conventional approaches to handling noisy data

Approaches to handling noisy time series fall into three general classifications: fil-
tering, smoothing, and prediction (Anderson & Moore, 1979). Filtering works in
real time, trying to recover the original value from the noisy signal 0(t) at time t.
The tuner on a radio or television is a classic example of a filter. Smoothing uses
a range Of values, (t — At, t + At), to estimate 0(t). There are many approaches
to smoothing, but perhaps the most familiar is a moving average. Prediction uses a
set of past values, (t — At, t), to estimate 0(t) for a set of future values, (t, t + At):
for example, by fitting an equation to past values in order to predict future values.

When generating reference modes from real data, one is generally concerned with
identifying trends and working with time series spanning the entire time horizon.
That is, for each point in time t, one can use information coming both before and
after t to estimate some value at t. Thus, one is generally looking to. select a method
for smoothing noisy time series. If one knows a priori the underlying probability
distribution of a given time series, then one can apply regression techniques to
estimate the parameters of the underlying distribution. Some variables in this study
might fit one of the many available parametric probability distributions. But this
cannot, in general, be assumed because of the nature of feedback.

One possibility is the use of non-parametric techniques to estimate the density
distribution (Hirdle, 1990; Scott, 1992). Such techniques do not assume a specific
underlying distribution, but rather, are based on the empirical distribution of a
given time series. However the application of smoothing techniques introduces some
problems. Smoothing always distorts oscillations in time series in one or more ways.
Frequencies may be entirely eliminated, peaks flattened out, and delays introduced.

Smoothing also introduces the problem of truncating the first and last parts of a

58

time series since most procedures use an interval of values to estimate a given point.
Thus, one is often not sure whether or not some impOrtant features have been
removed by smoothing the time series, or whether the features that one is trying to

model are in fact, not just artifacts of the smoothing algorithm.

3.9.3 Solution to the sparse time series problem

In system dynamics modeling, one is generally concerned with identifying and study-
ing the underlying structure generating a particular pattern of behavior over time.
One uses numerical time series, not to identify the system of equations as one might
in traditional time series modeling, but to test the model’s behavior against real
data. The purpose of such a test is generally not to see whether or not the model
yielded the precise values of the Observed data, but whether the overall behavior
pattern is realistic. That is, one can make a distinction in system dynamics between
the real numeric values and realistic numeric values of a variable. The real numeric
value of a variable is the actual value that the variable takes on at a given point in
time. If the variable is the number of warrant requests on a given day, then there is
a real theoretical numeric value for the expected number of warrant requests on that
day. The problem of estimating the density distribution of the number of warrant
requests per day is concerned with estimating that numeric value, and it is this
distribution that is sensitive to the particular technique used to smooth the time
series. A realistic numeric value, however, is something more general. For any point
in time, there can be many values that would be realistic, only one of which is the
real numeric value of that variable at that time.

A good robust model should be able to describe the dynamics over a range of
situations. Given a variety of inputs, the model should be able to reproduce corre-

sponding outputs that are realistic. In system dynamics, researchers often test their

59

models using a variety of inputs to explore the model’s behavior over extreme condi-
tions, oscillations, and random perturbations (Forrester, 1961 / 1999, 1971; Forrester
& Senge, 1980; Richardson & Pugh, 1986; Sterman, 2000). Careful inspection of
the outputs and feedback loop behavior often reveals structural flaws or important
insights into the model’s behavior. These inputs are typically idealized in some form
as step functions, pulses, sine waves, or random samples from a parametric distribu-
tion. But there is no reason why a robust model should not also be able to handle
a much wider range Of inputs, including the results of not just a specific smoothing
algorithm, but the results from an entire collection of smoothing algorithms.

More specifically, a robust system dynamics model should be able to produce
reasonable approximations of smoothed numeric time series outputs given corre-
sponding smoothed numeric time series for an input, provided that both the input
and output numeric time series have been smoothed using the same algorithm. That
is, a robust system dynamics model should be able to reproduce the qualitative be-
havior of two different time series, each smoothed using a different algorithm or with
difl'erent smoothing parameters, provided that the model’s input (if there is any)

was also smoothed using the same algorithm and smoothing parameters.

3.9.4 Rates and stocks numeric time series

Rates were calculated by aggregating cases by dates of key events from 1 DM AT.
To generate time series for first offenses versus repeat offenses, or for each type of
relationship, the time series were calculated from subsets of I DM AT. The resulting
rates were stored in a matrix of time series, TSM AT, with various suffixes to indi—
cate the subset (e.g. TSMATall, TSM AT f irst, TSMATrepeat). The generation
of time series for stock variables was more complicated. Unlike rates, time series

of stock variables had to be calculated by first specifying the date variables that

60

indicated entering and exiting of the stock and then counting the number of cases

that were in that stock for each day (see Tables 3.5 and 3.6).

Table 3.5: Times Used to Generate Caseload Statistics

 

Variable Description

 

to Date of offense

t1 Date warrant was denied or authorized

t2 Date warrant was authorized

t3 Date of plea offer was accepted, case being dismissed, or trial

t4 Date of plea offer was accepted, case dismissed, case denied, or trial

 

Table 3.6: Entry and Exit Times for Caseload or Stock Variables

 

Range Stock variable
[t0, t1] Warrants

[t2, t3] Cases

[t0, t4] Total

 

 

All time series generated in R were then exported to a Vensim compatible text
file. Smoothing algorithms were implemented as separate Vensim models, which
read the original input and saved the output to data files that could be read by the
Vensim system dynamics models. Smoothed data sets were generated and compared
for first and third order exponential smooths with 30, 60, 120, and 180 day delays.
The mean values of the sparse time series were at first used as initial values in the
smoothing models in order to minimize differences between the cumulative totals
of the original and smoothed data. This approach was subsequently abandoned
as (a) starting with initial values of zero in the smoothing algorithm corresponded
to stocks in the system dynamics model variables being initially empty, and (b)
the resulting step input response of the system dynamics model corresponded to a

realistic step input associated with the prosecutor’s office establishing a specialized

61

domestic violence prosecution unit. Figure 3.6a shows a comparison between the
raw time series for warrant requests and the results of smoothing the times series
using a third-order 120 day delay exponential filter. The solid (vertical) lines show
that the warrant request time series is a Sparse time series, while the dashed line
shows the smoothed version of the warrant request time series. This smoothed time
series can be considered an estimate of the expected value of the number of warrant
requests per day. The mean of the sparse time series and smoothed time series
should be equal (the extreme of a smoothed time series would simply be a constant
value equal to the mean). Figure 3.6b shows the effects of varying a smoothing
parameter, specifically the delay, from 30 to 180 days. Notice that as one increases

the delay, the time series appears smoother with fewer high frequency oscillation.

3.10 Building system dynamics models

There were three major phases of constructing the system dynamics models. The
goal of the first phase was to build the smallest models that could reproduce the
total caseload over time. These started out as single-stock models that represented
dispositions as (a) strictly a function of caseload, (b) strictly a function of case at-
tributes, and (c) a mixture of caseload and case attributes. These models were only
descriptive in nature and did not provide any account of the underlying mechanisms.
The second phase of modeling focused on building the initial baseline model, which
essentially provided the first full dynamic hypothesis of how the prosecutor’s office
managed its domestic violence caseload. This model was used to identify key stock
variables, refine the organization of data by subgroups, and deve10p questions for
the initial interviews with key informants. The third phase of model building used

data from key informant interviews to revise the model and provide additional infor-

62

Figure 3.6: Comparisons of Warrant Request Time Series

(in cases per day)

 

NW

 

 

 

I I III‘

 

 

  

.II III III .I I III ‘IIIIIII. I r ‘ , Il
1998 1999 2000 2001
Year

CO

 

 

Raw time series
Smoothed time series (120 day delay) -----------

(a) raw versus smoothed time series with 120—day delay

 

‘
V / \ \ ’
/ ‘ \ I
/ / \ y x‘ ’
I
//’

 

 

 

 

 

 

1998 1999 2000 2001
Year

Smoothed time series (30 day delay)
Smoothed time series (90 day delay) __________________________
Smootbdtimesaies (120dnydelny) —— _ __ __ _ _ _
Smoothed time series (180 day delay) — ____________

 

(b) Smoothed time series with 30, 90, 120, and 180 day delays

63

mation on various functional relationships between variables and model parameters.

A modular approach was taken in the development of the baseline and revised
models. That is, submodels were developed and tested separately, i.e. partial-
model testing (Homer, 1983). That is, submodels or basic units of structure were
deveIOped, each entailing a dynamic hypothesis that the structure was capable of
reproducing the Observed time series behavior. Where inputs like arrests or warrant
authorizations were required from earlier stages of the prosecutor’s caseflow, real
inputs were used to drive the submodel and the simulated outputs were compared
against the real data. Thus, for example, real arrest rates were used to drive the
warrant processing submodel and the simulated results Of authorization and denial
rates compared against the real data. Such tests frequently revealed flaws in the
submodel’s formulation, which were subsequently revised and tested again. When
the submodel was structurally capable Of generating a reasonable reproduction of
the real data, uncertain model parameters were calibrated against the real data.
Calibrated parameters that were unrealistic indicated additional problems with the
submodel’s structure. After a submodel finally succeeded in reproducing the refer-
ence mode, additional models were built, often based on the first submodel. These
variations of the same submodel could then be compared in order to assess the hu-
pact of various modifications on the submodel’s ability to reproduce the reference
mode. In many cases, simplifying models had a negligible impact on the submodel’s
performance.

The use of partial-model testing has two main advantages over whole model-
testing during the formulation of a model. First, it minimizes the amount of in-
formation used to calibrate the model. As models get larger, more parameters are
introduced, which need to be calibrated and tested. In large models, parameters in

one part of the model can be adjusted to compensate for behaviors in another part

64

Of the model. This is what one would expect in large complex systems. The problem
in model building, however, is that with the available software, it is relatively easy to
fit large models. The price for fitting large models is that one does not know to what
extent the parameters in one part of the model are compensating for other parts of
the model. That is, the larger the model, the more Opportunity one has to adjust
constants in such a way that the simulated behavior more accurately reassembles
the real behavior. Partial-model testing avoids this by focusing on small submodels
with a few parameters and thereby limiting the number of parameters and interac-
tions. Thus, partial-model testing uses less information during model deveIOpment
and allows whole-model testing to reveal new structural flaws. The second main
advantage of partial-model testing is that it generally leads to a much easier devel-
Opment path and understanding of why a model behaves as it does. Careful study of
a single submodel, including dimensional consistency tests, testing and calibrating
against real data, and sensitivity analysis will lead to a more thorough understand-
ing of each component. It also is generally much easier to isolate the problem in a
submodel than trying to trace the problem down at the whole-model level.
Whether working on a model or submodel, the basic approach is the same. Initial
work focused on laying out the basic stock-and-flow diagram along with formulating
the basic relationships between variables. The dimensional consistency of units in
the equations frequently gives some important clues as to how an expression might
be formulated and provides one way to structurally check the model (Richardson
& Pugh, 1986). Thus all formulations included units and dimensional consistency
checks. Simulations were then used to explore and test the behavior of the model,
which often led to more modifications. Some models were unable to reproduce
the intended behavior after several iterations, which often indicated after further

analysis reasons for ruling out that particular structure. Models that passed this

65

stage of deveIOpment and appeared capable of reproducing the qualitative behavior
over time were then calibrated to smoothed data for cOmparisons. Models were
calibrated in Vensim by specifying the one or more output variables to match and
the model parameters to vary. Since output variables have different magnitudes, for
example warrant requests are on the order of 1 case per day while caseloads are on
the order of 100 cases, the output variables to match on were initially weighed by
dividing the time series values by their standard deviation. Better results seemed to

be achieved, however, by dividing each time series by their average value over time.

3.11 Key informant interviews

The second phase of model building generated many questions about realistic values
for certain parameters and critical relationships between relationships. It was also
important to establish whether or not patterns identified in the numerical time series
were valid from the perspective of stakeholders.

A snowball sampling procedure was used to identify key community informants,
who were selected on the basis of their expertise with domestic violence and pros-
ecution of domestic violence cases. Two initial contacts were made to a domestic
violence coalition coordinator and assistant prosecuting attorney. These key infor-
mants suggested other potential participants. A total of five key informants from
the community were interviewed, and included victim advocates, domestic violence
coalition coordinators, assistant prosecuting attorneys, and legal assistants. All five
key informants had experience working with victims of domestic violence and had
attended training workshOps specific to working with domestic violence.

A list of questions from the baseline model was prepared prior to the initial

contact with a key informant. The key informant was then contacted via telephone

66

or email to schedule an initial telephone call. The first part of the initial telephone
call included the reading of the consent script. Participants provided verbal consent
by continuing with the interview. The date of their consent was recorded in a log,
along with their contact information, participant number, agency, and total number
of interview hours. Interviews were unstructured with the list of questions serving
as a general guide. Handwritten notes were taken during the interview and then
typed to disk after the interview. Analysis of the interview notes was informal, and
involved reading the handwritten and typed notes, and identifying key informants’

descriptions of trends and feedback mechanisms in a laboratory notebook.

3.12 Conclusion

This chapter provided an overview of the methods used to generate and analyze the
numeric time series along with summary of the system dynamics approach taken
in this study. Specific attention was paid the construction Of smoothed time series
from sparse time series that could be used to generate the reference modes for the
various system dynamics models. The chapter also discussed the use of finite state
machines as a way to model the transitions of individuals within a social service

delivery system.

67

Chapter 4

Results

4.1 Overview

This chapter presents and discusses the results of this study. The first part of
the chapter focuses on documenting the violence against women (VAW) database.
Demographics, case attributes, and dispositions are considered with respect to all
the warrants in the VAW database, those selected for analysis, and first and repeat
arrest subsets. The second part of the chapter briefly describes three descriptive
models and compares how well they are able to reproduce the behaviors of the
real data. The third part focuses on the deveIOpment of the baseline model, going
through each submodel, its variations, and performance in response to real inputs.
The chapter then continues by evaluating the performance of the baseline model and
presents the results from sensitivity analyzes and analysis of patterns in feedback
loop dominance. The fourth section diagnoses some of the problems in the model’s
behavior in terms of identifying an additional positive feedback loop between first
time arrests and new cases. This is followed by a brief summary of the key informant

interviews and presentation of the revised model.

68

4.2 Demographics

Based on 2000 US. Census statistics, the jurisdiction of the prosecutor’s office cov-
ered a county of approximately 70,000 peOple. About 55,000 persons were 15 years
of age or older. Although criminal justice cases and individuals represent different
units of analysis, comparisons between the distributions of census demographics and
case demographics indicate difl'erences in arrests rates. That is, if the arrest rates
were the same over all groupings of individuals, then one would expect the demo-
graphic distributions of rates to be proportional to the demographic distributions
Of census data. One can make similar comparisons between different subsets of the
prosecutor’s Office’s data, e.g. between first arrests and repeat arrests. Table 4.1
through Table 4.3 show the results of comparing the distribution of census demo-
graphics against the demographics for all warrants, those selected in the analysis set,
first arrests, and repeat arrests, which are respectively selected with the following
binary variables: Warrants, Inset, First, and Repeats. These variables take on the
value of true if the case is in that specific set and otherwise false. Thus, all the
cases within the VAW that start out as warrant requests have a true value for the
variable Warrants. Inset indicates all the cases that are in the analysis set, which
is a subset of all the cases selected by Warrants. Firsts and Repeats are variables
that respectively indicate cases that are first domestic violence arrests and repeat
domestic violence arrests within the subset of cases indicated by Inset. Since a case
that is Inset is either a first domestic violence arrest or a repeat domestic violence
arrest, the union of all cases indicated by Firsts and Repeats should be identical with
Inset. The set relationships between cases indicated by Warrants, Inset, Firsts, and
Repeats is shown in Figure 4.1.

Differences between the demographic distribution of warrants and those selected

69

Figure 4.1: Subsets of Violence Against Women Database

VAW database
III-6358

 

 

 

 

 

 

for the analysis would suggest problems with (a) reliability of coding and data entry,
or (b) missing data mechanisms that correlate with demographics. Comparisons
between all warrants and those in the selected set for analysis (“inset”) in Tables 4.1-
4.3 reveal that any such discrepancies can be treated as negligible. Since first time
arrests are a unique one-time attribute of individuals, the demographic distribution
of suspects in first arrest cases is identical to the demographic distribution of suspects
at the individual level. That is, the census distributions are directly comparable to
the first arrest suspect distributions.

Overall, there were more male suspects than female suspects, and more female
victims than male victims (see Table 4.1), which would be consistent with the general
understanding of domestic violence that it is primarily committed by men against
women. Note that female suspects include battered women who were arrested by
the police and women who were abusing other women in same sex relationships, and

male victims includes cases where the victim was arrested and men who were being

70

abused by other men in same sex relationships. There was little variation between
the distributions of sex across the different subsets. HoWever, repeat arrests had a
higher prOportion of male su8pects and female victims than warrants, those in the
set, and first arrests.

Table 4.1: Distribution of Sex by Suspects and Victims Across Subsets of Violence
Against Women Database

 

 

 

 

 

 

 

 

 

Census Warrants Inset First Repeats
Suspects Victims Suspects Victims Suspects Victims Suspects Victims
Female 49% 22.9% 74.4% 23.2% 73.9% 25.2% 72.2% 16.1% 80.3%
Male 51% 77.1% 25.6% 76.8% 26.1% 74.8% 27.8% 83.9% 19.7%
Total 100% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0%

 

 

Warrants included information about race or ethnicity of the victim and suspect.
Table 4.2 compares the distributions of suspects and victims by all warrants, those
in the analysis set, first arrests, and repeat arrests. Whereas census figures treat
Hispanics as an attribute separate from race, warrants made no such distinction.
Thus the census race category of white is not directly comparable to warrant race
category of white non-Hispanic. Furthermore, with a small population that is 96%
white, small variations in the frequencies in other racial and ethnic categories will
have a disproportionate effect on percentage comparisons. Thus several repeat ar-
rests Of the same individual can severely skew the percentages. Nonetheless, such
differences cannot be ignored or go undocumented because they may point to impor-
tant biases in the criminal justice system’s response to racial and ethnic minorities.
And one might expect such biases to be more accentuated, not less, in a county
where the population is mostly white.

The vast majority of both victims and suspects were recorded as white non-

Hispanic. In comparison to 2000 county census demographics for persons 15 years

71

Table 4.2: Distribution of Race/ Ethnicity by Suspects and Victims Across Subsets
of Violence Against Women Database

 

 

 

 

 

 

 

 

Census Warrants Inset

Male Female Suspects Victims Suspects Victims
African American 3% 1% 4.4% 1.5% 5.1% 1.6%
Asian American 1% 1% 0.3% 0.2% 0.4% 0.2%
Hispanic 1% 1% 0.2% 0.2% 0.2% 0.2%
Native American 2% 2% 1.3% 1.0% 1.2% 1.2%
Other na na 0.1% 0.1% 0.0% 0.0%
Unknown na na 0.1% 0.1% 0.1% 0.1%
White non-Hispanic 95% 96% 93.7% 96.9% 93.0% 96.7%
Total 100.0% 100.0% 100.0% 100.0% 100.0% 100.0%

Census First Repeats

Male Female Suspects Victims Suspects Victims
African American 3% 1% 4.1% 1.7% 8.6% 1.3%
Asian American 1% 1% 0.2% 0.2% 1.3% 0.3%
Hispanic 1% 1% 0.3% 0.2% 0.0% 0.3%
Native American 2% 2% 1.3% 1.0% 1.0% 1.7%
Other na. us 0.0% 0.0% 0.0% 0.0%
Unknown na as. 0.1% 0.2% 0.0% 0.0%
White non-Hispanic 95% 96% 94.0% 96.8% 89.1% 96.3%
Total 100.0% 100.0% 100.0% 100.0% 100.0% 100.0%

 

 

 

 

72

 

of age or older, the census distribution of white females is consistent with the war-
rant distribution of white non-Hispanic females. In contrast, the distribution of
warrants with African American female victims is higher than the corresponding
census distribution (1.5% versus 1%), but lower for Asian American female victims
(0.2% versus 1%), Hispanic female victims (0.2% versus 1%), and Native Ameri-
can female victims (1.0% versus 2%). Relative to the census distributions, white
non-Hispanic males appear at nearly the same rate (94.0% versus 95%), but are
under-represented in repeat arrests (89.1% versus 94.0%). In contrast, cases in-
volving African American suspects appear more frequently than the corresponding
census figures would suggest (4.1% versus 3%), and at more than twice the rate for
repeat offenses (8.6% versus 4.1%). While Asian American suspects were less likely
to appear in comparison to the census statistics (0.2% versus 1%), they appear more
six times more frequently in repeat arrests (1.3% versus 0.2%). Hispanic and Native
American suspects are both under-represented in first arrests and repeat arrests.
Table 4.3 summarizes the age distributions. The age distributions of both sus-
pects and victims are concentrated in the range Of 15 and 44 years, which is con-
sistent with general demographic patterns in the criminal justice system. This does
not mean that persons under 15 or over 40 are not being victimized or perpetrating
violence against women and children. The age distribution of suspects and victims

reflect both age distributions in incidence rates and reporting rates.

4.3 Case attributes

Table 4.4 summarizes the distribution of charges at the time of arrest. Sexual
assault is typically a felony arrest, but the remaining charges are, for the most part,

misdemeanors. There are two major distinctions between domestic violence arrests

73

Table 4.3: Distribution of Age by Suspects and Victims Across Subsets of Violence

Against Women Database

 

 

 

 

 

 

 

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3:85 maOchsm @8505 mfioamzm 2585 $8025 SEES mfioqgm Snack 032
38.3% 42E «2...: 3:35: 339.0

 

 

 

 

74

and assault and battery arrests. First, police can make a warrantless domestic
assault arrest in Michigan if there is evidence of violence, and the victim and suspect
(a) are a current or former married couple, (b) share a residence, or (c) have a
child in common.l A warrantless arrest means that the police officers do not have
to directly witness the crime being committed in order to make the arrest. One
legal implication of this is that the arrest warrant is actually issued after the arrest
has been made. The second major distinction between a misdemeanor domestic
violence arrest and misdemeanor assault and battery is that misdemeanor domestic
violence arrests carry a maximum penalty of 93 days in jail in contrast to assault
and battery, which carries a maximum penalty of 90 days in jail. This means
that police officers are required to finger print suspects in misdemeanor domestic
violence arrests, which essentially provides a state wide mechanism to track domestic
violence suspects. Police departments are not required to finger print and report
misdemeanors with a maximum jail sentence of 90 days or less. This means that
a criminal background check through Michigan State Police would not reveal a
previous arrest for assault and battery. Prior to 1994, assailants arrested on assault
and battery could evade the system by moving to a different county. Each time they
were arrested would then essentially be treated as the first offense. So a misdemeanor
domestic assault having a maximum sentence of 93 days in jail means, with one
important exception of the “first” Offense, that domestic assault arrests will appear in
a criminal history background check. The exception is that Michigan law provides a
mechanism (769.4a) whereby first time convictions for domestic assault can receive a
deferred sentence, and upon completion of probation requirements, essentially have
no criminal record of the arrest and conviction. A second arrest and conviction

would then essentially appear as the first official arrest, conviction, and sentence.

 

1The law was amended in 2002 to include dating relationships.

75

Most cases in the prosecutor’s violence against women database involved misde-
meanor domestic violence arrests (79.8%), followed by sexual assault (12%), stalking
(5.5%), assault and battery (2.2%), and personal protection order (PPO) violations
(0.5%). These distributions are consistent between all warrants, those in the analy-
sis set, and first arrests. Repeat arrests, however, are less likely to involve domestic
violence (77.1% versus 79.5%) and sexual assault (8.7% versus 12.0%), but more

likely to involve stalking (10.3% versus 5.5%).

Table 4.4: Arrest Charges Across Subsets Of Violence Against Women Database

 

 

 

 

 

 

 

Warrants Inset First Repeat
Assault and battery 42 2.2% 38 2.6% 27 2.4% 11 3.5%
Sexual assault 228 12.0% 162 11.3% 135 12.0% 27 8.7%
Domestic violence 1516 79.8% 1136 79.0% 897 79.5% 239 77.1%
PPO violation 9 0.5% 8 0.6% 7 0.6% 1 0.3%
Stalking 104 5.5% 94 6.5% 62 5.5% 32 10.3%
Total 1899 100.0% 1438 100.0% 1128 100.0% . 310 100.0%

 

 

 

The VAW database included an Open ended text field describing the nature of the
relationship between the victim and suspect. Cases that could be clearly identified as
involving intimate partner violence were coded as domestic violence, cases that could
otherwise be clearly identified as involving two peOple living together where coded
as cohabiting, and the remaining cases were coded as other. Table 4.5 summarizes

the frequency distributions of the type of relationship.

4.4 Case dispositions

While a common perception of the criminal justice system is that most cases are
resolved in court trials, very few actually are. Table 4.6 summarizes the dispositions.

About half the cases either do not have the warrant authorized by the prosecutor’s

76

Table 4. 5: Type of Relationship Between Victim and Suspect Across Subsets of
Violence Against Women Database

 

 

 

Warrants Inset First Repeat
Domestic violence 745 37.7% 549 38.2% 438 38.8% 111 35.8%
Cohabiting 572 28.9% 342 23.8% 266 23.6% 76 24.5%
Other 659 33.4% 547 38.0% 424 37.6% 123 39.7%
Total 1976 100.0% 1438 100.0% 1 128 100.0% 310 100.0%

 

 

 

 

 

 

 

Office (39.2%) or end up eventually being dismissed (10.8%). Pleading no contest is
essentially the same thing as pleading guilty. Cases that are nolled or nolle prosequi
are cases where the prosecutor’s office dismisses the case because the lawsuit has
been abandoned. The remaining cases are resolved mostly through plea agreements
(40.5%). Only 1.4 percent of the cases are resolved through a court trial. Table 4.7
summarizes the reasons given by prosecutors for denying or dismissing a case, the

main one being lack of evidence.

Table 4.6: Dispositions Across Subsets of Violence Against Women Database

 

 

 

 

 

 

 

 

Warrants Inset First Repeat
Denied 695 39.2% 594 42.7% 490 44.5% 104 35.9%
Dismissed 192 10.8% 131 9.4% 94 8.5% 37 12.8%
Guilty at trial 11 0.6% 6 0.4% 5 0.5% 1 0.3%
Nolled 6 0.3% 6 0.4% 5 0.5% 1 0.3%
Not guilty at trial 15 0.8% 10 0.7% 8 0.7% 2 0.7%
Plead guilty 719 40.5% 541 38.9% 413 37.5% 128 44.1%
Plead no contest 137 7.7% 102 7.3% 85 7.7% 17 5.9%
Total 1775 100.0% 1390 100.0% 1100 100.0% 290 100.0%

 

 

Guilty dispositions, either through trial convictions or plea agreements, can re-
sult in a variety of sanctions. Table 4.8 summarizes the various combinations of
sanctions along with their distribution. Percentages are in terms of all cases within

the set, not just those cases where a finding of guilt was determined. Thirty-seven

77

Table 4.7: Distribution of Reasons Given by Prosecutor for Denial or Dismissal
Across Subsets of Violence Against Women Database

 

 

 

Warrants Inset First Repeat
Civil 6 0.9% 6 1.0% 5 1.1% 1 0.8%
Apologized 2 0.3% 2 0.3% 2 0.4% 0 0.0%
Complied with treatment 7 1.1% 7 1.2% 7 1.5% 0 0.0%
Plead to other charge 20 3.1% 18 3.0% 6 1.3% 12 9.7%
Lack of evidence 510 78.7% 473 79.2% 384 81.2% 89 71.8%
Dismissed by judge 2 0.3% 2 0.3% 0 0.0% 2 1.6%
Not in best interest Of justice 3 0.5% 3 0.5% 3 0.6% 0 0.0%
Other 46 7.1% 40 6.7% 30 6.3% 10 8.1%
Police request 3 0.5% 3 0.5% 2 0.4% 1 0.8%
Probate 12 1.9% 10 1.7% 8 1.7% 2 1.6%
Victim 37 5.7% 33 5.5% 26 5.5% 7 5.6%
Total 648 100.0% 597 100.0% 473 100.0% 124 100.0%

 

 

 

 

 

 

 

percent of cases that were in the analysis set (Inset) did not receive any type of
sanction. Approximately 11% that were in the analysis set (Inset) were referred
to some type of batterer intervention program (BIP). Delay of sentence (DOS) was
agreed to in approximately 14% of the cases in the analysis set (Inset).

The county has two batterer intervention programs, although neither meets the
minimum state standards for batterer intervention services and key informants gen-
erally felt that this was one of the major areas lacking in their community response.
Table 4.9 summarizes the referrals for cases receiving a guilty disposition. The 10-
week batterer intervention program (BIP) falls far short of the 26-week minimum
required by state standards. The 26-week BIP follows more of an anger management
model, but does not follow an accountability model like the Duluth model (Pence &
Paymar, 1993). Anger management for batterers is contraindicated (Gondolf, 2002;
Healey et al., 1998; Pence & Paymar, 1993). The “other” referrals are to substance

abuse assessment and treatment programs, individual psychological or ministerial

78

Table 4.8: Distribution of Consequences from Prosecution Across Subsets of Violence
Against Women Database '

 

 

 

 

 

 

 

 

 

 

Warrants Inset First Repeat

None 1223 61.4% 846 37.0% 668 37.2% 178 36.5%
BIP only 52 2.6% 25 1.1% 20 1.1% 5 1.0%
BIP and DOS 130 6.5% 100 4.4% 93 5.2% 7 1.4%
BIP and Jail 132 6.6% 95 6.6% 69 6.1% 26 8.4%
DOS only 196 9.8% 152 10.6% 128 11.3% 24 7.7%
Jail only 259 13.0% 220 15.3% 150 13.3% 70 22.6%
Total 1992 100.0% 1438 100.0% 1128 100.0% 310 100.0%

BIP=Batterer intervention program

DOS=Delay of sentence

counseling.

Table 4.9: Distribution of Counseling Referrals Across Subsets of Violence Against
Women Database

 

 

 

Warrants Inset First Repeat
10 week BIP 277 31.4% 186 28.6% 160 31.7% 26 17.8%
26 week BIP 38 4.3% 34 5.2% 22 4.4% 12 8.2%
Anger management 48 5.4% 9 1.4% 7 1.4% 2 1.4%
None 170 19.3% 125 19.2% 85 16.8% 40 27.4%
Other 348 39.5% 297 45.6% 231 45.7% 66 45.2%
Total 881 100.0% 651 100.0% 505 100.0% 146 100.0%

 

 

 

 

 

 

 

4.5 Time series statistics

The VAW database contained a number of date variables, which were used to cal-
culate time series of the number of events per day and estimate caseload statistics.
Table 4.10 summarizes the means and standard deviations of raw observed time

series of rate variables in units of cases per day for all cases in the analysis set, first

79

arrests, and repeat arrests. That is, there are on average 0.9843 warrant requests

per day. Along the same lines, Table 4.11 provides a summary of the means and

stande deviations for the raw estimates of the stock variables.

Table 4.10: Statistics for Raw Time Series of Rate Variables

(in units of cases per day)

 

 

 

 

 

 

Inset First Repeat

Mean SD Mean SD Mean SD
Warrant requests 0.9843 1.1647 0.7721 0.9990 0.2122 0.5090
Denials 0.3970 0.7736 0.3265 0.6648 0.0705 0.2911
Warrant request authorized 0.6037 0.8591 0.4606 0.7066 0.1431 0.4245
Meeting victim 0.3463 0.7007 0.2642 0.5589 0.0821 0.3207
Plea agreement accepted 0.4285 0.8528 0.3326 0.6926 0.0958 0.3594
Dismissed 0.0869 0.3247 0.0630 0.2672 0.0240 0.1739
Trial dates 0.0315 0.2290 0.0274 0.2076 0.0041 0.0640
Referred to 10 week BIS 0.1218 0.4074 0.1054 0.3662 0.0164 0.1424
Referred to 26 week BIS 0.0233 0.1596 0.0151 0.1218 0.0082 0.0903
Referred to anger mgt. 0.0062 0.0866 0.0048 0.0691 0.0014 0.0370
Referred to other counseling 0.1916 0.5615 0.1492 0.4422 0.0424 0.2446
Guilty but no referral 0.0787 0.2960 0.0541 0.2292 0.0246 0.1718
Received delay of sentence 0.1636 0.4937 0.1444 0.4273 0.0192 0.1602
Received jail 0.2047 0.5311 0.1410 0.4079 0.0637 0.2733
Received probation 0.3717 0.7865 0.2957 0.6528 0.0760 0.3190

 

 

4.6 . Descriptive models

The next step was to deve10p descriptive models capable of reproducing the general
trend in the prosecutor’s office domestic violence caseload. That is, they simply
attempted to reproduce the behavior pattern as Opposed to describing the underlying
mechanisms generating the behavior pattern. This was essentially analogous to
a large family of statistical modeling approaches where the goal is to deve10p a

mathematical representation of the data. All of the descriptive models were driven

80

Table 4.11: Statistics for Raw Time Series of Stock Variables

(in units of cases)

 

Inset First Repeat

Mean SD Mean SD Mean SD
Warrants 18.3292 5.9436 13.9432 4.6960 4.3860 2.0514
Cases 72.4887 22.1962 52.0678 14.7212 20.4209 8.4000

 

 

 

 

 

 

 

with real time series data of warrant requth that had been smoothed using a
120—day delay third order exponential smoothing algorithm.2

Each model was then calibrated to Caseload. There were several reasons for only
calibrating on Caseload (as opposed to also including Plea offers accepted and Dis-
missals). First, such simple models will be unable to replicate higher order dynamics
such as oscillations that are endogenous to the system. This means that there will
be a significant amount of error between the actual and simulated time series. So
one can either (a) try to optimize the fit on one observed variable and distribute the
error to the other observed variables, or (b) Optimize the fit on several variables and
spread the error across them. The second reason for only calibrating on Caseloads is
that it is a stock variable and the hypothesized determinant of the dispositions Plea
ofl'ers accepted and Dismissals, which are rates. That is, the question in this study
is focused on understanding whether or to what extent caseloads affect dispositions.
If one has distributed the error between both caseloads and dispositions, then one

is likely to underestimate the possible effects that caseload has on dismissals and

 

2A third order exponential smoothing algorithm was used because it is the lowest order smooth-
ing algorithm where peaks are approximately distributed symmetrically (as opposed to asymmet-
rically) and neighboring points around a peak are weighed more heavily than distant points. The
decision to use a 120-day delay was chosen by comparing various delays and looking for shortest
delay that clearly identified the general trends. Ultimately, however, the question is not whether
the optimal smoothing algorithm was selected, but whether the model reproduces realistic time
series behavior over a wide range of inputs generated from a variety of smoothing algorithms and
hypothetical scenarios.

81

plea offers being accepted. Moreover stocks are generally more reliable than rates
as observable measures. Thus, calibration was restricted to Optimizing the fit to
Caseloads.

Calibration was achieved by Optimizing the fit between the actual smoothed time
series of Caseload and each descriptive model’s simulated time series of Caseload
using the Powell Optimization procedure in Vensim with the original values as the
starting point. This procedure tries to Optimize the fit between two or more time
series by varying the constants over a given range. The degree Of fit or payoff

function, P, is calculated as the sum squared differences between actual and model

values:

P = i-[WKMKQ —Ai(t))]2,

i=1

where n is the number of variables to fit to, W,- is the weight for the i-th variable,
M;(t) is the models value for the i-th variable at time t, and A;(t) is the actual value
for the i-th variable at time t. Weighting the differences between the model and
actual values has no impact on the fit when there is only one variable in the payoff
function P (i.e., when n = 1). However, when the payoff function P is written in
terms Of more than one variable (n > 1), one might decide to assign different weights
to each difference because one either wants to (a) weight more reliable measurements
of the actual values more heavily than less reliable measurements, or (b) adjust for
differences in the scaling of variables.

The constants available for modification will vary from model to model. Con-
stants were added incrementally to the calibration procedure if they improved fit

and drOpped in favor of estimates from real data in the VAW database if they did

82

not improve fit. The results from calibration were a set of values for each model
that Optimized the fit between the actual and simulated. Caseload.

Figure 4.2 shows the smoothed and nomad warrant requests data used to drive
the descriptive models. Normed time series is a subscripted variable and [War-
Rquuth TS] designates the subscript being referenced, which is in this case warrant
requests authorized. Real120 refers to the name of the real data set used to drive
the specific simulation.

Figure 4.2: Smoothed Time Series Of Warrant Requests Generated from Violence
Against Women Database

 

4

 

 

 

 

 

 

1998 1999 2000 2001
year

Normed time serieleVarRquuthTS] : Rea1120 Cases

The first model, PACM120 in Figure 4.3, modeled Plea offers accepted and
Dismissals as functions Of Caseload. Dismissals was defined in terms of Capacity
gap, the difference between some theoretical Prosecutor caseload capacity and the
actual Caseload. Adjustment times were defined in terms Of Median time to plea
oflers accepted and Median time to cases dismissed. Medians were used at this stage
as more robust estimators of central tendency, which was an assumption that would
turn out to be problematic in later models.

The results after calibrating PACM120 are shown in Figure 4.4. PACM120 was
calibrated by modifying Prosecutor caseload capacity. Observed variables (solid
line) are shown with PACM120’s simulated results (dashed line) for Caseload, Plea

83

Figure 4.3: Descriptive Model with Dispositions as a Function of Caseload Pressure,
PACM120 .

 

 

 

 

 

 

 

Median time to plea
offers accepted
Normed time
series
Q .1. Caseload
Plea Offers
Warrant requests accepted
authorized
Capacity 39
fi- Dismissals
¢ Prosecutor .
Median time to caseload capacny
cases dismissed

offers accepted, and Dismissals. The best way to evaluate how well the model
performs behaviorally is to visually compare the simulated data against the real data
(Sterman, 2000). Traditional fit statistics alone do not say very much about how well
the model reproduces the Observed behavior because they focus on point-by-point
fit, which can be very misleading. For example, all three of the following descriptive
models correlated with r > 0.8, yet they departed from the Observed behavior in
noticeable ways. What one wants to do in assessing fit is not just know how much
error there is, but the nature of the error. Theil inequality statistics (Sterman, 2000;
Theil, 1966) provide one way to assess where the errors are distributed by dividing
the error into three components: bias (U M ), unequal variation (U S ), and unequal

covariation (U C ) Specifically,

84

UM ___ arr—2132

 

 

MSE
Us (5M - 5’02
MSE
U0 2(1 - T)SMSA
MSE

where IV!- is the mean of the model’s time series, 31- is the mean Of the actual time
series, SM is the standard deviation of the model’s time series, SA is the standard
deviation of the actual time series, M SE is the mean squared error or %2(M, —A,~)2,
and r is the correlation between the model and actual time series (Theil, 1966). The
three components sum to one, that is, U M + U S + U C = 1.

Generally speaking, one is most concerned with systematic errors as Opposed to
random or unsystematic errors. A high U M statistic indicates bias in a model and
systematic error, usually from poorly estimated parameters. A high U 5 statistic can
indicate systematic error in terms of either the model not reproducing the general
trend or having the wrong amplitudes in oscillations. And, a high U 0 indicates
random or unsystematic error. When U S + U C = 1, the model has the same mean
and trend and is unsystematic unless one is interested in studying the oscillations.
The mean absolute error divided by the mean of the observed variable (M AE /mean)
was used to assess the size of the error. M AE /mean is dimensionless and reported
as percentages. A M AE /mean = 9% indicates that the model had an average error
between simulated and actual values of nine percent from the actual data.

PACM120 did very well for a single stock model in terms of reproducing general
behavior pattern. Single stock models are inherently limited in their ability to
generate more complicated behavior modes. Specifically, single stock variables are

unable to generate oscillating behaviors. The size Of the error was relatively low,

85

only 9%, most of which was unsystematic, U C = 0.97. PACM120 did not, however,
do so well with reproducing the behavior of the rates, Plea offers accepted and
Dismissals. Plea offers accepted had a moderately sized error of 16%, but half of
that was systematic, U M = 0.49. Dismissals had an even larger error of 31%.
However, U 5 + U C = 0.92 z 1. Thus, if one is not looking to study the oscillations
(which single stock systems cannot reproduce anyway), then one can consider the
error unsystematic even though the size of the error is large.

PACM131 in Figure 4.5 modeled Dismissals as a function Of caseload, the same
as PACM120, but Plea offers accepted was written as a function of warrant requests
authorized. This essentially describes the situation where plea Offers are accepted
on the basis of the attributes of a criminal case, which might be assumed to be
stochastic.

PACM131 was calibrated by varying Proportion of warrants POA and Prosecutor
caseload capacity. PACM131 did about the same as PACM120 in reproducing the
Observed caseload (see Figure 4.6). But PACM131 performed dramatically worse
with modeling Plea ofiers accepted and Dismissals than PACM120. The amount of
error in Plea ofers accepted increased from 17% to 21% with even more bias than
PACM120. The amount Of error in Dismissals was more than 170% with a most of
that error now concentrated as bias and systematic (U M = 0.81).

PACM142 made Dismissals a function of Warrant requests authorized (see Figure
4.7. This would describe the situation where all dispositions from prosecution (plea
Offers and dismissals) could be described strictly in terms of the attributes of cases.
PACM142 was calibrated by varying Proportion of warrants POA, Mean time to plea
ofiers accepted, Mean time to cases dismissed, and Proportion of warrants dismissed.
PACM142 did about as well as reproducing Caseload as PACM120 and PACM130.
PACM142 did a much better job of reproducing Plea offers accepted, with an average

86

Figure 4.4: Simulated Results from PACM120

(a) Caseload (M AE/mean = 9%, U M = 0.02, U 5 = 0.00, U0 = 0.97)

 

200

4x "L‘ “ —\
I, v \M

 

 

 

 

 

 

 

 

0
1998 1999 2000 2001
year
Caseload : ReallZO Cases
Caseload : PACM l 205im ----------------- Cases

(b) Plea Offers accepted (M AE/mean = 16%, U M = 0.49, U S = 0.01, U C = 0.49)

r‘~ — ’ \
’1 ______ ” m~ A
r ““““
I V
I
l
I
I
I
I

 

 

 

 

 

 

 

 

0
1998 1999 2000 2001
year
Plea Offers accepted : Real 1 20 Cases/Day
Plea Offers accepted : PACMIZOSim - - -' Cases/Day

(c) Dismissals (MAE/mean = 31%, U" = 0.08, U5 = 0.16, UC = 0.76)

 

    

 

 

 

 

 

 

 

0.6 -
0 I:
1998 1999 2000 2001
year
Dismissals : Rea1120 Cases/Day
Dismissals : PACMIZOSim ----------- Cases/Day

87

Figure 4. 5. Descriptive Model with Dispositions as a Function Of Case Attributes
and Caseload Pressure, PACM131

  

 

 

 

 

 

Proportion of
warrants
POA
_Normed
time series Median time to
plea otters
accepted
(:3.
Warrant requests ' Plea offers
authorized accepted
Capacity
gap
W Dismiss‘ais/ \
‘ Prosecutor
caseload
v Median time to .
cases capacity
0 dismissed

error of only 9% (down from 17% in PACM120 and 21% in PACM130), which was
mostly unsystematic. With exception to 2001, PACM142 did an excellent job of
reproducing Plea offers accepted. It did not, however, do a good job Of reproducing
Dismissals with a mean error of 98% (versus 30% for PACM120 and 171% for
PACM130), which was mostly systematic in terms of bias. That PACM142 did
better than PACM130 at reproducing Plea offers accepted when both formulated
Plea offers accepted as a function Of Warrant requests authorized might seem at
first surprising. But all three Of these models were calibrated against the Observed
data and errors redistributed to Optimize the fit Of Caseload. The effect of this
procedure was to trade error in one variable for another. And, more importantly,
making Dismissals a function of Warrant requests authorized essentially decoupled

Dismissals from Caseloads.

88

Figure 4.6: Simulated Results from PACM131

(a) Caseload (MAE/mean = 10%, U” = 0.08, U5 = 0.01, UC = 0.90)

 

200

\ * ,—-- -‘

‘i ‘ c
’ ------ " \M
I
I \/

 

 

 

 

 

 

 

 

0
1998 1999 2000 2001
year
Caseload : ReallZO Cases
Caseload : PACMl 31 sim ----------------- Cases

(b) Plea offers accepted (MAE/mean = 21%, U“ = 0.56, U5 = 0.16, U0 = 0.28)

 

 

 

 

 

 

 

 

2
0 ,
1998 1999 2000 2001
year
Plea Offers accepted : Rea1120 Cases/Day
Plea Offers acceptedzPACMl3lsim ---- Cases/Day

(c) Dismissals (MAE/mean = 171%, U” = 0.81, U5 = 0.14, UC = 0.05)

 

 

 

 

 

 

 

 

2
--------- ”I -~‘-‘ ‘l'“—---"
I”, mfl
1998 1999 2000 2001
year
Dismissals : Rea1120 Cases/Day
Dismissals : PACM13 1 sim ----------- Cases/Day

89

Figure 4.7: Descriptive Model with Dispositions as a Function of Case Attributes,
PACM141 -

Proportion of
warrants POA Mean time to plea
Offers accepted

    
 
 
 
 

Normed time
series

  
   
 

 

 

 

   

e : :
Warrant requests Plea offers
authorized accepted

‘ ’D'smlssalsKProportion of

warrants

dismlssed

Mean time to
cases dismissed

While all three descriptive models performed reasonable well at reproducing
Caseload, PACM120 did a generally better job of reproducing Plea ofi'ers accepted
and Dismissals than PACM130 and PACM142. The implication is that caseloads
provide a better descriptive account Of dispositions than case attributes. However,
none of these models provided an account as to how or why that might be the case.
While system dynamics models can include such highly aggregated relationships,
the goal of system dynamics is generally tO understand how the structure of the

feedback loops might generate the dynamic behavior pattern of interest.

4.7 Baseline model

The primary purpose of the baseline model was to deve10p an initial structure Of

feedback loops capable of reproducing the primary reference mode. This model was

90

Figure 4.8: Simulated Results from PACM142

(a) Caseload (MAE/mean = 10%, U" = 0.08, U5 = 0.00, UC = 0.92)

 

 

 

 

 

 

 

 

200 \
X” - UAW
0
1998 1999 2000 2001
year
Caseload : Rea1120 Cases
Caseload : PACM14Zsiln ----------------- Cases

(b) Plea Offers accepted (M AE/mean = 9%, U M = 0.09, U 5 = 0.05, U C = 0.87)

 

 

 

 

 

 

 

 

 

2 A
0 z
1998 1999 2000 2001
year
Plea Offers accepted : Rea1120 Cases/Day
Plea Offers accepted : PACM1428im - - -- Cases/Day

(c) Dismissals (MAE/mean = 98%, U“ = 0.85, U5 = 0.07, UC = 0.08)

 

 

 

 

 

 

 

 

0.8 ' ..... ‘
A’ ‘‘‘‘‘‘ f 1 - f ’ l \ ‘ -
0 /
1998 1999 2000 2001
year
Dismissals : ReallZO Cases/Day
Dismissals : PACM1425im ----------- Cases/Day

91

also used to focus questions for interviews with key informants and to further refine
the reference modes. The baseline model was developed using a modular approach,
starting with the assailant submodel, then the warrant processing submodel, and
finally the the case processing submodel. The warrant processing and case process-
ing submodels were initially deveIOped using the real data as exogenous inputs as
Opposed to the simulated values from the preceding submodel. Thus, the warrant
processing submodel was developed using the real arrest data for first time and re-
peat Offenses for inputs, while the case processing submodel was developed using

the real authorization rates for first time and repeat offenses for inputs.

4.7 .1 Arrest submodel

After examining the caseload by first and repeat arrests, it became evident that
repeat arrests represented a significant portion of the prosecutor’s Office caseload.
Figure 4.9 shows the overall trends of first time arrests and repeat arrests. The
total height of the bars represents the total number of arrests for that year. The
black portion of the bar represents the first time arrests for that year, whereas the
gray portion represents the repeat arrests for that year. First time arrests were
individuals who did not have a prior record of arrest in the VAW database, while
repeat arrests had a prior record of arrest in the VAW database. Since both first
arrests and repeat arrests contribute to the caseload, repeat arrests could potentially
consume a significant portion of prosecutor’s Office resources. Moreover, if holding
assailants accountable impacts assailants’ behaviors, then there would be a feedback
lOOp linking case dispositions with rearrest and cessation rates. Thus, it became clear
that one would eventually want to include an arrest submodel as part of the baseline
model and disaggregate cases by first time versus repeat arrests or cases.

Arrests are a rate (cases per unit time), while the “supply” of cases that are at

92

Figure 4.9: Trends in First Time Arrests Versus Repeat Arrests

I Firsts
Repeats

Year

 

 

risk Of an arrest is generally limited. That is, arrest rates are constrained by the
number of cases committing criminal behaviors. Most arrests in the VAW database
are first time arrests (see Figure 4.9). If the number Of domestic violence cases at
risk Of arrest remain constant, then one would expect the sum of first time and
repeat arrests to be constant over time. This could be represented as a transfer Of
cases from first time arrests to repeat arrests, with no net change of cases entering
or leaving the system. The basic arrest submodel representing this logic is shown
in Figure 4.10, which has one stock Of individuals with no prior domestic violence
arrest, No prior DV arrest, and one stock Of assailants with priors, Prior DV arrest.
No prior DV arrest represents cases with no prior domestic violence arrest and at
risk Of an arrest. Prior DV arrest represents cases with prior domestic violence
arrests and at risk of repeat arrest. With a January 1, 1998 through December 31,

2001 time horizon, First time arrests refers to arrests where the case had no prior

93

domestic violence arrest on or after January 1, 1998, and Repeat arrests refers to
arrests where the case had a prior domestic violence arrest on or after January 1,
1998.

Although the arrest submodel includes three feedback loops (B1, B2, and B3),
it is essentially descriptive in nature. The arrest submodel does not provide any
explanation as to how or why individuals are arrested, how their behaviors increase

the risk of arrest, or why they stop or continue being at risk of arrest.

Figure 4.10: Arrest Submodel

 

 

 

 

 

 

 

Average time to
repeat arrest
Q¢=——_l Prior DV @ R
Exiting arrest M
m
81
Average time
to exit
Average time to
first arrest
Fl
8
New cases No prior
flab DV
arrest

 

 

 

The arrival or creation of individuals at risk of arrest is formulated as constant
flow of cases per day, New cases, into No prior DV arrest. This represents the

creation of cases that are at risk Of being arrested but have not yet been arrested.

94

It is critical to note that the flow and accumulation of cases in the baseline model
includes both assailants and victims that were arrested. ‘That is, the baseline model
does not disaggregate arrests by assailants and victims of domestic violence.

The time to being arrested after onset of violence is modeled as an exponential
distribution, some cases being arrested quickly while others taking much longer.
The rate First time arrests going out Of the stock No Prior DV Arrests is written as
a flmction of No Prior DV Arrests, forming the balancing feedback loop that moves
cases from NO Prior DV Arrests to Prior DV Arrest (B3). Specifically,

N P ' DV t
First time arrests = O ’70,. arres . (4.1)
Average time to first arrest

 

Some of these cases in the stock Prior DV Arrest will be re-arrested at the rate
of Repeat arrests, which is determined by the the constant Average time to repeat
arrest and the stock Prior DV arrest, forming another balancing feedback loop (B2).

The specific equation for Repeat arrests is,

Prior DV arrest
Average time to repeat arrest '

 

Repeat arrests = (43)

Since cases in Prior DV arrest do not change states when there is a repeat arrest,
cases moving “out of” Prior DV arrest via Repeat arrests do not actually leave
Prior DV arrest. Mathematically, the flow Repeat arrests has no net effect on the
stock Prior DV arrest. While this representation might be confusing from a system
dynamics perspective, it is clearer from a non-system dynamics view because both
First time arrests and Repeat arrests are, in the real system, rates of cases moving
through the system in units of cases per day. A more typical system dynamics
oriented representation of Repeat arrests might be to disaggregate Prior DV arrest
into several stocks, each representing the accumulation of another prior. This is

certainly possible, but such a disaggregation would (a) increase the complexity of

95

the model and number of constants that would need to be identified, while also
(b) reducing the number of cases available for estimating the constants for the
additional stocks. Such a modification might work if one had a longer time horizon.
But with only a four year time horizon, the Opportunity to Observe multiple rearrests
is limited. Technically speaking, the cases become heavily censored to the right as
one tries to distinguish the number Of rearrests. Thus, the representation of Repeat
arrests as a flow from Prior DV arrest to Prior DV arrest is the result Of a trade—Off
between the time horizon and level of aggregation.

Some cases will cease to be at risk Of another arrest. Some cases will migrate
to avoid further prosecution, some assailants might displace their battering tactics
from criminal to non-criminal behaviors, a few might die, and others might stop
abusing their intimate partners. These cases leave Prior DV arrest through the
rate Exiting that is a function of the Prior DV arrest and the Average time to exit,
which forms another balancing feedback loop (Bl). The expression for Exiting is
similar to the previous equations,

Prior DV arrest

Exitin = .
g Average time to exit

 

(4.3)

Tables 4.12 and 4.13 summarize the variables in the basic assailant submodel.

Table 4.12: Variables in Arrest Submodel

 

 

Name Units Mean SD
First time arrests Cases/ day 0.72 0.15
No prior DV Cases 92 19
Repeat arrests Cases/day 0.19 0.08
Prior DV arrest Cases 148 60
Exiting Cases/day 0.59 0.24

 

Overall, the behavior of the arrest submodel performs reasonably well in terms of

96

Table 4.13: Constants in Arrest Submodel

 

 

Name Units Value
New assailants Cases/ day 0.797
Average time to first arrest Days 127
Average time to repeat arrest Days 765
Average time to exit Days 250

 

reproducing the general trends in First time arrests and Repeat arrests, as depicted

in Figure 4.11. Table 4.14 summarizes the fit statistics. However, the real data show

indications of second or higher order behavior that the arrest submodel is unable to

Figure 4.11: Simulated Results from Arrest Submodel

 

 

 

 

 

 

 

replicate.
1 (A
_ _ - - ————————————————————— 4
’ ’ 43V \M
0 r
1998 1999 2000 2001
Year
First time arrests : Real Cases/Day
First time arrests : Alcal ------------- Cases/Day

(a) First offense arrests

0.4

 

 

a
I
I
t
4
I
I
t
I
I
I
I
I
I

 

 

 

 

 

 

1998 1999 2000 2001
Year
Repeat arrests : Real Cases/Day
Repeat arrests : Al cal ---------------- Cases/Day

(b) Repeat offense arrests

4.7 .2 Warrant processing submodel

The deveIOpment Of the warrant processing submodel started with developing a basic

descriptive model and then proceeded with the development of underlying mecha-

nisms for actually processing the warrants. While warrant requests do accumulate,

97

Table 4.14: Summary of Arrest Submodel Fit

 

Variable r fifi'f—I U M U S U C Source(s) of error

First time arrests 0.91 9% 0.00 0.24 0.76 Unsystematic
Repeat arrests 0.93 13% 0.01 0.00 0.99 Unsystematic

 

 

 

 

 

 

 

 

decisions on whether to deny or authorize a warrant happen on the order of hours
to days, which is very short relative to the four year time horizon Of the baseline
model. Having stock variables change quickly relative to the time horizon appears
to introduce a computational problem for the Optimization algorithm in Vensim.
Specifically, calibrating a warrant processing submodel formulated as stocks took
approximately 20 minutes on a AMD Durron 600 MHz system with 196MB in con-
trast to less than 1 minute for all the other submodel structures in the baseline
model. This could become prohibitive in a revised model with additional struc-
tures. Thus a decision was made to treat the variables in the Warrant processing
submodel as auxiliaries instead Of stocks. The resulting submodel is shown in Figure
4.12. There are no stocks in the warrant processing submodel, thus there are no
feedback lOOps within the warrant processing submodel itself.

Warrant requests arrive from First time. arrests and Repeat arrests. Although
first time and repeat arrests are likely to differ in any number Of dimensions (hence
the reason for disaggregating arrests into first time and repeat offenses), all warrant
requests are basically processed the same way whether or not the warrant request
involves a first or repeat Offense. Thus, the basic structure Of processing warrants
is the same for both first time arrests and repeat arrests. When the basic structure
of a model is repeated, it is Often easier to understand the model by subscripting
variables. Thus, Warrant requests is simply a subscripted variable with two ele-

ments, first and repeat, where Warrant requests[ first] = First time arrests while

98

Figure 4.12: Warrant Processing Submodel

Fraction of cases
with probable cause
4/ \a.
mum
\ Anthem
13:13:: Warrants that can -
\ be reviewed
Warrant/
. - requests Effect of being short
Ffigge/ staffed on warrant
Productivity revrews
reviewing warrants
Prosecutors needed Prosecutors assigned

for warrant review t0 warrant revrew

99

Warrant requests[repeat] = Repeat arrests. Real numerical time series for First
time arrests and Repeat arrests were used for the testing and calibration Of the

warrant processing submodel.
Warrant requests generate a demand for prosecutors to review warrants, Prose-

cutors needed for warrant review, which is formulated 88,3

Prosecutors needed for warrant review,- =
Warrant requests.- /

Productivity reviewing warrants,- .

The actual number Of warrant requests that can be reviewed is constrained by
the number of warrant requests available for review and the resources available for

reviewing warrants. This is formulated as,

Warrants that can be reviewed; = MIN (Warrants requestsg,
Z I DZ (Warrant requests.- ,
SU M jes(Warrant requests J-)):l:
Effect 0 f being short staffed on warrant reviews).

Since warrant requests are not accumulated in this submodel, all requests have to
be decided upon as they come in. To handle this, Denials is formulated as the sum
of the cases that do not have probable cause and cases that cannot be reviewed

because there are not enough prosecutors. Specifically,

 

3The function ZIDZ(x,y) is used instead of standard division where x/O would result in a
discontinuity. When y is not zero, ZIDZ(x,y) equals x/y. When y is zero, ZIDZ(x,y) equals zero.
The subscript i is an element of the set S = first, repeat. The expression SUMj€S(') means sum
the elements within the brackets over the subscript j.

100

Denials, = (1 — Fraction 0 f cases with probable cause):
Warrants that can be reviewedi-i-

(Warrant requests.- — Warrants that can be reviewed.)

Authorizations is simply the product of Fraction of cases with probable cause and

Warrants that can be reviewed,

Authorizationsi = Fraction 0 f cases with probable cause-:1:
Warrants that can be reviewedg.

The Effect of being short staffed on warrant reviews is simply the number of cases

per day that the Prosecutors assigned to warrant review can process, that is,

Effect 0 f being short staffed on warrant reviews = Productivity reviewing warrants:

Prosecutors assigned to warrant review.

Table 4.15 lists the variables while Table 4.16 lists the constants. The resulting
behavior of the initial warrant processing submodel is shown in Figure 4.13, where
the solid lines show the actual values from the smoothed reference mode and the
dashed lines show the simulated values. Figures 4.13a—d show how the calibrated
model appears to do an excellent job of replicating the rates variables. And Ta-
ble 4.20 summarizes the fit statistics, where First time authorizations and Repeat

authorizations have no error since the submodel is being driven by the real data.

101

Table 4.15: Variables in Warrant Processing Submodel

 

 

Name Units Mean SD
Warrants that can be re- Cases/day 0.73 0.15
viewed/first]

Warrants that can be re- Cases/day 0.19 0.08
viewed/repeat]

Authorizations/first] Cases/ day 0.40 0.08
Authorizations/repeat] Cases/day 0.12 0.05
Denials/first] Cases/day 0.32 0.07
Denials/repeat] Cases/day 0.07 0.03
Prosecutors assigned to war- Persons 0.52 0.24
rant review

Efiect of being short staffed Cases/day 4.1 1.9
on warrant reviews

Prosecutors needed for war- Persons 0.09 0.02
rant review/first]

Prosecutors needed for war- Persons 0.02 0.01

rant review/repeat]

 

Table 4.16: Constants in Warrant Processing Submodels

 

 

Name Units Value
Productivity reviewing war- Cas / person/ day 8
rants

Number of prosecutors Persons 2

Fraction of cases with proba- Dimensionless 0.555
ble causeffirst]

Fraction of cases with proba- Dimensionless 0.641
ble causeIrepeat]

102

Figure 4.13: Simulated Results from Warrant Processing Submodel

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

\Am 0.4
0 ’ ,
1998 1999 2000 2001 1998 1999 2000 2001
Year Year
First time authorized : Real Cases/Day Repeat authorized : Real —-—-—— Cases/Day
First time authorized : Clea] ---------- Cases/Day Repeat authoriud : C lcal ------------ Cases/Day

(a) First Offense authorizations

 

 

 

 

 

 

 

(b) Repeat offense authorizations

 

 

 

 

 

 

 

 

 

0.6 0.2
//\/ W I ’ - E/\h ’ I
0 0
i998 1999 2000 2001 1998 i999 2000 2001
Year Year
First time denials : Real Cases/Day Repeat denials : Real Cases/Day
First time denials : Clcal ------------- Cases/Day Repeat denials : Clcal --------------- Cases/Day

(c) First Offense denials

(d) Repeat Offense denials

Table 4.17: Summary of Warrant Submodel Fit

 

 

 

 

 

 

 

 

Variable r {345 U" U5 U0 Source(s) of error
First time arrests 1.00 0% - - - NO error

Repeat arrests 1.00 0% - - - NO error

First time authorized 0.97 9% 0.50 0.18 0.31 Systematic, bias
Repeat authorized 0.96 9% 0.13 0.09 0.78 Unsystematic
First time denials 0.86 12% 0.11 0.05 0.84 Unsystematic
Repeat denials 0.90 22% 0.14 0.18 0.68 Unsystematic

 

 

103

4.7 .3 Case processing submodel

The vast majority Of warrant requests authorized result in either a dismissal or
plea agreement. Less than 2 percent of authorized warrants actually go to trial
(see Table 4.6 on page 77). Thus dispositions in the case processing submodel were
limited to plea agreements and dismissals. Prosecuting cases requires resources over
time, which must be allocated between the different types of cases. The simplest
model of this is to consider the rate that plea Offers can be accepted as prOportional to
the available resources, which is inversely prOportional to the number of cases being
actively prosecuted. Hence, the time that it takes to negotiate a plea agreement is,
unlike the time it takes to review warrants, variable. The basic structure of the case
processing submodel is shown in Figure 4.14.

Again, the basic structure is considered the same for first and repeat offenses.
Cases that have been authorized enter the stock Of cases being actively prosecuted,
Prosecutions.

Cases that are being actively prosecuted, Prosecutions, create a demand on pros—
ecutor’s office resources, Prosecutors needed for prosecuting cases. The number of
Prosecutors needed for prosecuting cases is a function of prosecutor’s Office caseload,
Prosecutors (cases), divided by the number of cases that can be prosecuted per per-
son per day (cases / person / day), Productivity prosecuting cases, and the desired time

to successfully prosecute a case (days):

Prosecutors needed for prosecuting cases = Prosecutions /

Productivity prosecuting cases
Desired ave days to prosecute cases

 

104

Figure 4.14: Case Processing Submodel

Ave days to Q
dismiss cases 4

 

 

 

 

r >9
W Plum

 

 

 

    
  

Authorizations BS

Prosecutors
allocated

Prosecutors needed/
for prosecuting cases 66)
Desired ave days to/

prosecute cases

\Prosecutors
assigned to cases

   

Productivity
prosecuting cases

105

How that demand is met depends on whether or not there are enough resources.
If there are enough resources, then the number of Prosecutors allocated applied to
Plea offers accepted equals the number of Prosecutors needed for prosecuting cases,
which forms the the balancing feedback loop B5. However, if there are not enough
resources, then the number of Prosecutors allocated to Plea offers accepted is a
function of the number of Prosecutors assigned to cases, which forms the balancing
feedback loop B6.

The actual number of prosecutors allocated, Prosecutors allocated, depends on
the number needed, Prosecutors needed for prosecuting cases, and the number of
prosecutors assigned to prosecute cases, Prosecutors assigned to prosecute cases (as

Opposed to reviewing warrants). This is written as,

Prosecutors allocated,- = MIN (Prosecutors assigned to cases:
Z I DZ (Prosecutors needed for prosecuting casesr,
S U M jes (Prosecutors needed for prosecuting casesj),

Prosecutors needed for prosecuting 60888;).

The actual rate the plea Offers are accepted is function of the number of prose-
cutors allocated to the securing plea agreements and the productivity of prosecutors
prosecuting cases. Thus, Plea offers accepted, is written as a product Of the Prose-

cutors allocated and Productivity prosecuting cases. Specifically,

Plea offers accepted,- = Prosecutors allocated“:

Productivity prosecuting cases.

Cases that do not result in a plea Offer being accepted are dismissed, but up until
that point, these cases are still being prosecuted, and hence contribute to Prosecutors

needed for prosecuting cases. Cases are dismissed via the flow Dismissals, which is

106

written as a function of Prosecutions and Ave days to dismiss case, and forms the

feedback loop B4. Specifically,

Prosecutions,-
Average days to dismiss case '

 

Dismissals.- 2

Thus, Dismissals increases as the number of cases in Prosecutions increases and
decreases as the Average days to dismiss case increases. Table 4.18 summarizes the

variables in the case processing submodel and Table 4.19 summarizes the constants.

Table 4.18: Variables in Case Processing Submodel

 

 

Name Units Mean SD

Pmsecutionslfirst] Cases 50 17

Prosecutions/repeat] Cases 15 7.8

Dismissals/first] Cases/day 0.03 0.02

Dismissals/repeat] Cases/ day 0.02 0.01

Prosecutors needed for prose- Persons 0.31 0.11

cuting cases/first] A

Prosecutors needed for prose- Persons 0.09 0.05

cuting cases/repeat]

Prosecutors assigned to cases Persons 1.48 0.25 E1
Prosecutors allocated/first] Persons 0.31 0.11 '
Prosecutors allocated/repeat] Persons 0.09 0.05

Plea ofl'ers accepted/first] Cases/ day 0.30 0.10

Plea ofl'ers accepted/repeat] Cases/day 0.09 0.05

 

 

Table 4.19: Constants in Case Processing Submodel

 

 

Name Units Value
Ave days to dismiss cases Days 786
Desired ave days to prosecute Days 167
cases

Productivity prosecuting Cases / person/day 0.96
cases

 

107

A comparison of the case processing submodel after calibration against the real
data is shown in Figure 4.15. The submodel did a better job of reproducing the
behavior pattern for first Offenses than repeat offenses. With exception of 2000, it
did especially well at reproducing the behavior pattern for first time prosecutions
(Figure 4.15a). Although it was able to reproduce the general behavior pattern for
repeat prosecutions (Figure 4.15b), the simulated behavior pattern appears to lag
the real behavior pattern, indicating a problem with a misspecified delay. And it
is generally unable to reproduce suggested oscillations in the real data, especially
Figure 4.15d through Figure 4.15f. These oscillations in Figures 4.15d through
4.15f do not appear in the real data of warrant authorizations (see Figure 4.19c
and 4.19d). That is, the oscillations are not the result of an exogenous input. Nor
could they be generated by a simple parametric variation in the case processing
submodel since it is a first order system and first order systems are incapable Of
generating oscillations. Thus, the oscillations must be endogenous to a higher order
system, either a more complicated version Of the case processing submodel involving
two or more stock variables or an interaction between various components of the
prosecutor’s office casefiow, resources, and information. Table 4.20 summarizes the
fit of the case processing submodel. Like the warrant processing submodel, the case
processing submodel was developed using real data for input (Authorizations, which

are broken out as First time authorized and Repeat authorized).

4.7 .4 Allocation submodel

Prosecutor resources are distributed in prOportion to various resource demands in
the allocation submodel (shown in Figure 4.16). The allocation submodel has two
main balancing loops, B7 and B8, which distribute prosecutor resources between

warrant reviews and prosecuting cases. Loop B7 allocates prosecutors to reviewing

108

Figure 4.15: Simulated Results from Case Processing Submodel

 

 

 

 

 

 

 

 

80 , - - j
0
1998 1999 2000 2001
Year
First time prosecutions : Real —— Cases
First time prosecutions : ModelAl --------- Cases

(a) First time cases

 

 

 

 

 

 

 

 

 

0.6
0 r
1998 1999 2000 2001
Year
First time POA : Real Cases/Day
First time POA : ModelAl ------------ Cases/Day

(c) First Offense plea aggreements

 

 

 

 

 

 

 

0.2
0 ’ a
1998 1999 2000 2001
Year
First time dismissals : Real Cases/Day
First time dismissals : ModelAl ------- Cases/Day

(e) First Offense dismissals

 

 

 

 

 

 

 

 

40
0
1998 1999 2000 2001
Year
Repeat prosecutions : Real Cases
Repeat prosecutions : ModelAl ------------ Cases

(b) Repeat Offense cases

 

 

 

 

 

 

 

 

 

0.2
0
1998 1999 2000 2001
Year
Repeat POA : Real Cases/Day
Repeat POA : ModelAl -------------- Cases/Day

(d) Repeat Offense plea agreements

 

 

 

 

 

 

 

 

0.08
0 l , _ . - - _
1998 1999 2000 2001
Year
Repeat dismissals : Real —— Cases/Day
Repeat dismissals : ModelAl ---------- Cases/Day

109

(f) Repeat Offense dismissals

 

Figure 4.16: Allocation Submodel

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m|=o=anto£=<

 

 

110

Table 4.20: Summary Case Processing Submodel Fit

 

 

 

Variable r filgf—a‘é U M U S U C Source(s) of error
First time authorized 1.00 0% - - - No error
Repeat authorized 1.00 0% - - - No error

First time prosecutions 0.98 9% 0.41 0.11 0.48 Systematic, bias
Repeat prosecutions 0.98 15% 0.57 0.14 0.42 Systematic, bias

 

 

 

 

 

 

First time POA 0.93 13% 0.13 0.03 0.84 Unsystematic
Repeat POA 0.92 18% 0.15 0.06 0.79 Unsystematic
First time dismissals 0.70 30% 0.14 0.01 0.85 Unsystematic
Repeat dismissals 0.74 37% 0.04 0.21 0.75 Unsystematic

 

warrants while 100p BS allocates prosecutors to prosecuting cases.

The mechanism described by 100p B7 is as follows: As the number of cases
increases in Prosecutions, the number of Prosecutors needed for prosecuting cases
increases, which decreases the number of Prosecutors assigned to warrant review,
lowers the Effect of being short staffed on warrant reviews and lowers Warrants that
can be reviewed. This slows Authorizations and ultimately decreases Prosecutions.

B8 competes with loop B7 for resources. As there are more cases in Prosecutions,
there are more Prosecutors needed for prosecuting cases, which increases Total pros-
ecutors needed. This increases the Prosecutors assigned to cases and Prosecutors
allocated, which increases the rate of Plea ofi‘ers accepted. As Plea offers accepted
increases, Prosecutions decreases.

The Total prosecutors needed is the sum of prosecutors needed for reviewing

warrants and prosecutors needed for prosecuting cases, which is written as,
Toto prosecutors needed = SU M jes (Prosecutors needed for warrant reviewj)+

S U M jes (Prosecutors needed for prosecuting casesj).

Allocation of prosecutors is formulated to be directly proportional to demand. That

111

is, the larger the demand for prosecutors for a particular activity relative to other
activities, the greater the allocation. This allocation 'scheme does not reflect any
prioritization. Prosecutors assigned to warrant review and Prosecutors assigned to

cases written as,

Prosecutors assigned to warrant review = Prosecutors available at Z I DZ (
S U M jes (Prosecutors needed for warrant review ,- ) ,

Total prosecutors needed),

and

Prosecutors assigned to cases = Prosecutors availabl e1:
ZI DZ (SU Mjes(Prosecutors needed for prosecuting easesj),
Total prosecutors needed) .

The equations for Effect of being short stafied on warrant reviews and Warrants
that can be reviewed have already been covered in Section 4.7.2, and the equation
for Prosecutors allocated was covered in Section 4.7 .3. The only new variable in the

allocation submodel is Total prosecutors needed, which is summarized in Table 4.21.

Table 4.21: Variables in Allocation Submodel

 

Name Units Mean SD
Total prosecutors needed Persons 0.52 0.18

4.7 .5 Behavior of baseline model

Figure 4.17 shows a general overview of the resulting baseline model after combining

the various submodels. Note that in the overview, feedback loops B5, B6, and B8

112

all appear to be within the same feedback loop. The formulation for the allocation
of prosecutors under various conditions introduced three separate mechanisms, each
of which was represented by a feedback 100p. At the level of the overview, however,
these distinctions disappeared.

The baseline model’s behavior is strictly endogenous, meaning behavior is gen-
erated entirely from within the model’s structure as Opposed to being driving by
external inputs from real data as was done during the development of the warrant
processing and case processing submodels. Some minor recalibration was required

to Optimize the fit with the real data.

4.7.5.1 Behavior of simulated time series

Figure 4.18 shows the simulated first time and repeat arrest rates against the actual
data. '

Figure 4.19 shows comparisons of the simulated data for the warrant sector
against the corresponding variables from the real data. Although this part of the
model does a reasonable job reproducing the overall trend and means, it does not
replicate the shorter variations in contrast to response of the warrant submodel’s
performance with real data for input (see Figure 4.13 on page 103), which is in large
part due to using the output from the arrest submodel. Likewise, the simulated
data from the prosecution sector reproduces the overall trend and means, but not
the shorter variations (see Figure 4.20 on page 117).

With very few feedback 100ps between the various submodels, one should not
expect this baseline model to do more than reproduce the general trends. Table
4.22 summarizes the fit statistics along with an evaluation of the type of error based
on the Theil statistics. Overall, the model did a reasonable job of reproducing the

means and general trends. There were some problems with Repeat arrests, First time

113

Figure 4.17: Overview of Baseline Model

 

 

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114

Figure 4.18: Simulated Results of Arrests from Baseline Model

 

 

l 0.4

 

 

 

 

 

 

 

 

 

 

 

 

 

1998 1999 2000 2001 1998 1999 2000 2001
Year Year
First time arrests : Real ——————- Cases/Day Repeat arrests : Real Cases/Day
First time arrests : BaselineAl --------- Cases/Day Repeat arrests : BaselineAl ----------- Cases/Day
(a) First time arrests (b) Repeat offense arrests

authorized, First time dismissals, and Repeat dismissals that need to be investigated

further. Repeat dismissals is the most troubling because of the large oscillations.

4.7 .6 Sensitivity analysis

There are three types of sensitivity to variations in parameters and structure that one
might consider: numerical, behavior mode, and policy (Richardson & Pugh, 1986;
Sterman, 2000). Questions about numerical sensitivity are concerned with the extent
specific values from the model vary in response to changes in model parameters or
structure, behavior mode sensitivity focus on changes in behavior patterns, and
policy sensitivity raise issues about the extent that policy recommendations vary in
response to changes in a model.

The structure of the feedback loops in the baseline mode can be divided into
two sets that are separated in terms of feedback. The first set contains the arrests,
while the second set contains the warrants, prosecutions, and allocation. The two

sets are isolated in terms of feedback in the sense that variables in the second set do

115

 

Figure 4.19: Simulated Results of Warrants from Baseline Model

 

 

 

 

 

 

 

 

1998 1999 2000 2001
Year
First time authorized : Real Cases/Day
First time authorized : BaselineAl ----- Cases/Day

(a) First offense authorizations

 

 

 

 

 

 

 

0.6
/—/\\
0
1998 1999 2000 2001
Year
First time denials : Real Cases/Day
First time denials : BaselincAl -------- Cases/Day

(c) First time denials

0.4

 

 

'
’
r
a
I
4
I
;
a
r

...... _
-‘:-/’-\,_\

 

 

 

 

 

0
1998 1999 2000 2001
Year
Repeat authorized : Real ——-——- Cases/Day
Repeat authorized : BaselineAl -------- Cases/Day

0.2

Repeat denials : Real

(b) Repeat offense authorizations

 

 

.“
'
a
a
a
a
a
o
a
r

 

’

..... f\

 

 

 

1998

2000

Year

 

Repeat denials : BaselineAl ----------

116

(d) Repeat denials

2001

Cases/Day
Cases/Day

 

 

Figure 4.20: Simulated Results of Prosecutions from Baseline Model

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

80 40
1998 1999 2000 2001 1998 1999 2000 200!
Year Year
First time prosecutions : Real Cases Repeat prosecutions : Real Cases
First time prosecutions : BaselineAl -------- Cases Repeat prosecutions : BaselineAl ---------- Cases

(3) First time prosecutions

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.6
0
1998 1999 2000 2001
Year
First time POA : Real Cases/Day
First time POA : BaselineAl ---------- Cases/Day
(c) First offense plea agreements
0.2
0 /
1998 1999 2000 2001
Year
First time dismissals : Real Cases/Day
First time dismissals : BaselineAl ----- , Cases/Day

(e) First time dismissals

(b) Repeat offense prosecutions

 

 

 

 

 

 

 

 

 

0.2
/\—/\/\A I '
o A, - . . ’
1998 1999 2000 2001
Year
Repeat POA : Real Cases/Day
Repeat POA : BaselineAl ------------ Cases/Day

((1) Repeat offense plea agreements

 

 

 

 

 

 

 

 

 

0.08
{AR
1998 1999 2000 2001
Year
Repeat dismissals : Real —— Cases/Day
Repeat dismissals : BaselineAl -------- Cases/Day

117

(f) Repeat dismissals

"Eu

 

Table 4.22: Summary of Baseline Model Fit

 

 

 

Variable r -A%% U M U S U C Source(s) of error

First time arrests 0.91 9% 0.00 0.26 0.74 Unsystematic

Repeat arrests 0.93 13% 0.10 0.00 0.99 Systematic, bias

First time authorized 0.88 14% 0.18 0.34 0.48 Systematic, bias and trend
Repeat authorized 0.87 19% 0.07 0.01 0.91 Unsystematic

First time denials 0.86 16% 0.12 0.28 0.60 Unsystematic

Repeat denials 0.85 26% 0.07 0.12 0.81 Unsystematic

First time prosecutions 0.99 6% 0.31 0.26 0.43 Systematic, bias and trend
Repeat prosecutions 0.99 17% 0.71 0.16 0.12 Systematic, bias

 

 

 

 

First time POA 0.94 9% 0.05 0.01 0.94 Unsystematic
Repeat POA 0.93 17% 0.03 0.00 0.97 Unsystematic
First time dismissals 0.74 23% 0.07 0.05 0.89 Unsystematic
Repeat dismissals 0.68 39% 0.09 0.29 0.62 Unsystematic

 

 

 

not feedback either information or material flows to the first set. Three sensitivity
analyses were conducted. The first analysis considered the sensitivity of observed
variables to increases in the number of new cases the system. The second analysis
considered the impact of oscillations in the Average time to first arrest. And the

third analysis examined the impact of varying the number of prosecutors.

4.7.6.1 Sensitivity to the number of new cases

The original value for New cases was 0.797 cases per day. Varying New cases along
a random uniform distribution between i50% (from 0.39 to 1.20 cases per day)
showed no noticeable impact on the qualitative behavior of any of the observed
variables. Increasing the range of the random uniform distribution did eventually
reveal changes in the qualitative behavior of the baseline model (see Figures 4.21
through 4.25). At New cases :8 2.4, First time authorized, Repeat authorized, First
time denials, First time POA, and Repeat POA all begin to show noticeable changes

in their qualitative behavior over time. However, this is nearly three times the base

118

 

rate of 0.797 cases per day. That is, according to the baseline model, the rate that

new cases come into the system can increase by as much as 300% before the system
begins to change behavior modes.

Figure 4.21: Sensitivity of Authorizations to Increase in Number of New Cases

 

Sensitivi \

50% 75% 95% 100%
First time author'md
2.014

 

 

2000 2001 2002

 

Sensitivi _ ......
50% 75% ET? " ‘3 95%[:jloo'% 1.. '1':
Repeat authorized
0.5450

 

 

4.7.6.2 Frequency response

Making arrests endogenous to the model with a. simple two-stock structure dra-
matically reduced the complexity of the inputs to the warrant and case processing

sectors. One might therefore want to know how the system responds as a whole to

119

Figure 4.22: Sensitivity of Denials to Increase in Number of New Cases

 

s .. .
50% E3394 95%100% -
Firsttimedenials

2.545

 

 

 

 

 

1998 1999 2000 2001 2002

120

Figure 4.23: Sensitivity of Prosecution Caseload to Increase in Number of New Cases

 

Sensitivi

50% 75% 95% [:1 100%
First time prosecutions

280.45

 

 

1998 1999 2000 2001 2002

 

WW ,. ..
50% a 75% 95% [:3 100% .‘izzé
Repeat prosecutions

103.66

 

 

 

1998 1999 2000 20m 2002
Year

121

Figure 4.24: Sensitivity of Plea Offers Being Accepted to Increase in Number of
New Cases

 

50% D 75% 95%
rim time POA
1.220

   

 

01998 1999 2000 2001 2002

 

Sensitivi
50% 75% 95% 100%

 

 

 

POA
0.4 l 59
0 ‘ _—
1998 1999 2000 2001 2002

122

Figure 4.25: Sensitivity of Dismissals to Increase in Number of New Cases

 

Sensitiv‘

50% gem 95% 100%
First time dismissals

0.3568

 

 

50%fl35%--95%100%-
Repeatdismissals
0.1313

 

 

1998 1999 2000 2001 2002
Year

123

higher frequency oscillations. This can be considered by varying a model parameters
in the arrest submodel to simulate a higher frequency oscillation in arrest rates. A
simple sinusoidal wave was used to drive the Average time to first arrest (see Figure

4.26).

Figure 4.26: Oscillations Used for Studying F‘i'equency Sensitivity of Baseline Model

 

400

 

 

 

 

 

   

1 1 1 1 1 1 1 1 \
‘1 "1 "1 '1 1 :1 :1 1 1 :1 :1 1 ' '1 I1
1 1‘ 1' 1'1'1' 1'1'1‘1 1 ‘ ‘ 1
I I I I I I I I I I I I
."."i"3':'.'".".".'"‘.'1'"'
I I I I I I I I I I I
1 1 1:1 1:1 1:1 1:1 1'1 ' '
I I I I I I I I I I l I I I I I
1: :1:1:1:1:1:1:1:1:1: '1:'1l1'
'1'1 1‘1‘1‘1 1'1'1l '
1 1 1 1 1 1 1 1 1 1 1
1' I ‘1 |1 .1 1 ‘1 ‘1 ‘1 I .1 ‘ |1
I J J; J L4

1998 1999 2000 2001

 

 

Year
Average time to first arrest : Osc360 days
Average time to first arrest : Osc90 ---------- days

(a) First time prosecutions

Osc360: Average time to first arrest = 200 + sin(t - 21r/360)
Osc90: Average time to first arrest = 200 + sin(t - 21r/90)

The results of subjecting the baseline model to a 360-day oscillation and 90-
day oscillation in the average time to first time arrests are shown in Figures 4.27
and 4.28. The 90—day oscillation (Osc90) had an significant impact on first time
arrests resulting in non-differentiable peaks or spikes, which had effects that cascaded
through the entire system. These spikes put the model under an extreme test. The
baseline model started to show effects of discontinuities under the 90—day oscillation
with first and repeat arrest plea offers accepted (Figures 4.28c and 4.28d). This was
caused by the sharp peaks in the warrant requests placing a very brief but intense
demand on prosecutor resources, temporarily creating a shortage of resources for

prosecuting cases and negotiating plea agreements. While these effects were not

124

 

evident in the effects from the 360-day oscillation on repeat arrests as shown in
Figure 4.28c, the 360—day oscillation did create similar discontinuities as the 90-day
oscillation for repeat arrests Figure 4.28d. The baseline model clearly has some
difficulties handling the extreme conditions of oscillations on the order of 90 days

or less.

4.7.6.3 Sensitivity to number of prosecutors

The baseline model should show some sensitivity to the number of prosecutors avail-
able. To test this, the number of prosecutors available was varied along a uniform
random distribution from 0.1 to 4.0 prosecutors. The results are shown in Figures
4.29 through 4.33. Figure 4.29 shows a bifurcation in First time authorized, that
is, a change in the behavior mode that depends on the number of prosecutors. As
the number of prosecutors drOps below 0.6, behavior mode of First time authorized
switches from a strictly increasing function to increasing and then decreasing func-
tion. The baseline model did not display any such pattern with Repeat authorized.
The behavior modes for the other main variables appeared to be relatively robust
in that they did not appear to change behavior modes with variation in the number

of prosecutors.

4.7.6.4 Sensitivity to smoothing parameter

The submodels and baseline model were deveIOped and calibrated using time series
that were exponentially smoothed with a third order, 120-day delay. To evaluate
the sensitivity of the model to assumptions based on the smoothing parameters, five
sets of smoothed time series were generated, each with a different delay (30, 60, 90,
120, and 180 days). All five sets were generated using the same basic third order
exponential delay.

125

 

Figure 4.27: Sensitivity of Arrests and Warrants to Frequency

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

   

 

 

 
  
    

 
 

 

 

 

 

 

 

 

 

 

 

 

 

40 0.8
.i‘éiwggm'
l : l E : E l I l l ; : i l i l '.
1:21:1313,::15:E :
i 1.1 1 1‘ 11 '1 1‘ ,1 H 1l " :1 S 1. 1--
0 5 11 '1 A .'i MutiLii .(1' g; '51 0 1
1998 1999 2000 2001 1998 1999 2000 2001
Year Year
Firsttimearreats:0sc360 -—-———-———— Cases/Day Repeatarrests:Osc360 —-—-—-—— Cases/Day
First timearrests : Osc90 ------------- Cases/Day Repeatanests : Osc90 --------------- Cases/Day
(a) First time arrests (b) Repeat ofiense arrests
4 0.6
3 .1 g
F: 3 1
0 :1, 1-" '1, 0
1998
Year
First time authorized:0sc360 -— Cases/Day Repeat authorized:0sc360 —— Cases/Day
First time authorized: Osc90 ---------- Cases/Day Repeat authorized: 0sc90 ------------ Cases/Day
(c) First offense authorizations ((1) Repeat arrest authorizations
4 0.4
:‘1‘ 5“ :‘1‘ I.K 5‘1‘ 5‘1 ’ -
0 .' ' ‘ H ’ 0 '
1998 1998 1999 2000 2001
Year

First time denials : Osc360 —— Cases/Day Repeat denials: Osc360 —-——— Cases/Day
First time denials : Osc90 ------------- Cases/Day Repeat deriials : 0sc90 --------------- Cases/Day

(e) First arrest denials (f) Repeat arrest denials

126

 

 

Figure 4.28: Sensitivity of Prosecutions to Frequency

 

 

200 60

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0 0 ,
1998 1999 2000 2001 1998 1999 2000 2001
Year Year
First time prosecutions : Osc360 —-—-— Cases Repeat prosecutions : Osc360 ——————— Cases
First time prosecutions : Osc90 ------------ Cases Repeat prosecutions : Osc90 -------------- Cases
(a) First arrest prosecutions (b) Repeat arrest prosecutions
2 0.4

  
 

—-a"ll
““‘L‘.'_

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0 / ‘ - r t
1998 2001
First time POA : Os0360 —— Cases/Day Repeat POA : Osc360 Cases/Day
First time POA : Osc90 -------------- Cases/Day Repeat POA : Osc90 ----------------- Cases/Day “a
(c) First arrest plea offers accepted (d) Repeat arrest plea offers accepted

 

 

 

0.4 0.03 a
-§,-~.r “'4‘ ~r“ ~‘zl

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0 0 . '
1998 1999 2000 2001 1998 1999 2000 2001
Year Year
First time dismissals : Osc360 ———- Cases/Day Repeat dismissals : Osc360 ——-— Cases/Day
First time dismissals : Osc90 ---------- Cases/Day Repeat dismissals : Osc90 ------------ Cases/Day
(e) First arrest dismissals (f) Repeat arrest dismissals

127

 

 

Figure 4.29: Sensitivity of Authorizations to Decrease in Number of Prosecutors

 

50% dhm 95% [:3 100% I
First time authorized
0.4423

 

 

 

1998 1999 2000 2001 2002
Year

 

 

 

 

 

 

ol998 1999 2000 2001 2002

128

Figure 4.30: Sensitivity of Denials to Decrease in Number of Prosecutors

 

Sensitivi

50% [375% 95% 100% -
First time denials

0.6858

 

 

 

01998 1999 2000 200] 2002
Year

 

Sensitivi

50% arm 95% E21 100%
Repeat denials

0.2172

 

 

 

 

 

1998 1999 2000 2001 2002
Year

129

 

Figure 4.31: Sensitivity of Prosecution Caseload to Decrease in Number of Prose-
cutors

 

 
  
 

Sensitivi

50% flwx. 95% 100%
First time prosecutions

60.91 1

 

,/

 

01998 1999 2000 2001 2002
Year

 

   
 

e \z.
3. ‘,

 

Sensitivi
50% d7”. 95% [:1 100%
Repeat prosecutions

 

 

 

 

[998 1999 2000 2001 2002
Year

130

 

Figure 4.32: Sensitivity of Plea Offers Being Accepted to Decrease in Number of
Prosecutors

 

Sensitivi ‘ _ _ _
50% [£794 95% {:23 100% g; "
First time POA

0.3647

 

 

01998 1999 2000 2001 2002
Year

 

 

Sensitivi
50% dwx. 95% [j 100%
POA

Repeat
0.1359

 

 

 

 

i998 1999 2000 2001 2002

131

 

 

Figure 4.33: Sensitivity of Dismissals to Decrease in Number of Prosecutors

 

 

 

 

 

 

 

 

 

 

Sensitivi
50% 75% 95%100% \\\\\
Ifinnthnecfisufisufls
0.0774
01993 1999 2000 2001 2002
Year
Sensitivi ‘
50% 75% 95% 100% j: \‘
Repunrfiunkmfls
0.0288

 

   

 

 

 

1998 1999 2000 2001 2002
Year

 

 

132

If the baseline model is robust with respect to assumptions about the smoothing
parameters, then the baseline model’s performance in reproducing the time series
behavior would ideally remain constant as the smoothing parameters were varied.
Specifically, if real input and output data are smoothed using two different param-
eters, Tland 7'2, a model that is insensitive to assumptions about smoothing should
be able to reproduce the outputs corresponding to the inputs for both and 7'2
equally well. To test this, real data sets smoothed using different parameters were
used as inputs to the baseline model, and the results were compared against the
corresponding variables in the real data set. The results are summarized in Tables
4.23 through 4.27.

As the delay was shortened, the errors in Authorizations for both first and re
peat arrests increased (7% for first time cases and 11% for repeat arrests), but the
systematic component of the error tended to decrease. Authorizations was there-
fore sensitive to the delay in terms of both the size of the error and component of
error. Likewise, Denials was sensitive to the delay, with relatively large errors for
repeat arrests. Dismissals for first time arrests showed a pattern similar to Denials.
Dismissals for repeat arrests indicated a dramatic increase in the error, going from
26% to 80%, although the systematic bias was relatively low for delays less than 180
days. Similar results were found for Plea ofl’ers accepted. However, Prosecutions for
both first time and repeat offenses appeared to be relatively insensitive to changes
in the smoothing parameter. First time arrests kept the error rate to 10% across
all five sets, while repeat arrests kept the error rate to between 16 and 17%. Note,
however, that Prosecutions is a stock and accumulates quantities over time whereas

the remaining observed variables are all rates.

133

 

 

 

(a) First Timc arrests

#-

Table 4.23: Sensitivity of Authorizations to Smoothing Delays

 

 

 

 

 

 

 

 

 

 

 

 

Delay (days) 7' gg- UM U5 UC

30 0.73 16% 0.12 0.16 0.72
60 0.88 11% 0.25 0.18 0.56
90 0.95 10% 0.40 0.18 0.42
120 0.97 9% 0.50 0.18 0.31
180 0.99 9% 0.62 0.19 0.20

(b) Repeat Arrests

Delay (days) r {5% U M U 5 U C

30 0.86 19% 0.03 0.14 0.82
60 0.93 12% 0.07 0.12 0.81
90 0.95 10% 0.11 0.10 0.79
120 0.96 9% 0.13 0.09 0.78
180 0.98 8% 0.18 0.07 0.75

 

 

 

 

(a) First Time Arrests

Table 4.24: Sensitivity of Denials to Smoothing Delays

 

 

 

 

 

 

 

 

 

 

 

 

Delay (days) r g UM U5 U0

30 0.55 22% 0.03 0.16 0.81
60 0.69 16% 0.06 0.11 0.83
90 0.80 13% 0.09 0.07 0.84
120 0.86 12% 0.11 0.05 0.84
180 0.92 11% 0.14 0.04 0.82

(b) Repeat Arrests

Delay (days) r £23?- U M U S U C

30 0.67 42% 0.03 0.22 0.75
60 0.81 29% 0.07 0.21 0.72
90 0.87 25% 0.11 0.20 0.69
120 0.90 22% 0.14 0.18 0.68
180 0.94 19% 0.19 0.14 0.67

 

 

 

 

134

 

 

 

 

 

 

 

Table 4.25: Sensitivity of Dismissals to Smoothing Delays

(a) First Time Arrests

 

 

 

 

 

 

 

 

 

 

 

 

 

Delay (days) r fig U M U S U C

30 0.40 53% 0.03 0.35 0.62
60 0.61 35% 0.06 0.16 0.78
90 0.74 26% 0.08 0.06 0.86
120 0.82 20% 0.10 0.02 0.88
180 0.91 14% 0.11 0.00 0.89

(b) Repeat Arrests

Delay (days) r 737?.- U M U 5 U c

30 0.40 80% 0.01 0.54 0.46
60 0.54 57% 0.03 0.45 0.52
90 0.65 45% 0.05 0.40 0.55
120 0.74 37% 0.08 0.36 0.56
180 0.86 26% 0.17 0.33 0.51

 

 

 

 

 

(a) First Time Arrests

Table 4.26: Sensitivity of Plea Offers Accepted to Smoothing Delays

 

 

 

 

 

 

 

 

 

 

 

 

 

Delay (days) r MfaEr U M U S U C
30 0.68 19% 0.00 0.05 0.94
60 0.85 13% 0.02 0.00 0.97
90 0.91 11% 0.04 0.00 0.96
120 0.94 9% 0.04 0.02 0.95
180 0.97 8% 0.03 0.07 0.90
(b) Repeat Arrests
Delay (days) r fl U” U3 U0
30 0.73 32% 0.02 0.12 0.86
60 0.86 23% 0.03 0.04 0.93
90 0.90 19% 0.05 0.01 0.94
120 0.93 16% 0.08 0.00 0.92
180 0.97 12% 0.15 0.02 0.83

 

 

 

 

 

135

 

 

 

(a) First Time Arrests

Table 4.27: Sensitivity of Prosecutions to Smoothing Delays

 

 

 

 

 

 

 

 

 

 

 

 

Delay (days) r %% U M U S U C

30 0.94 10% 0.16 0.06 0.78
60 0.95 10% 0.18 0.04 0.78
90 0.96 10% 0.20 0.03 0.76
120 0.97 10% 0.24 0.02 0.74
180 0.98 10% 0.35 0.01 0.65

(b) Repeat Arrests

Delay (days) r 11:29: U M U 5 U C

30 0.97 17% 0.61 0.18 0.20
60 0.98 17% 0.63 0.20 0.16
90 0.99 17% 0.65 0.22 0.12
120 0.99 17% 0.67 0.25 0.09
180 0.99 16% 0.67 0.29 0.05

 

 

 

 

 

 

 

4.7 .7 Dynamic behavior of feedback loops

The main interest in this study is the dynamic relationship between caseload and
accountability, as measured as a proportion of warrant requests that result in plea I]
offers being accepted. The first part of this relationship is to understand how the

pattern of feedback 100p dominance changes over time with respect to prosecutor’s

 

office caseload, Prosecutions. This first result provides a dynamic account of how, '
according to the baseline model, the prosecutor’s office manages its domestic violence
caseload. The second part of this relationship is to identify the pattern of feedback
100p dominance over time with respect to the proportion of cases that are held

accountable, specifically:

 

136

Z Plea offers accepted,-

P th ld t bl = ‘
ercen e accoun a e ZWar‘rant requests.-

(4.4)

 

This second result shows how accountability is dynamically related to caseload.

Table 4.28 summarizes the major feedback 100ps in the baseline model. All eight
feedback 100ps are balancing or negative feedback 100ps, as indicated by the “B”
prefix. That is, there are no reinforcing or positive feedback 100ps (which would be
denoted with a “R” prefix) in the baseline model. Feedback 100ps B4 through B8
are subscripted. For example, there is one B4 feedback 100p for cases involving first
time arrests and another feedback 100p for cases involving repeat arrests. Identifying
patterns of feedback 100p dominance therefore means identifying which of these
feedback 100ps (individually or in various combinations) dominate the behavior of
a given variable of interest during a given time interval.

Analyzing a model in terms of feedback loop dominance has typically been done
through various ad hoc testing procedures where the gains of 100ps are modified in
order to identify changes in behavior patterns. Such approaches, while insightful,
can miss more subtle dynamics, especially when it comes to identifying shadow
feedback 100ps. A more formal approach involves systematically testing whether or
not and in what combinations various feedback 100ps change the behavior pattern
of a specific variable during a given interval of time.

Time series can be decomposed into three basic or atomic behavior patterns
(Ford, 1999): linear, exponential, and logarithmic. A system in equilibrium is a
special case of a linear behavior pattern. An exponential behavior pattern corre-
sponds to a variable that is increasing or decreasing exponentially. That is, not only

is the variable increasing or decreasing, but the rate that it is increasing or decreas-

137

 

 

 

Table 4.28: Major Feedback L00ps in Baseline Model

 

 

Loop Description Subscripts (i) Variables
Bl Cases exiting stock - Prior DV arrest, Exiting
of cases with prior
DV arrest
B2 Repeat arrests - Prior DV arrest, Repeat arrests
B3 First time arrests — No prior DV arrest, First time or-
rests
B4 Dismissals first, repeat Prosecutions, Dismissals
B5 Prosecutions with first, repeat Prosecutions, Prosecutors needed for
enough staff prosecuting cases, Prosecutors allo-
cated, Plea ofi'ers accepted
B6 Prosecutions when first, repeat Prosecutions, Proswutors needed for
short staffed prosecuting cases, Prosecutors as-
signed to cases, Prosecutors allocated,
Plea ofers accepted
B7 Allocation of prose- first, repeat Prosecutions, Prosecutors needed for
cutors to authorizing prosecuting cases, Total prosecutors
warrants needed, Pmsecutors assigned to war-
rant review, Efi'ect of being short
stafi'ed on warrant reviews, Warrants
that can be reviewed, Authorizations
B8 Allocation of prose- first, repeat Prosecutions, Prosecutors needed for

cutors to prosecuting
cases

prosecuting cases, Total pmsecutors
needed, Prosecutors assigned to cases,
Prosecutors allocated, Plea oflers ac-
cepted

 

138

 

 

 

ing is increasing. Finally, a logarithmic behavior pattern indicates a variable that is
increasing or decreasing, but the rate that the variable is increasing or decreasing is
decreasing. These atomic behavior patterns can be identified by looking at the sign

of the atomic behavior pattern index (ABPI), B(|6:c/6t|)/0t. Specifically,

linear B(|8z/0t|)/3t = 0,
exponential 6(|6x/6t|)/0t > 0,
logarithmic 6(laz/Bt|)/6t < 0.

Ford (1999) prOposes a formal procedure of testing a model’s feedback 100ps for
identifying not only the set of dominant feedback 100p, but also shadow feedback
100ps. The advantage of this procedure is that it leads to a complete and formally
defensible understanding of the dynamic relationship between a specific variable
during a given period of interest in terms of one or more feedback 100ps. The main
disadvantage is that the the number of steps involved with the procedure grows
“exponentially” with the number of feedback 100ps and variables to consider.

Since the differential equations for the baseline model are solved numerically as
simulations, the derivatives (e.g. 622/073) used for identifying the atomic behavior

pattern need to be approximated. Specifically,

6:1:(t) ~A$(t) _IDt — zt—At
61: ~ At " At '

 

One consequence of approximating the derivatives in this way is that two time points
are required to estimate the second order derivative, which means the first value after
a transition should be ignored. A second consequence is that the approximation will
be sensitive to numerical integration errors. If the numerical integration errors are

random or oscillate, then the approximated ABPI will also tend to oscillate. Gen-

139

 

 

 

erally, this is not a problem when the ABPI indicates an exponential or logarithmic
behavior pattern. However, when the ABPI approaches zero, these oscillations can
make it difficult to identify and locate the start of a linear behavior patterns. A
linear behavior pattern was assumed in cases where (a) the oscillations of the ABPI
were centered around zero, and (b) the amplitude of oscillations decreased over
time. The start of such linear behavior patterns was taken as the first crossing of

the horizontal axis.

4.7 .7 .1 Dynamics of managing prosecution caseloads

Figure 4.34 shows the reference atomic behavior pattern index for Prosecutions of
first arrests (thick line) along with the plot of Prosecutions of first arrests (thin
line). The atomic behavior pattern changes whenever the ABPI reaches or crosses
the y-axis. To aid the identification of the specific time intervals in which the atomic
behavior pattern is uniform, the horizontal axis is now in units of days, not years.
To facilitate better examination of potential equilibrium conditions, the time hori-
zon or horizontal axis has also been extended by one year, from 1461 days to 1826
days. The vertical dashed lines at t = 133 and t = 1158 indicate times when the
ABPI crosses the y-axis. The corresponding intervals between these times of uni-
form atomic behavior pattern are labeled P1, P2, and P3. P1 corresponds to the
situation where there is an increase in arrests when the caseload is empty. P2 cor-
responds to the situation where the increase in arrests continues and prosecutor’s
office caseloads increases in response, along with an increase in cases being disposed
through dismissals and guilty pleas. And P3 corresponds to the case where prose-
cutor’s office caseload has reached an equilibrium, that is the rate that arrests lead
to new cases on the prosecutor’s offices caseload matches the rate that cases are

disposed through dismissals and plea agreements. The question is then to identify

140

 

 

the immediate feedback loops that dominate the behavior of Prosecutions of first
arrests during each of these intervals. Prosecutions has five candidate feedback 100ps
to consider: B4 through B8 (see Table 4.28 on page 138).

Figure 4.34: Reference Atomic Behavior Pattern Index (ABPI) for First Arrest
Prosecutions

t=133 t==1158
P3

 

80 Cases
0.00025

40 Cases //

 

 

 

 

0 Cases :
-0.00025 .
0 332 664 996 1328 1660

 

 

 

 

 

Tam I]
Prosecutiomflrst] : Reference Cases s,—
ABPI Prosecuiomflrst] : Reference

 

 

During P1 (from 0 to 133 days), feedback loop B7 dominates the behavior of
Prosecutions of first arrests with a positive ABPI, indicating an exponential atomic
behavior pattern. That is, the prosecutor’s caseload for first arrests is growing
exponentially for first arrests and this is driven by B7, the allocation of prosecutors
to authorizing warrants. This makes sense since initially there are no cases to
prosecute and the prosecutor’s office domestic violence caseload is primarily focused

on authorizing warrants.

141

The behavior of Prosecutions of first arrests changes from growing exponentially
to growing logarithmically in P2 (from 134 to. 1158 days). No single feedback loop
dominates Prosecutions during this time period. Instead, three pairs of shadow
feedback 100ps dominate the behavior pattern of Prosecutions: B4 and B5; B4
and B6; and, B4 and B8. The B4 feedback 100p is dismissals. The feedback 100p
B5 describes the prosecution of cases when there are enough resources to meet all
the demands of the current prosecution caseload. B6 describes the prosecution of
cases when there are not enough prosecutors to meet the demands of the current
caseload. And, B8 describes the allocation of prosecutors to the prosecution of cases.
This means that no single feedback loop dominates Prosecutions during P2. Absent
from these pairs is B7 , which allocates prosecutors to the authorizing of warrants.
This can be interpreted as a shift in focus of activity from reviewing warrants to
prosecuting cases.

That each pair of shadow feedback 100ps dominate the behavior of Prosecutions
of first arrests during this period means that a change in any one pair of shadow
feedback loops can change the behavior pattern of Prosecutions. That is, one has
to modify both B4 and one of the other pairs in order to see a fundamentally
different behavior mode. For example, if one wanted to control prosecutor’s office
caseload during this period by modifying the structure of prosecutions in terms of
feedback loops, one would have to modify both the dismissal mechanism (B4) and
one additional feedback 100p (B5, BG, or BB). Modifying only one feedback 100p
will have no effect on the qualitative behavior of the Prosecutions.

At t = 1158 days, the behavior pattern of Prosecutions of first arrests changes
from logarithmic to linear in P3 (from 1159 to 1826 days) as Prosecutions of first
arrests reaches equilibrium. During P3, all five feedback 100ps (B4, B5, B6, B7 , and

BB) dominate Prosecutions of first arrest, and a change in any one mechanism will

142

 

 

result in either an exponential or logarithmic behavior pattern.

There are only two phases for Prosecutions of repeat arrests (see Figure 4.35 on
page 144): P1 (from 0 to 328) where Prosecutions displays an exponential behavior
pattern, and P2 (from 329 to 1826 days) where Prosecutions displays a logarithmic
behavior pattern. Like the prosecution of first arrests, B7 dominates Prosecutions
of repeat arrests during P1. That is, the prosecutor’s office caseload of repeat arrests
grows exponentially and is primarily controlled by the allocation of prosecutor re-
sources to authorizing warrants. Similarly, during P2, there are four pairs of shadow
feedback loops dominating Prosecutions of repeat arrests: B4 and B5; B4 and B6;
and, B4 and B8. That Prosecutions for repeat arrests does not have a third phase
is due to the limited time horizon.

There is essentially nothing surprising about the similarity between the dynamics
of the Prosecutions with respect to first and repeat arrest since they are essentially
the same in terms of the structure of their feedback 100ps. Somewhat surprising is
the presence of shadow feedback loops during P2. One might expect other feedback
loops to directly control the behavior pattern of Prosecutions for first and repeat
arrests. To consider this possibility, remote feedback loops in the arrest submodel
were tested for their impact on Prosecutions.

During P1 of first arrests, the feedback BB also dominated the exponential growth
behavior pattern of Prosecutions. B3 is the first arrest feedback 100p. However,
during P2 of first arrests, the feedback 100ps in the arrest submodel (Bl, B2, and
B3) did not dominate Prosecutions of first arrest. Thus, during P2, the behavior
of Prosecutions of first arrests is entirely driven by feedback 100ps directly related
to Prosecutions. During P3, B3 (first arrests) again dominates the behavior of
Prosecutions. In contrast, during P1 of repeat arrests, Prosecutions of repeat arrests

is dominated by both B2 (repeat arrests) and B3 (first arrests). And during P2,

143

 

 

Figure 4.35: Reference Atomic Behavior Pattern Index (ABPI) for Repeat Arrest
Prosecutions

=328
P1

 

40 Cases
0.00025

-----‘--

20 Cases

0 Cases
000025

 

 

 

w --

996 1328 1660
line

O
M
N

 

Prosecutbmkepeat] : Reference Cases
ABPI Prosecut'nnshepeat] : Reference

 

144

 

 

 

Prosecutions of repeat arrests is dominated by Bl (cases exiting the stock of cases
with prior DV arrest) and B3 (first arrests). The results are summarized in Table

4.29 on page 145.

Table 4.29: Dominance of Arrests Feedback L00ps on Prosecutions Across Phases
of L00p Dominance

 

P1 P2 P3
first arrests B3 none B3
repeat arrests 32 and B3 B1 and B3 -

 

 

The main implication of this is that first arrests dominate the qualitative be
havior of the prosecutor’s office domestic violence caseload for both the prosecution
of first arrests and repeat arrests in most phases of loop dominance. Interestingly,
during P2 where first arrests are being actively prosecuted, first arrests have no qual-
itative impact on the behavior of the prosecutor’s office caseload with respect to first
time arrests being prosecuted. In contrast, first arrests have a qualitative impact on
the behavior of the prosecutor’s office caseload of repeat arrests in both P; and P2.
Thus, even with this simple baseline model, the feedback dynamics of prosecutor’s
office caseload can involve some subtle complexities about the relationships between
various mechanisms directly connected to the prosecutor’s office and the relationship

between the dynamics of arrest and the dynamics of the prosecutor’s caseload.

4.7 .7 .2 Dynamics of accountability

The main question in this study is the dynamic relationship between assailant ac-
countability and domestic violence caseloads. Accountability, as measured in (4.4),
is dynamically related to the prosecutor’s office caseload if one of the feedback loops

regulating caseloads during a particular phase also regulates accountability. Note

145

 

 

 

that the Percent held accountable includes subscripted terms from both first arrests
and repeat arrests. Thus, Percent held accountable can be directly influenced by
both first and repeat arrests, and the feedback 100ps B4 through B8 need to be
tested separately for both first and repeat arrests.

Figure 4.36 shows that there are two phases of atomic behavior patterns to be
considered with Percent held accountable: P1 (from 0 to 837 days) and P2 (from
838 to 1826 days). P1 represents a period where the Percent held accountable grows
logarithmically while P2 corresponds to a period where Percent held accountable
has reached an equilibrium at approximately 48%. That is, only 48% of the warrant
requests result in a plea agreement. The remaining 52% either have their warrants
denied or result in a dismissal.

Figure 4.36: Reference Atomic Behavior Pattern Index (ABPI) of Percent Held
Accountable

t=837

 

0.6 Drml
le-OOS Dmll

 

--—-lp--Ib--

0.3Drml
0Drml

 

   

 

0 Drml
-1e-005 Drml

 

 

0 332 664 996 1328 1660
Tam

 

Peroem ink! accourlabb : Reference Drml
ABPI percent hekl accomtable : Reference Dlml

 

146

 

 

During P1, feedback loops B3 (first arrests), B5 (prosecutions with enough staff
for first arrests), B6 (prosecutions when short staffed for first arrests), and BS (allo-
cation of prosecutors to prosecuting cases) each dominate the logarithmic growth of
Percent held accountable. More specifically, each of these has the effect of limiting
Percent held accountable from an otherwise exponential growth rate to a logarithmic
growth rate.

During the subinterval between 0 and 133 days, B3 (first arrests) is the only
feedback loop that is controlling both the growth of Percent held accountable and
Prosecutions (for both first and repeat arrests). Thus caseload management mecha-
nisms are not affecting accountability during this initial phase. That makes intuitive
sense since the prosecutor’s office caseload is fairly small.

During the subinterval from 134 to 837 (328 to 837 for repeat arrest), Percent
held accountable and Prosecutions have feedback 100ps BS, B6, and BB in common,
although the nature of this dynamic relationship between Percent held accountable
and Prosecutions is more complicated since B5, 86, and B8 influence the behavior
pattern of Prosecutions only as members of a shadow feedback 100p pair with B4.
Thus, under ordinary conditions, Percent held accountable and Prosecutions are
not related dynamically in terms feedback loop dominance. However, a change
in the behavior pattern of Prosecutions would have an impact on the behavior
pattern of Percent held accountable, since in order to change the behavior pattern of
Prosecutions one would have to simultaneously modify B4 and either B5, BG, or BS.
That is, during this subinterval, one would not be able to change the dynamics of how
the prosecutor’s office manages its domestic violence caseload without also impacting
the feedback 100ps controlling accountability. The converse is not true. That is, one
could change the behavior pattern of Percent held accountable by modifying B5, B6,

or B8 without impacting the behavior pattern of Prosecutions.

147

 

 

During P2 from 838 to 1826 days, feedback 100ps Bl, B2, B4 (for both first arrests
and repeat arrests), and B7 (for both first arrests” and repeat arrests) dominate
Percent held accountable. In the subinterval from 838 to 1158 days, Percent held
accountable and Prosecutions of first arrests are both dominated by feedback loop
B4 (dismissals), although B4 is only one member in a shadow feedback 100p pair
with B5, B6, and B8. So the analysis here is similar to the second subinterval of P1,
where changes in the behavior pattern of Prosecutions of first arrests will mean a
change in the behavior pattern of Percent held accountable. And again, the converse
is not true. Changing the behavior pattern of Percent held accountable by modifying
B4 will not affect Prosecutions.

However, during the subinterval from 1158 to 1826 days of P2, Percent held ac-
countable and Prosecutions of first arrests both have B7 (allocation of prosecutors
to authorizing warrants) as a dominant feedback 100p. This corresponds to the pe-
riod where the baseline model is in steady state or equilibrium. Note that during
this period, the entire model has, in fact, reached equilibrium. Thus, the feedback
mechanism associated with allocating prosecutors to review warrants is controlling
both the prosecutor’s office caseload of first arrest domestic violence cases and the
proportion of warrant requests that result in the first arrest being held account-
able. But, this only happens when the model has reached equilibrium. Thus, the
baseline model indicates that there is a caseload management mechanism impact-
ing accountability, but only during a specific phase of feedback 100p dominance,
namely, equilibrium. During the other phases, accountability and caseload are only

conditionally controlled through the same mechanisms.

148

 

 

4.7 .8 Summary of baseline model

The baseline model, which simply modeled flows of cases through the criminal justice
system, did a reasonable job given its simplicity of reproducing the observed time
series, although it was unable to reproduce what seem like important oscillation in
the dismissals of repeat arrests (see Figure 4.20 on page 117). The baseline model
also appears to be sensitive to higher frequency oscillations. Analysis of the base-
line model in terms of dominance feedback 100ps suggests that accountability and
prosecutor’s office caseload have one controlling feedback loop in common when the
system is in equilibrium, namely, the allocation of prosecutor resources to warrant
reviews. Differences between prosecutions of first arrests and repeat arrests suggest

a need to further analyze and disaggregate arrests.

4.8 First versus repeat offenses

Figure 4.37 shows the general annual trends of warrant requests by first offenses,
repeat offenses, and the type of relationship between victim and offender. Recall
that first and repeat offenses refer not to previous convictions, but simply whether
or not there was a prior warrant request on or after January 1, 1998. Repeat offenses
include individuals who were arrested on or after January 1, 1998 where the warrant
request was denied or the case dismissed. Individuals who had a domestic assault
related arrest prior to January 1, 1998 would still be considered first offenses in
this analysis. Furthermore, first and repeat offense would also include cases where
victims were arrested and the warrant denied or the case dismissed.

While Figure 4.37a shows a relatively stable number of first offense warrant
requests per year with a slight decline starting in 2000. Repeat offenses for all

cases, however, are increasing until 2001. Breaking down the warrant requests by

149

 

 

the type of relationship reveals that four—year prevalence rate of domestic violence
relationships is remaining constant, with a transfer of cases from first offenses to
repeat offenses (see Figure 4.37b). The patterns for cases involving cohabiting and
other types of relationships are more complicated (Figures 4.37c and 4.37d). Figure
4.37c shows an increasing trend from 1998 through 2000 that would be consistent
with an “amplifying” mechanism, i.e. a positive feedback loop where the number first
time arrests feed back via some mechanism to increase the likelihood of more first
time arrests—the opposite of a general deterrence effect. Figure 4.37d suggests that
from 1998 to 2000, the number of arrests equals the number of new cases becoming
at risk of an arrest, that is, some type of replacement mechanism. The decline
in 2001 could be the delayed effect of a general deterrence mechanism. Thus the
general trends in Figures 4.37 suggest fundamentally different types of mechanisms
with respect to the effects of arrest and prosecution that seem to depend on the
type of relationship between the suspect and victim. A
Figure 4.38 shows the results of breaking down the warrants, first by suspect / victim

sex (maleto-female and female-to-male) and then by suspect / victim sex for a subset
of cases where (a) both parties were 18 years of age or older, and (b) the type of
relationship was domestic violence. The patterns depicted in both Figures 4.38a

and 4.38b are similar to each other as well as the patten in Figure 4.37b, which is

 

consistent with a closed system of assailants with no replacement of new cases. And
more specifically, the overall decline in Figures 4.38a and 4.38b starting in 1999 and
continuing through 2001 would be consistent with (a) general deterrent effects, (b)
specific deterrent effects after the first contact with the criminal justice system, (c)
treatment effects from intervention, or (d) displacement effects whereby assailants
continue to abuse, but shift their tactics from criminal to non-criminal behaviors.

All four of these have been prOposed as explanations for declines in assailants’ arrest

150

 

Cases

Cases

40

Figure 4.37: Warrant Requests by Type of Relationship and Year

I Firsts
Repeats

Year

 

(a) All warrant requests

80 100

60

20

 

0

Year

(c) Cohabitting cases

 

 

 

 

O
a! _.
a s-
8
o 8 —
o - .
V I Firsts
o _ Repeats
N
o _.
Year
(b) DV cases

I Firsts
Repeats

Year

 

 

(d) Other cases

151

 

 

rates after contact with the criminal justice system.

Figures 4.38c and 4.38d are also consistent with each-other, as well as with 4.37c
but are in stark contrast to the patterns in Figures 4.38a and 4.38b. This lends
support to the claim that the feedback 100ps structuring women’s contact with the
criminal justice system as suspects is fundamentally different from the feedback loops
structuring men’s contact with the criminal justice system as suspects. Furthermore,
women’s contact with the criminal justice system as suspects appears to involve a
positive feedback 100p.

There are two possible explanations for differences between arrest patterns of
male and female suspects in domestic violence cases. The first is that police generally
correctly identify the assailant, but (a) the deterrence and intervention effects on
suspects depend the suspect’s sex, and (b) interventions with batterers have been
geared toward male abusers. So while arrests, prosecution, and sanctions might
deter male abusers, those same interventions have no impact Or are detrimental
to female abusers. Advocates of this position point to the gender “symmetry” of
domestic violence, the lack of victim and advocacy services for men who experience
abuse, and the general stereotype that abuse is something primarily done by men
to women. If this is the case, then one would expect that female and male suspects
would have similar trajectories after arrest within the criminal justice system.

The competing explanation is that the presence of female suspects is generally
the result of police incorrectly identifying the assailant as the victim during a re-
sponse to a domestic assault. This might happen, for instance, as assailants become
more skilled at battering and manipulating law enforcement officers on the scene.
Victims might then be at increased risk of being arrested in the course of defend-
ing themselves. If this is the situation, then one would expect the prOportion of

warrants being denied to be higher for female suspects than male suspects. And

152

 

 

Figure 4.38: Warrant Requests by Suspect / Victim Sex and Year

 

 

   

 

 

     

O
m _
N o
o —
o 1-
° _.
N O _
(D
8 .
8 - 8 o -
s a 0
o g _ o
v- 8 —
o I Firsts I Firsts
m ‘ Repeats 8 - Repeats
o — o _
Year Year
(a) Male to female (b) Male to female adult DV
0 _
CO
to -
N
a 8‘
«‘8 m
0 '- f
O s
I Firsts '— I Firsts
Repeats u, p Repeats
o .1
Year Year
(c) Female to male (d) Female to male adult DV

153

 

this association should get stronger as one narrows the selection of cases to adult
domestic violence relationships. One would also expect a higher prOportion of fe-
male suspects to have first appeared as victims than male suspects, and that this
association would get stronger as one selected cases of adult domestic violence.
Table 4.30 shows the frequency distributions of dispositions by male-to—female
and female-to-male suspect-victim relationships, along with their respective column
percentages. Female-to-male cases are about 50% more likely than male-to-female

cases to result in the warrant request being denied.

Table 4.30: Dispositions by Suspect /Victim Sex

 

 

 

 

 

 

 

 

Male-to-female Female-to—male
Disposition Freq. % fieq %
Denied 354 37.8 137 57.3
Dismissed 86 9.2 22 9.2
Guilty at trial 4 0.4 l 0.4
Nolled 5 0.5 l ' 0.4
Not guilty at trial 10 1.1 0 0
Plead guilty 404 43.1 70 29.3
Plead no contest 74 7.9 8 3.3
Total 937 100.0 239 100.0

Considering only the subtable with cells of five or more cases in Table 4.31,
x2(2, N = 1073) = 24.85, p = 4.0e — 6, and 43 = 0.15.4 This suggests that there is
indeed an association between suspect / victim sex and disposition.

If the same analysis is applied to the subset of cases where (a) both the suspect
and victim are 18 years of age or older, and (b) there is clear evidence that the
relationship is between intimate partners, cases involving female-to—male suspect-

victirn relationships are 75% more likely to have their cases dismissed (as opposed

 

‘4) is a measure of association with values that range from 0 to l, with 0 indicating no association
between the variables and 1 indicating perfect association between two variables.

154

 

 

Table 4.31: Test of Association Between Disposition Suspect /Victim Sex

 

 

 

 

Male-to-female Female-to-male
Disposition Freq. Freq
Denied 354 137
Dismissed 86 22
Plead guilty 404 70

 

 

 

x2(2,N = 1073) = 24.85, p = 4.0e — 6, ¢ = 0.15

to 50% for all types of relationships) (see Table 4.32).

 

 

 

Table 4.32: Dispositions by Suspect /Victim Sex for Adult Domestic Violence Cases
Male-to-female Female-to—male
Disposition Freq. % Freq %
Denied 127 32.1 63 56.3
Dismissed 37 9.3 10 8.9
Guilty at trial 2 0.5 1 0.9
Nolled 3 0.8 1 - 0.9
Not guilty at trial 1 0.2 0 0
Plead guilty 192 48.5 36 32.1
Plead no contest 34 8.5 1 0.89
Total 396 100.0 112 100.0

 

 

 

 

 

Selecting the same subtable, x2(2, N = 465) = 17.56, p = 1.5e— 5, and d) = 0.19,
indicating that the association gets stronger (d) = 0.19 for adult domestic violence
cases versus ¢ = 0.15 for all types of relationships) (see Table 4.33).

To test whether female suspects were more likely than male suspects to have
first appeared as a victim on a warrant, the finite state machine shown in Figure
4.39 was used to generate the frequencies for each the transitions depicted. The test
is whether the number of transitions from female victim to female suspects relative
to the number of transitions from the initial state to female suspects is greater than

the corresponding relation for male suspects.

155

 

 

Table 4.33: Test of Association Between Disposition SuSpect / Victim Sex for Adult
Domestic Violence Cases

 

 

Male-to-female Female-to-male
Disposition Freq. Freq
Denied 127 63
Dismissed 37 10
Plead guilty 192 36
Plead no contest 34 1

 

 

 

 

 

x’(2,N = 465) = 17.56, p = 1.5e — 5, a = 0.19

Figure 4.39: Finite State Machine to Test Paths of Suspects by Sex

Female Warrant with _, Female
victim female suspect suspect
Warrant with /
female victim Warrant with
female suspect

 

/
\

Warrant with
male suspect

Warrant with
male Vimlm \
Warrant with_> Male
male suspect» 3039“”

156

 

 

The results of running this analysis for all cases are listed in Table 4.34. Indeed,
female suspects are much more likely than male suspects to have first been recorded
as victims of domestic violence. Running the same analysis on cases involving adult
domestic violence showed a similar result (see Table 4.35), with the strength of

association increasing from 43 = 0.26 to 45 = 0.35.

Table 4.34: Suspects by Previous State and Sex of Individual

 

 

 

 

 

 

 

 

Male Female
Previous state Freq. Esq
Initial 784 92.9% 208 73.2%
Victim 60 7.1% 76 36.5%
ITotal ] 844 100.0%[ 234 100.0%J

 

x2(1.N = 1128) = 77.4, p = 1.4e — 18, ¢ = 0.26

Table 4.35: Suspects by Previous State and Sex of Individual for Adult DV

 

 

 

 

 

 

 

 

Male Female
Previous state fieq. Freq
Initial 320 94.4% 72 69.9%
Victim 19 5.6% 34 32.1%
[Total [ 339 100.0% I 106 100.0% |

 

x20, N = 445) = 53.9, p = 2.1a - 13, ¢ = 0.35

4.9 Key informant interviews

The formulation and analysis of the baseline model generated questions for key
informant interviews about the model’s formulation, validity of various trends and
structure, and additional feedback 100ps. A total of seven interviews were conducted

with five key informants. Three of the key informants had victim advocacy positions,

157

‘t

 

 

while the other two key informants worked for the prosecutor’s office. All five
key informants had attended a variety of domestic violence trainings. All five key
informants had experience working with victims of domestic violence, with a range

of between 4 to approximately 10 years experience.

4.9.1 Victim arrests

The three key informants with victim advocacy positions reported a trend of victims
of domestic violence being arrested by police. These were not dual arrests, but
single arrests where the police arrested the victim instead of the assailant. One
described the trend as increasing from 1998 through 2000, and getting better in
2001. Several reasons were given for the decline starting in 2001. First, victim
advocates would talk with individual police officers on a case-by-case basis after a
victim was arrested. The nature of these conversations focused on helping officers
identify victims of domestic violence and helping officers understand the dynamics of
domestic violence. Second, the domestic violence shelter and police departments had
increasingly disagreed on issues of sharing information about victims between victim
advocates and law enforcement. This conflict deteriorated victim advocates’ access
to law enforcement officers from 1998 through 2000. In 2000, however, changes in the
leadership of both the police department and domestic violence shelter resulted in a
renewed sense of c00peration and access to police officers in cases where victims were
arrested. Third, the prosecutor’s office started in 2001 to have only one assistant
prosecuting attorney handle all of the domestic violence cases, with exception of
sexual assaults, as Opposed to dividing the work between two assistant prosecuting
attorneys. This simplified communication with the prosecutor’s office for victims
and victim advocates, making it much easier to respond quickly to cases where the

victim had been arrested.

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4.9.2 Batterer intervention programs

All of the key informants with knowledge of batterer intervention programs and state
standards (four out of the five) reported that the batterer intervention programs in
their community were ineffective and did not hold assailants accountable. None
of the programs followed the minimum standards of a Duluth-like accountability

model.

4.9.3 Trends

Key informants reported no change in the severity or intensity of domestic violence
over the four year period. Nor did key informants report any general trends in the
demographics of victims or assailants. Two key informants did, however, report
that the increased outreach efforts from 1998 to 2001 had resulted in an increased
awareness in the community of domestic violence and an increased demand for ser-
vices. One key informant reported that a number of repeat assailants that had been

consuming a significant amount of time and energy moved out of the jurisdiction.

4.9.4 Victim advocacy

Three of the five key informants emphasized the importance of having a skilled do—
mestic violence victim advocate working with the prosecutor’s office. This position
was funded under the grant supporting the coordinated community response and
filled by a person with substantial victim advocacy experience. The victim advo-
cate was given a list of all meetings scheduled with victims for the week. The victim
advocate would meet with the victim before the initial meeting with the assistant
prosecuting attorney, be with the victim during the meeting, and with time permit-

ting, follow up with the victim after the meeting. Unlike victims seeking domestic

159

 

 

 

 

violence shelter or calling the crisis hotlines, who were more likely to identify their
experience as domestic violence, victims in the criminal justice system were more
likely to see the assailant’s behavior as an isolated incident. The victim advocate
would assess for patterns of domestic violence, provide the victim with some basic
information about domestic violence (e. g., power and control wheel, cycles of abuse),

facilitate referrals to local resources, and help the victim with safety planing.

4.9.5 Prosecution

Staring in 1995, the prosecutor’s office implemented an evidence based no-dr0p pros-
ecution policy, which meant that cases would be prosecuted without requiring victim
testimony and the prosecutor would not dismiss the case if the victim wanted the
charges dropped. Starting in 2001, the prosecutor’s office moved to vertical prose-
cution, which meant that the same prosecutor handled the case, from the warrant
review to the final disposition.

While most of the cases that were prosecuted resulted in plea agreements or
dismissals, some did go to trial. The assistant prosecuting attorney selected the
cases that would go to trial on the basis of wanting to set a precedent for future
plea negotiations. For example, a case where the suspect had only one criminal
charge but a pattern of abusive behaviors might be pushed to trial as a way to raise
the “going rate” for that type of case, where the “going rate” would be the likely
sanction for a case with similar attributes. Meanwhile, the defense bar was closely
monitoring the types of cases that were pushed to trial and their outcomes.

Key informants did report some effects of caseload pressure on decisions affecting
case disposition, but this was primarily limited to cases receiving more generous
plea offers. These were described as times of “bad judgment” where the assistant

prosecuting attorney might offer a delay of sentence for an assailant with a pattern of

160

 

 

 

abuser where ordinarily no such offer would be made. These periods were reported

as being infrequent and limited in time, on the order of one or two weeks.

4.9.6 Resource issues

Key informants reported three major resource issues. First, raising awareness of
domestic violence in the community through increased outreach and victim services
increased demand for victim services. A federal grant made the increased outreach
and victim services possible. However, the demand for services remained steady even
after the grant ended. Thus the domestic violence shelter and victim advocates were
faced with the problem of having to meet the same demand for services, but with
fewer resources.

Second, funding a domestic violence victim advocate for the prosecutor’s office
allowed the victim advocate to be available for most meetings with the prosecutor.
When the position was no longer funded, the victim advocate was forced to divide
time between the prosecutor’s office and domestic violence shelter, with shelter crises
taking priority over meetings in the prosecutor’s office. The result was less victim
advocacy in the prosecutor’s office.

Third, between 10 and 25% of the assistant prosecuting attorney’s time assigned
to domestic violence cases was devoted to seeking and justifying funding for the
domestic violence unit. This time was not distributed evenly, but concentrated
in brief periods when proposals and grants were being prepared. Meetings with
victims would often be rescheduled during these periods to the following weeks,
which made it less likely that victims would show up for the meetings with the
assistant prosecuting attorney. The assistant prosecuting attorney was also much
less likely to visit crime scenes and interview other witnesses during such periods,

delegating these tasks to police officers. The net effect was less assessment of the

161

 

 

 

 

pattern of violence, less safety planning, and weaker criminal cases.

4.9.7 Rural issues

Closely related to resource issues were what might be called rural issues. Several
key informants identified specifics of providing services to domestic violence victims
in rural communities. For example, jurisdictions were geographically larger, which
resulted in longer travel time. Longer travel times meant longer delays in terms
of meeting with victims to provide advocacy and more resources for investigating
and interviewing crime scenes. Rural communities are also small communities, and
several key informants pointed out that individuals fighting against domestic vio-
lence were quickly identified and often became targets for assailants. For example,
assailants were more likely to effectively access and use local media to slander in-
dividuals. Although not true for all rural communities, this one was outside the
circuit of speakers and various professional resources that one might tap into for
support and continuing education. The result was that professionals felt more iso-
lated, and used more financial resources for travel to conferences and other types of

professional deveIOpment opportunities.

4.10 Revised model

Analysis of the baseline model and key informant interviews identified five new
feedback structures for the revised model: safety planning, community awareness,
resource allocation, “going rate”, and prosecutor meetings with victims. Each of
these structures represents an additional submodel, with a corresponding need for
numerical time series data. The numerical data that might be used to generate

such time series, especially the shelter outreach and contact data, was unavailable

162

 

 

at the time of this writing because the original grant funding the data collection
had been extended another six months, ending in March 2003. Thus, in contrast to
the descriptive and baseline models, the revised model is conceptual in nature.

In order to distinguish the existing structure of the baseline model and revised
model, italics will be used to denote the new variables in the revised model. Vari-
ables in the revised model represent general concepts, which would typically be
disaggregated in a numerical model.

Safety planning represents a critical balancing feedback 100p (B1) to positive
feedback loop effect of arrests of assailants resulting in assailants learning how to get
victims arrested (R1) in Figure 4.40. Safety planning is the outcome of Meetings with
victims and counteracts the effect that some assailants will learn how to manipulate
the system. Specifically, victim advocates and the assistant prosecuting attorney
can, during meetings with victims, assess for patterns of domestic violence and help
the victim develop safety plans, which might help the victim identify more Options
and anticipate some of the tactics that the assailant might use as a consequence of
his contact with the criminal justice system.

First arrests increases the level of Community awareness, and this increases
the likelihood of more incidents of domestic violence being reported, resulting in a
reinforcing feedback 100p (R2) in Figure 4.41. For example, a coworker or neighbor
who one did not suspect of being a batterer is arrested for domestic violence. It
is possible that Repeat arrests also contributes to Community awareness, but it is
less clear whether the effect is to increase or decrease Community awareness as
something that increases reporting. For example, Repeat arrests might discourage
individuals from reporting as they feel increasingly frustrated with arrests having
no desirable impact on the abuser.

The resource allocation structure shown in Figure 4.42 introduces four feedback

163

 

 

Figure 4.40: Safety Planning in Revised Model

sift; ”\

Meetings with

' victims
No prlor R1
DV 0
39

Safety
planning

 

 

 

 

 

 

 

 

New cases

Figure 4.41: Community Awareness in Revised Model

 

Prlor DV

at

Community @ Flrst
awareness

arrest

 

 

 

 

 

 

 

 

No prior
DV

 

 

 

164

loops. First, there is the effect that as more prosecutors are allocated to seeking
funding for the domestic violence unit, there are more prosecutors to allocate, and
more prosecutors to seek funding (R3). DV unit funding also creates a demand
on Prosecutors needed, which increases the Prosecutors allocated to seeking funding
(B3). This might happen, for example, when funding levels go below the desired
goal and there is an increased pressure to find new grants. When more prosecutors
can be allocated, Prosecutors allocated, there can be more Meetings with victims,
which decreases the demand for prosecutors, Prosecutors needed, forming a balancing
feedback loop (B2). Meeting with victims is also within another feedback loop.
Specifically, as there are more Meetings with victims, there is more demand for
prosecutors to meet with victims relative to demand to for funding the DV unit,
thus Prosecutors allocated to finding funding for the DV unit goes down, the DV
unit funding goes down, and the funding for the victim advocate position decreases,

which decreases number of or delays Meetings with victims (B4 in Figure 4.42).

Figure 4.42: Resource Allocation in Revised Model

B10

     

Meetings with

victims “Humor.

allocated

 

 

165

 

 

 

The Going rate is a stock variable that is perceived, imperfectly, by the assistant
prosecuting attorney and defense attorneys (see Figure 4.43). When the Going rate
is high, more cases can be disposed through Plea agreements faster, which lowers the
Prosecution caseload, and decreases the cases that are Dismissed. Fewer dismissals
has the effect of increasing the Going rate. Thus, a higher Going rate has the effect
of increasing the Going rate, forming a reinforcing feedback 100p (R5).

If one expects there to be some deterrence effect from arresting and prosecut-
ing assailants, then a higher Going rate should lower Repeat arrests, which would
decrease the Warrant requests and the number of Warrants denied. And fewer war-
rants being denied will have the effect of further increasing the Going rate, forming
another reinforcing feedback 100p (R4).

The assistant prosecuting attorney develops a better understanding of the case
by meeting with the victims (see Figure 4.44). So more Meetings with victims means
more Plea agreements, which lowers the Prosecution caseload, and this lowers the
number of Prosecutors needed, for meeting with victims, and thus fewer prosecutors
are allocated to meet with the victim, Prosecutors allocated, which reduces the
number of Meetings with victims. This forms the balancing feedback loop B5. The

resulting revised model is shown in Figure 4.45.

4.11 Conclusion

This chapter described the results, including descriptions of the violence against
women (VAW) database, comparisons with census statistics, and dispositions. Three
descriptive models were presented. Analysis of the fit statistics suggested that a
descriptive model based on dispositions being modeled as a function of caseload

performed better than models where dispositions were modeled as a function of case

166

 

 

Figure 4.43: “Going Rate” in Revised Model

 

Going rate

     

 

   
 

Effects of @
dispositions on
going rate
Warrants Dlamlaaala

 

Prosecution
caseload

 

 

 

Plea
agreements

167

 

 

Figure 4.44: Prosecutor Meetings with Victims in Revised Model

 

 

 

;/ "3.17333"

 

 

Prosecutors
needed
Meetings with Prosecutors 9|“
victims allocated agreements

 

Q...)

168

 

 

 

 

Figure 4.45: Overview of Revised Model

           

  

Effects of

 

 

 

 

 

 

 

dispositions on
Exiting going rate
Warrants Dismissals
Prior DV Repeat
arrests
Community First
awareness arrests
NOON” Meetings W ’ Prosecutors Plea
V ‘ victims allocated —> agreements
Safety
planning

 

New cases 4/ DV unit
funding

169

attributes. The chapter then presented the baseline model. Analysis of the baseline
model showed that it did a reasonable job of reproducing the behavior of the real
system given its simplicity.

The main result of the baseline model in terms of the study was that account-
ability and the prosecutor’s office caseload of first arrests were both controlled by
the feedback loop representing the mechanism of allocating prosecutor resources to
warrant reviews, but only when the system was in equilibrium.

One problem in the baseline model concerned the aggregation of first and repeat
arrests. Disaggregating arrests by other variables led to an important insight into
a potential positive feedback loop between the first time arrests of male assailants
and the risk of arrest of female victims.

Finally, the baseline model was used to motivate questions for key informant
interviews. The key informant interviews provided further support for the claim
that there exists a positive feedback loop linking first arrests of male assailants and
the arrest of female victims. Victim advocacy emerged as a critical component of
prosecuting domestic violence cases, and key informants suggested several feedback
mechanisms that related to the prosecution of criminal domestic violence cases.
These were summarized in the presentation of feedback loops that would be added

to the baseline model to form a revised model.

170

 

 

 

Chapter 5

Conclusion

5. 1 Overview

This chapter provides a summary of the major findings, along with their policy
implications, strengths and limitations of the approach taken in this research, and

directions for future research.

 

5.2 Major findings and discussion -«._

 

There were nine major findings in this study:

Finding 1: Descriptive models with dispositions written in terms of caseloads out- '
performed similar models with dispositions written in terms of case attributes.
The major implication of this finding is that, at some level, diSpositions are

affected by the size of the prosecutor’s caseload. That is, there is evidence in

 

supporting the caseload pressure hypothesis.

Finding 2: The baseline model, formulated as a simple flow of cases from arrest

to dispositions, did a reasonable job of reproducing the observed time series.

171

The model was structurally unable to reproduce what might be some impor-
tant oscillations in the dismissals of repeat arrests. The major implication of
this is that casefiow dynamics alone can explain the general four-year trends,
but not some oscillations like those seen in the dismissals of repeat arrests.
That is, the baseline model is a good robust model for studying the general
trends of caseflows, but additional structures are needed for studying some

key oscillations like dismissals of repeat arrests.

Finding 3: Sensitivity analyses point to problems in the baseline model’s response
to higher frequency oscillation. Higher frequency oscillations can be indica-
tions of information mechanisms. Information feedback mechanisms include
such things as perception of caseloads or the “going rate”, awareness of domes-
tic violence resources, court rulings, and actual paper work. The implication is
that additional structures are needed for studying oscillations like dismissals
of repeat arrests, which are likely to be information mechanisms. That is,
things like perception of caseload, the “going rate”, and the awareness of do-
mestic violence resources need to be added to the baseline model in order to

reasonably represent some variables like dismissals of repeat arrests.

Finding 4: The baseline model was sensitive to reductions in prosecutor resources.
Specifically, cutting prosecutor resources changed the dynamics of warrant
reviews from authorizing warrants on the basis of case attributes to denying
warrants because of limited resources. The implication is that the primary im-
pact of cutting prosecutor resources on the dynamics of prosecuting domestic
violence cases is on the denial of warrants, not the dismissal of cases or plea of-
fers being accepted. Specifically, cutting prosecutor resources essentially puts

a cap on the number of cases that can be authorized, and this makes the level

172

 

of prosecutor resources the main determinate of warrants being authorized, as
opposed to whether or not there is probable cause. That is, cutting prosecu-
tor resources causes warrant reviews to be dominated by caseload pressures as

Opposed to professional norms.

Finding 5: The baseline model was insensitive to increases in new cases. Increasing

the rate that individuals flowed into the criminal justice system generally did
not, surprisingly, affect the dynamics prosecutor caseloads or case dispositions.
The implication is that the structure of prosecutor’s office caseflows is robust
with respect to increases in new cases. What this means is that, according to
the baseline model, policy changes that increase the number of new cases and
thus arrests will generally not affect the prosecution dynamics. That is, when
there are adequate resources for the prosecuting domestic violence cases, the
prosecutor’s office can absorb relatively large increases innew cases without
affecting the caseflow dynamics of prosecution outcomes or having to increase

prosecutor resources.

Finding 6: Accountability and prosecution caseload of first arrests shared a com-

mon dominating feedback IOOp, allocation of prosecutors to authorizing war-
rants, but only when the model was in equilibrium. The implication is that
accountability and prosecution caseload are controlled by a common feedback
loop when caseloads are in a steady state, that is, when caseloads are neither
increasing nor decreasing. Moreover, structural changes during steady state
to increase accountability would also have the unintended consequence of also
changing the dynamics of caseloads. That is, if prosecution caseloads were sta-
ble, one would have to counteract the effects on prosecution caseload of policy

changes to increase accountability in order to avoid changes in the dynamics

173

 

 

 

of case dispositions.

Finding 7: There were strong indications of a positive feedback IOOp linking the
first arrest of male assailants and the subsequent risk of arrest for female
victims. Victim advocacy and safety planning with female victims at the
prosecutor’s office are potentially vital interventions that might be counter-
acting some of the effects of the positive feedback IOOp linking first arrest of
male assailants and the subsequent risk of arrest for female victims. The main
implication is that female domestic violence arrests represent female victims

being arrested, not female perpetrators of domestic violence.

Finding 8: An underlying assumption in this study was that the prosecutor’s of-
fice Operated under fixed funding constraints. Thus, resource allocation was
achieved by managing caseloads as Opposed to increasing revenues. However,
key informants pointed out that a significant portion of their time (up to 25%)
went into grant writing and reporting (i.e., maintaining or increasing their re
sources). The main implication is that resource allocation is dynamic. That
is, trying to increase prosecutor resources can consume a significant portion of
resources, which ultimately affects the outcomes of prosecutions. This can lead
to even more demand for prosecution resources. Thus, the resource allocation

problem for the prosecutor’s office is dynamic.

Finding 9: An assumption in the baseline model had been that the infrequent
nature of trials meant that they had little impact on the prosecutor’s office
caseload and holding assailants accountability. However, key informants re-
ported that trials were critical for establishing the “going rate” of a criminal
offense, and that this “going rate” determined subsequent negotiations of plea

agreements between the assistant prosecuting attorney and defense attorneys.

174

That is, the feedback loops between trials and the “going rate” need to be

included in future system dynamics models.

5.3 Limitations of study

There are five major limitations of this study: community racial / ethnic demograph-
ics, lack of replication, use of sparse time series, uncertainty in validity of identifying
first time arrests, and peripheral role of stakeholders. The last four stem from an
original decision to focus on understanding and developing methods for subsequent
studies. This design decision was partly motivated by the possible availability of
additional data from an ongoing evaluation study of the county’s coordinated com-
munity response effort to domestic violence. However, the funding for the evaluation
study was extended by six months, which effectively postponed the availability of
additional data sets until April, 2003. This limited the numerical data available for
this study to the existing prosecutor’s office VAW database, which increased the
importance on being able to extract and evaluate time series data from an other-
wise messy database, and this eventually led to the postponement of the initial key

informant interviews.

5.3.1 Community racial/ ethnic demographics

The population was mostly white non-Hispanic (see Table 4.2). Race/ ethnicity, as
a case attribute of victims and offenders, was thus less likely to have a measur-
able effect on the disposition of cases. In turn, this would increase the effects of
caseloads on case dispositions relative to case attributes. Case attributes could well

play an equal if not larger role than caseload on case dispositions in more diverse

communities.

175

 

 

 

 

5.3.2 Lack of replication

The second major limitation of this study and its findings was the single case study
design. Single case study designs are inherently limited in their lack of replication
and the results cannot be generalized beyond the single case. The decision to focus
on a single case of a prosecutor’s office was originally motivated by (a) the desire
to understand and deve10p methods that might be subsequently applied in a mul-
tiple case study design, and (b) the potential availability of numerous data sets
from other researchers working on an evaluation study of the county’s coordinated
community response to domestic violence. The main implication of being limited to
the Violence Against Women (VAW) database from the prosecutor’s office was that
there were no independent means of validating its contents, and there were obvious
indications of inconsistency in data entry. This resulted in more emphasis being
placed on understanding the contents of VAW database, data cleaning, construction

of variables for analysis, and checking variables.

5.3.3 Sparse time series

Deciding that it was important to handle sparse time series introduced major prob-
lems in terms of both representing the real data and evaluating the final results of the
model. First, using a smoothing algorithm had the effect of introducing transients
that were not present in the original raw time series and did not, at a conceptual
level, make sense. This was specifically true for rates such as First arrests and
Repeat arrests, which appeared to gradually increase in 1998 when the raw data
indicated that they started out in 1998 near their mean. While this did not affect
the baseline model’s performance, it made it difficult to interpret the results in real

terms. This gradual increase or transient response could have been offset by adjust-

176

 

 

 

ing the initial values of the smoothing algorithm, but this would have complicated
the initialization of the baseline model. Ordinarily, this would not be a problem,
but since the model was required to satisfy a range of inputs and outputs from
different smoothing algorithms (a consequence of the approach to handling sparse
time series), each smoothing algorithm would have implied a different procedure
to initialize the model. Similar problems appeared with the smoothed time series
being delayed. Both approaches might be solved by selecting a class of smoothing
filters that minimizes some of these distortions or providing ways of compensating
their output in terms analytically related to the parameters used in the smoothing
algorithm.

Second, analyzing the sensitivity of the simulated model to variations in smooth—
ing parameters (smoothing delays) turned out to be more elusive than expected.
While summary statistics provided a means of comparing model and real data in a
systematic way, it was difficult to assess what different patterns Of comparisons actu-
ally meant. More theoretical work on this approach is needed in terms of analytical
results, simulation studies, and demonstrations with other data sets.

Third, generating the summary statistics manually drastically limited the amount
of variation that could realistically be studied. For example, it would have been good
to not only vary the length of the delay in the smoothing algorithm, but the order
of the delay and even the type of smoothing algorithm. But, doing so would have
generated hundreds of data sets that needed to be compared. This is more of an
implementation issue. Automating some of these procedures clearly helped, but
more s0phisticated routines could generate a family of smoothed data and run the

comparisons with the real data.

177

 

 

 

5.3.4 Validity of identifying first time arrests

The fourth major limitation of this study concerned the procedure used to identify
first time arrests. Specifically, first time arrests were identified according to their
first appearance in the Violence Against Women (VAW) database starting January
1, 1998. Anyone with an arrest prior to January 1, 1998 would have the first arrest
after that date count as a first arrest as Opposed to an actual repeat arrest. This
would have the effect of elevating the number Of cases appearing as first time arrests.
The distortion would be the highest immediately after January 1, 1998, and then
gradually decline as one considered more recent offenses. This introduced a question
about the validity of the identification of first time arrests in this study. Additional

prosecution, police data, and shelter data might have helped answer this question.

5.3.5 Stakeholders

The fifth major limitation of this study was that stakeholders had a peripheral role
at the end of the model building. The problem of improving the capacity of a
prosecutor’s office to hold assailants accountable by understanding how domestic
violence caseloads were managed was not defined in terms of the prosecutor’s Office.
The prosecutor’s office was, in fact, much more concerned about victim safety and
supporting the critical role of the victim advocate. Ideally, stakeholders should be
included at the beginning of a project in defining the problem, the purpose of the
model, and the criteria for evaluating the model. Deciding to involve stakeholders
late in the modeling effort was part of the trade—off between focusing on methods
and problem solving. But future system dynamics studies should, unless purely con-
cerned with method, begin by meeting with potential stakeholders and identifying
the problem to be solved.

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5.4 Policy implications

As a single case study design, the policy implications are only provisional. The main
policy implication of this study concerns the positive feedback loop from first arrest
of male assailants to female victims being arrested, which represents an unintended
consequence of mandatory arrest policies. That is, one unintended consequence
of mandatory arrest policies might be that some assailants learn, through their
first contact with the criminal justice system the criteria for an arrest, and begin
using that knowledge in their manipulation Of the criminal justice system to get
victims arrested as a battering tactic. Key informants pointed out that this also
happened with child protective services (CPS), where the assailant would learn the
CPS worker’s criteria, and use that knowledge to manipulate CPS to gain custody
over children, and thereby use the children as a battering tactic to manipulate their
mothers.

Experienced victim advocates understood these risks and would work aggres-
sively with victims in terms of safety planning. This was especially critical in
criminal cases, where victims might not identify themselves in a domestic violence
relationship and minimize the severity of the pattern of abuse. Information about
patterns of domestic violence, helping the victim assess her own safety, and provid-
ing resources such as shelter and legal advocacy appeared to counteract the effects
of some assailants using the criminal justice system and CPS against the victim.
But this required victim advocates with significant experience working with victims
in the area of domestic violence. Thus, the main policy recommendation would be

for more stable funding of domestic violence victim advocates.

179

 

5.5 Directions for future research

The immediate next step is develOping the revised model and formulating the feed-
back relationships described by key informants. The key informant interviews pro-
vided a basis for identifying several dynamic problems. Thus, the revised model
can be better oriented toward solving a specific problem. It should also be possible
to calibrate and test the revised model with the availability of additional numerical
data from police departments and domestic violence shelters.

A major limitation of this study was the lack of replication. So an obvious
next step is to consider several diverse prosecutor’s offices, and compare the results
of specifically calibrating the revised model to each county’s prosecutor’s office.
Qualitative differences between the fit should indicate structural differences between
the counties in terms of feedback 100ps. This would lead to further refinement and
understanding of how accountability and prosecutor’s office caseloads are related.

A general model should also be able to, with proper parameterization, reproduce
related phenomena. One possibility would be to extend the model to the arrest
and prosecution of driving under the influence (DUI) cases, which also result in
a high volume of referrals to diversion or counseling type interventions programs.
This would be a good test for both the baseline and revised model, although it
might ultimately be more difficult to successfully adapt the revised model to the
prosecution of DUI cases. Differences in performance between the two domains
would indicate either similar structures that had been excluded from the model or
structural differences between domestic violence and DUI cases.

A fourth direction for future research concerns the theory of analyzing feedback
IOOp dominance. In system dynamics, the relationship between structure and behav-

ior of complex dynamic systems'is thought of in terms of feedback loop dominance.

180

 

Deepite recent efforts to formalize and automate the analysis of feedback 100p dom-
inance, the results have been disappointing. The alternative has been to rely on
the existing ad hoc methods that can lead to misperceptions of model behavior. If
the goal of system dynamics is to make a contribution to the understanding of com-
plex systems, then it seems essential that both (a) the underlying theory of feedback
loop dominance be extended, and (b) that methods be developed for more efficiently
and systematically identifying patterns of feedback loop dominance. For example,
it seems that one should with at least simple models be able to analytically relate
various features of feedback 100p dominance. It seems equally important to develop
or extend existing procedures for automatically identifying patterns of feedback 100p

dominance, especially for larger models.

5.6 Conclusion

One of the challenges for this study was to develop methods for studying com-
munity responses to domestic violence that paid attention to problem of modeling
small populations. The emphasis on developing skill and a method for applying
system dynamics to the general problem of increasing assailant accountability led to
a disprOportionate effort being spent on a variety of technical issues as Opposed to
problem formulation, model building, and involvement of stakeholders. A quicker
and more productive route to actually develOping a model that might have some
immediate benefits to stakeholders in terms of implementation could have been pro-
duced with earlier involvement of stakeholders at the stage of defining the problem
and purpose of the model, but not without sacrificing a certain degree of under-
standing the differences between a system dynamics approach and other methods.

Specifically, paying attention to issues such as working with sparse time series and

181

 

 

differences between descriptive and mechanistic accounts of the data led to theoret-
ical insights that had real consequences in terms of how one might evaluate claims
involving complex systems.

For example, it is common in statistical model building to focus on estimating
various parameters as if these parameters are inherently meaningful. But there are,
in fact, many possible formulations that can describe the same set of behaviors.
To develop a sense of what a parameter means, one must have a sense of what it
does not mean and why. This is not something that can simply be done through an
Operational definition. It requires a familiarity with the field of possible meanings.
And to achieve that, one must not look narrowly at fitting one model, but develop
and consider a variety of models that all claim to account for a similar concept. This
was, abstractly speaking, the approach that emerged in Chapter 3 when considering
the problem of sparse time series, and in Chapter 4 when comparing and contrasting
the descriptive and baseline models.

Accounting for feedback loops and analyzing the relationship between their struc-
ture and resulting behavior is critical if one is going to try and understand the inter-
actions and behaviors of complex systems. System dynamics is a promising method
for doing this, especially when one can use both numerical time series and involve
stakeholders in defining the purpose of modeling and as key informants. However,
more work needs to be done in relating the structure of feedback 100ps to under-
standing the system’s behavior in terms of patterns of feedback 100p dominance.
Otherwise, fully analyzing system dynamics models of complex and emerging social

problems will have limited application in social work and the social sciences.

182

 

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