Logrolling in the Supreme Court

Echo Marie Keif
A Thesis Submitted to the Faculty of
The Wilkes Honors College
in Partial Fulfillment of the Requirements for the Degree of
Bachelor of Arts in Liberal Arts and Sciences
with Concentrations in Economics and Mathematics
Harriet L. Wilkes Honors College of
Florida Atlantic University
Jupiter, FL
May 2008
Echo Marie Keif
This thesis was prepared under the direction of the candidate’s thesis advisors, Dr. Keith
Jakee and Dr. Terje Hoim, and has been approved by the members of her supervisory
committee. It was submitted to the faculty of The Honors College and was accepted in
partial fulfillment of the requirements for the degree of Bachelor of Arts in Liberal Arts
and Sciences.
Dr. Keith Jakee
Dr. Terje Hoim
Dr. Martin Sweet
Dean, Wilkes Honors College
I would like to acknowledge Dr. Keith Jakee for pushing me to define and
redefine my claim. His guidance led me to research logrolling and apply it to my chaotic
fancies of analyzing the First Amendment. He has apprenticed me into the art of research,
for which I am very thankful. I would also like to acknowledge Dr. Terje Hoim who has
spent countless hours explaining the mathematics behind and within this thesis. She has
taught me the language of mathematics and changed my academic direction for the better.
Finally, I would like to acknowledge Dr. Martin Sweet for his information packed
meetings exposing me to the realm of law and politics.
Echo Marie Keif
Logrolling in the Supreme Court
Wilkes Honors College at Florida Atlantic University
Thesis Advisors:
Dr. Keith Jakee and Dr. Terje Hoim
Bachelor of Arts in Liberal Arts and Sciences
Economics and Mathematics
While studies have considered the presence and impact of logrolling (vote
trading) on legislative actors, little work has questioned the possibility of judicial
logrolling among Supreme Court Justices. Supreme Court Justices are usually assumed to
be free from constituencies and political party pressures. This assumption is derived from
life-long appointments that do not require the endorsement of reelection. However, public
choice would predict the presence of logrolling in cases where intense differences in
preferences exist among justices. We only expect to see logrolling when vote trading has
the potential to change voting outcomes. Thus, to study the probability of logrolling
plurality, majority, and unanimous decisions must all be considered. Essentially, I will be
altering previous models of legislative logrolling in accordance with the conditions of the
Supreme Court to describe possible logrolling scenarios. This study does not aim to prove
the existence of logrolling among Supreme Court Justices, only that it is a possibility.
INTRODUCTION............................................................................................................... 1
CONCEPTUAL FRAMEWORK ...................................................................................... 5
PUBLIC CHOICE PERSPECTIVES .................................................................................. 5
LITERATURE REVIEW ................................................................................................. 8
LOGROLLING DEFINED ............................................................................................... 11
WHAT IS LOGROLLING? ........................................................................................... 11
ADAPTED JUDICIAL LOGROLLING MODEL................................................................ 12
TRANSLATION DIFFICULTIES .................................................................................... 17
BACKGROUND ON THE SUPREME COURT ............................................................. 18
THE SUPREME COURT INSTITUTIONIALIZED ............................................................. 18
ROLE OF LAW CLERKS ............................................................................................. 19
HOW DECISIONS ARE MADE .................................................................................... 21
GAME THEORY MODEL AND SCENARIOS.............................................................. 28
SETTING UP THE GAME ............................................................................................ 28
5.1.1 SINGLE DEALING PRISONERS' DILEMMA ......................................................... 33
5.1.2 REPEATED DEALINGS AND SUPERGAMES ........................................................ 35
5.1.3 FINITELY REPEATED DEALINGS PRISONERS' DILEMMA ................................... 38
POSSIBLE STRATEGIES.............................................................................................. 42
5.2.1 PLAYING GRIM ................................................................................................ 42
5.2.2 PLAYING TIT-FOR-TAT AND TAT-FOR-TIT ...................................................... 44
PAYOFFS AND COOPERATION ................................................................................... 45
5.3.1 FOLK THEOREM............................................................................................... 45
5.3.2 SOCIAL CONTRACT THEORY ........................................................................... 47
GAME THEORY CASE STUDIES ................................................................................. 49
SELECTION OF CASE STUDIES................................................................................... 49
CASE STUDIES ......................................................................................................... 50
6.2.1 FORCING UNAMITY ......................................................................................... 50
6.2.2 INCONSISTENT IDEOLOGY ............................................................................... 55
IMPLICATIONS OF LOGROLLING.............................................................................. 61
CONCLUSION ................................................................................................................. 64
REFERENCES.................................................................................................................. 66
POSSIBLE DIAGRAM OF VOTES BEFORE LOGROLLING .............................................. 15
POSSIBLE DIAGRAM OF VOTES AFTER LOGROLLING ................................................ 16
CONCURRING BEHAVIOR OF JUSTICES ..................................................................... 23
DISSENTING BEHAVIOR OF JUSTICES ....................................................................... 24
REDUCED GAME TREE OF LOGROLLING SCENARIO .................................................. 30
EXPANSION OF DECISION NODE FROM REDUCED GAME TREE ................................. 31
FURTHER EXPANSION OF DECISION NODE................................................................ 32
THE PRISONERS' DILEMMA ...................................................................................... 34
JUSTICE A'S POSSIBLE FUNCTIONS ........................................................................... 37
STAGE GAME OF A REPEATED PRISONERS’ DILEMMA .............................................. 38
FINAL STAGE OF A REPEATED PRISONERS’ DILEMMA .............................................. 39
A RESTRICTED STATEGIC FORM .............................................................................. 45
5.10 PAYOFF REGIONS ..................................................................................................... 46
EXTENSIVE FORM OF POSSIBLE BROW LOGROLL .................................................... 54
EXTENSIVE FORM OF POSSIBLE BAKKE LOGROLL..................................................... 59
While studies have considered the presence and impact of logrolling on legislative
political actors, little work has questioned the possibility of judicial logrolling among
Supreme Court Justices. Public choice models assume that voters seek to maximize the
number of votes in line with their own preferences (Downs, 1957). One approach to
maximize support for a position is the formation of logrolling coalitions among voters.
“Issues involved in a logroll are known to promise high benefits to a minority group and
to impose low costs on others, or the reverse” (Stratmann, 1992: 1164). Logrolling is a
type of political exchange, specifically vote trading, which occurs in the presence of
intense disparities between voter preferences (Mueller, 1989: 82).
Supreme Court Justices are usually assumed to be free from constituencies and
political party pressures, which create conditions ripe for legislative logrolling. This
assumption is derived from life-long appointments that do not require the endorsement of
reelection. In a system of checks and balances, it is vital that the Supreme Court be an
unflagging defender of the Constitution and the rights that it ensures to everyone equally.
Each case should manifest a commitment to equal treatment (Buchanan, 1975). It is often
argued that the courts should promote a justice by rule of law, not an arbitrary,
distributive justice (Hayek, 1944). These, however, are normative views of the Supreme
Court; history is littered with examples to the contrary, such as what Segal and Epstein
(2006) call trumping values, values of distributive justice rather than of real equality
under a common constitution.
Public choice theory would predict the presence of logrolling based upon the
intense differences in preferences among justices. This is not simply a matter of ideology.
An adaptation of a basic preference model of legislative logrolling asserts that while a
justice’s ideology will affect every vote he or she makes, “logrolling should be observed
only on issues for which the vote is close” (Stratmann, 1992: 1166). It is assumed that
there would be no need to trade votes in a decision for which those votes will not change
the outcome. For instance, we would not expect to observe logrolling if a unanimous
decision already existed. The legislative model would also predict that no logrolling
would occur after a majority decision had been reached, such as 6-3, 7-2, or 8-1
decisions. However, judicial decisions are distinct from those of legislative voting. In the
judicial sphere, plurality decisions will not hold the same weight as unanimous
decisions.1 Thus, the strength of a precedent decision will depend on every vote, not
merely on which side won a majority vote. So, it will be essential to consider not only
plurality and 5-4 decisions, but also other majority and unanimous court decisions, when
determining the probability of judicial logrolling.
Thomas Stratmann has developed an insightful model of legislative logrolling
illustrating how and why logrolling occurs (Stratmann, 1992). Although this model is
meant to analyze legislative actors, it has the potential to be altered in accord with the
conditions applicable to the Justices of the Supreme Court, often referred to as the “super
legislature” (O’Brien, 2005: 218). My study has adapted Stratmann’s basic preference
Plurality decisions are defined as decisions of no real majority, where the justices are unable to produce a
coherent and unified decision. “[U]nlike other Court decisions, plurality decisions are open to criticism
purely on the basis of their form; they are a body of cases exhibiting pathological decisionmaking that can
be identified without reference to a subjective evaluation of results” (Plurality Decisions and Judicial
Decisionmaking, 1981: 1127-1128). Precedents derived from plurality decisions are not considered as
highly as those of majority and unanimous decisions. Unanimous decisions are 9-0 decisions and hold the
strongest weight as precedent for future cases.
model to fit Supreme Court decision-making through the implementation of game theory
scenarios. Considering the depth of this study, it would be impossible to analyze every
Supreme Court decision, just as it would be infeasible to study whether logrolling has or
has not affected every legislative vote. Thus, this paper will be confined to Supreme
Court cases where logrolling may be an explanation for odd voting behavior among
justices. For our purposes, odd voting behavior will be characterized as a justice voting
against his or her particular ideological stance.2 These cases will be hand picked and
represent sample cases. Judicial logrolling is uncharted territory with sparse evidence and
little research. I only hope to offer a small glimpse into what may occur in another black
box of government.
This study does not aim to prove the existence of logrolling among Supreme
Court Justices, only that it is a possibility. In Chapter 2, I provide a concise literature
review of public choice perspectives, what logrolling encompasses, and previous studies
of logrolling within a legislative framework, including a brief exposure to the attitudinal
model of justice voting proposed by Segal and Spaeth (2002). In Chapter 3, I present a
formalized preference model of logrolling borrowing heavily from Stratmann (1992). In
Chapter 4, I provide a description of the Supreme Court as an institution and how
decisions are made. In Chapter 5, I employ game theory to illustrate the mechanics of
justice voting and how logrolling could occur in a judicial setting. In Chapter 6, I extend
my game theoretic model to map out actual Supreme Court cases and possible logrolling
A justice’s ideological stance can be measured in countless ways, including the Quinn-Martin and SegalCover scores, which act as ideological proxies. While each proxy is measured in a slightly different way,
both offer a great deal of insight into the patterns behind judicial decision-making.
scenarios. Then, in Chapter 7, I sum up the implications of the existence or absence of
judicial logrolling in the Supreme Court.
This chapter will explore why it is important to consider the possibility of
logrolling among Supreme Court Justices. A short, but crucial, introduction to public
choice perspectives on justice will begin to outline what is at stake. Finally, a concise
literature review will bring us to the present.
This study proceed in the spirit of James Buchanan and his political economy,
adopting the theory that “In so far as individuals exchange, trade, as freely-contracting
units, the predominant characteristic of their behavior is ‘economic’” (Buchanan, 1964:
220). This proposition reduces every action, every decision, to the realm of economics.
Thus, we enter the sphere of politics and jurisprudence with this thought in mind.
The question of whether justices logroll strikes at the core of what we believe
justice should be. We would like to think that law is not meant to have an arbitrary
enforcement. While distributive justice may at first appear as a great leveler and the
epitome of fairness, it is really nothing more than the imposition of moral institutions on
the governed people. For this reason, it has been argued that justice should embody the
rule of law and the equal treatment of unequals (Buchanan, 1975; Hayek, 1944).
For those unfamiliar with these terms, rule of law implies that the government is
bound by fixed and announced rules beforehand. Laws are the rules of the game, in our
case of Supreme Court decision-making. The main idea is that these rules make it
possible for actors to foresee with fair certainty how authority will use its coercive
powers in given circumstances and allow individuals to plan one’s affairs on the basis of
this knowledge. In accordance with most public choice literature, it is assumed that
political, and likewise judicial, actors are fallible. Therefore, it is essential to reduce an
authority figure’s powers of discretion. Moreover, it is impossible to know if a piece of
legislation or a judicial decision will assist particular people more than others. This is a
prominent argument against arbitrary government and distributive justice.
Under an arbitrary government, political actors must provide for the actual needs
of the people as they arise and then choose deliberately between them. This choice
creates distinctions of merit between the needs of different people, allows somebody’s
views to determine whose interests are more important, and imposes distinctions of rank
among people. If the state foresees the effects of alternative actions on a particular
people, it chooses between different ends. Instead of assisting people in the advancement
of their own ends, the government chooses ends for them and the law becomes nothing
more than an instrument for lawmakers to influence outcomes. To this end the
government, and hence the courts, can become a moral institution, which imposes its
views unto the people. On the other hand, a government by the rule of law relies on the
general conviction of what is fair and reasonable and proposes a complete system of
values where every person matters (Hayek, 1944).
It is important to note that planning often involves deliberate discrimination
between the particular needs of different people, by allowing one person to do what
another must be prevented from doing. Formal equality (justice) is necessarily
incompatible with government policies aimed at material or substantive equality of
different people (distributive justice) (Hayek, 1944). This is simply because in order to
produce the same result for different people, it is necessary to treat them differently
(Buchanan, 1975; Hayek, 1944). It follows that to give different people the same
objective opportunities is not to give them the same subjective chance. Thus, while the
rule of law may produce economic inequality, it is not designed to affect a particular
person in a particular way and imposes no view on what ought to be.
The principles behind operating under the rule of law are to safeguard individual
liberties, liberties that cannot exist without the law, and to prevent the endowment of
unlimited power to the government (Hayek, 1944). The term unlimited government has a
very specific meaning here. For constitutional choice to be relevant, the power of the
government, and likewise the courts, must be limited, meaning “the behavior of
governments as well as the behavior of individuals and nongovernmental entities can be
constrained by rules laid down at a constitutional level of deliberation” (Brennan and
Buchanan, 2000: 9.1.30). Without limits on government power, the
normative argument must necessarily be directed at those who hold political
power currently and who are, personally, wholly unconstrained as to the uses to
which such power might be put. In such a nonconstitutional model of the political
process, there are no formal or legal protections against […] arbitrary action on
the part of the state. Reformers must “preach” to the powerful, and the hope for
moderation rests only with the moral-ethical precepts that the powerful might
have come to acknowledge, and to live by […] (Brennan and Buchanan, 2000:
This study will proceed under this assumption, that unlimited governmental power is
dangerous and thus the principles of rule of law are even more necessary.
This theory of the rule of law is directly related to our case of the Supreme Court,
where justices hear countless cases and make innumerable judgments. It seems
reasonable to want justices to be impartial actors who operate under a rule of law, rather
than by whims and personal vendettas. By applying this new perspective to our judicial
framework, it is unclear where logrolling fits, but it is certainly not in alignment with
justice. The idea of justices trading our liberties like chattel to be won or lost becomes a
frightening possibility when justice is traded for distributive justice, and rule of law for
moral institutions.
The benefits and costs of logrolling are still not clear. Proponents of logrolling
extol optimistic claims that logrolling could be welfare enhancing and provide the
socially optimal amount of different public goods (Coleman, 1966). Critics of logrolling
assert that welfare loss is clearly associated with vote trading; like transfers, logrolling is
a negative-sum game (Riker and Brahms, 1973; Schwartz, 1975). A negative sum game is
defined as a game where the sum of the payoffs in a game is negative. This means that
whenever one player receives a positive payoff, another player must receive a negative
payoff, or equivalently, a loss greater than the associated gains. In the context of the
Supreme Court, this assumption would imply that while some justices may gain from
logrolling, other justices or possibly society must lose a larger amount. While this study
will not focus on it, another question to ask about logrolling is who is receiving the
benefits of this political exchange. Whether society benefits or simply the political actors
that negotiate the trade, it is important to know who is winning and who is losing.
Thomas Stratmann was among the first economists to develop an empirical model
of legislative logrolling. His logrolling model is a three-equation simultaneous probit
model with full information. He considers variables of ideology, constituency,
characteristics, and political party affiliations. His studies provided evidence of logrolling
and paved the way for analysis to come. He is also responsible for the basic preference
model of legislative logrolling that we will adapt to fit judicial actors in Chapter 3.
Stratmann’s work has been groundbreaking and demonstrated the first empirical evidence
of logrolling.
There are many models of judicial decision-making within the realm of political
science. One of the most prominent is the attitudinal model which attributes the justices’
decisions to ideological differences (Epstein and Segal, 2006; Segal and Spaeth, 2002;
Segal and Spaeth, 1993). Another model of interest is historical institutionalism, which
focuses on changes in precedent and the evolution of the Supreme Court as an indicator
of the voting behavior of the justices (Kritzer and Richards, 2002). Judicial logrolling is
becoming a more commonplace explanation for judicial voting behavior as a possible
strategy to legislate from the bench. A great body of scholarship in political science
suggests that Supreme Court Justices
engage in a variety of strategic behaviors within the judiciary in attempting to
influence which cases are selected and how they are decided. These practices
include internal lobbying, exhortation, logrolling, and other forms of bargaining
(Peabody, 2007: 209). […] Indeed, given the diversity of views about how to
interpret legal materials properly, judicial logrolls and other promises and
compromises would often seem essential for creating majority opinions with any
sense of coherence, unity, and force (Peabody, 2007: 226).
However, judicial logrolling is most often relegated to a footnote or a short paragraph on
its possible role in voting. This is related to the abstractness of logrolling and the
difficulty associated with measuring its existence, especially in the judicial sphere where
no clear constituencies are defined.
I advance that while ideology drives preferences, it is the intense differences in
preference that set the stage for judicial logrolling and change precedent. There are
massive collections of scholarship on strategic voting within a case (Wahlbeck, Spriggs,
and Maltzman, 1998; Wahlbeck, Spriggs II, and Maltzman, 1999; Wahlbeck, Spriggs II,
and Maltzman, 2000; Schwartz, 1992; Epstein and Spaeth, 2006; Segal and Spaeth,
2002). For example, justices can attempt to win votes by agreeing to soften their opinions
through a process of give-and-take.3 However, this study will focus on the possibility for
logrolling among different cases and expand upon the current literature. This will be the
work of my study, to take these models to the next dimension.
How decisions are made and a brief exposure to these strategies is explored further in Chapter 4.
The purpose of this section is to present a clear model of judicial logrolling that I
have derived from Thomas Stratmann’s legislative model of logrolling. This formal
definition of logrolling will aid in the comprehension of the game theory scenarios to
Logrolling is essentially vote trading. It is a type of political exchange that arises
due to intense differences in preferences. In the realm of jurisprudence, the judicial
logrolling hypothesis “holds that on multi-judge courts there may be “norms of
reciprocity” whereby unanimity is maintained by rotation of opinion writing by other
judges on a panel” (Farhang and Wawro, 2004: 309). Essentially, judicial logrolling
creates an “illusion of unanimity” as “judges sign on to decisions that they disagree with
based on the understanding that when it is their turn to write in the rotation they will have
wide discretion and can count on the deference of their colleagues” (Farhang and Wawro,
2004: 309).
This definition of judicial logrolling may be slightly too specific for the purposes
of this study. Therefore, in this study logrolling will be defined merely as the trading of
votes between two or more justices across one or more cases, such that the outcome of
those decisions are altered in accordance with the justices’ preferences. This proposition
that justices logroll can easily be derived from public choice theory, which supposes that
voters seek to maximize the number of votes in line with their own preferences (Downs,
1957). This explanation of logrolling is the model that we continue to follow.
Let us begin by altering Stratmann’s basic preference model of logrolling to
accommodate judicial actors. Let (x, y) and (z, w) be two pairs of mutually exclusive
judicial issues or cases. So x and y are two opposing sides to one court case and, likewise,
z and w are two opposing sides to another separate and unrelated court case. Assume that
the justices’ preferences with respect to each pair are separable and that each votes
candidly. “A logrolling situation exists if xPy and zPw, but ywPxz, where P stands for
social preference” (Stratmann, 1992: 1163). The social preference P refers to the
relationship that exists between the two sides of the case. Like any preference relation, P
can represent “preferred to.” Suppose that x is originally the majority opinion in the first
case and z is originally the majority opinion in the second case, then, after a logroll
occurs, y will become the majority in the first case and w will become the majority in the
second case. Essentially, through logrolling the minority opinions become the majority
opinions. It is generally proposed that logrolling can occur due to disparities in voter
preference intensities (Mueller, 1989: 82). Stratmann provides the following critical
example, illustrating how logrolling could occur.
The supporters of y, a minority, feel very intensely about this issue and care much
less about z’s beating w. The supporters of w, also a minority, intensely favor its
victory and care little about x’s defeating y. The coalition of y- and w-backers can
secure their joint victory, and it is in their interests to do so (Stratmann, 1992:
Thus, logrolling is only possible if y’s supporters voted for w and w’s supporters voted
for y.
Furthermore, “[i]ssues involved in a logroll are known to promise high benefits to
a minority group and to impose low costs on others, or the reverse” (Stratmann, 1992:
1164). In the judicial setting, we would predict that the justices within an intense minority
would attempt to convince particular justices of the majority opinion with less intense
preferences to reverse their vote. This implies that moderate justices are more likely to
logroll when solicited by justices with more extreme views. This theory is in line with the
concept of a swing vote and the deciding of plurality and 5-4 decisions. However, we
must somehow take into account that, unlike legislative logrolling, judicial logrolling
may have different levels of importance due to the varying weights assigned to plurality,
majority, and unanimous decisions.
Two characteristics will be present in the case of logrolling. First, both y and w
would be defeated in the absence of logrolling and, secondly, that both y and w must
pass in the presence of logrolling. Thus, no trade would occur if a unanimous decision
was already obtained without a logroll. To elaborate, suppose that P is defined as “strictly
preferred to,” then the logrolling situation could be represented as
x ≻ y and z ≻ w, but yw ≻ xz.
Now let x and y represent separate sides of one case, and let z and w represent separate
sides of another case on the Supreme Court’s docket. Further, suppose that x represents
pro-gun rights interests, while y represents anti-gun rights interests. Likewise, suppose
that z represents pro-choice arguments, while w represents pro-life arguments. Then, by
the previous model, x is preferred to y and z is preferred to w in the absence of logrolling.
However, the resulting votes imply that y and w are preferred to x and z. In other words, x
and z may be expected to win a majority of the votes, while y and w may only be
expected to win a minority of the votes. Thus, in the absence of logrolling, pro-gun rights
and pro-life arguments will be preferred to anti-gun rights and pro-choice arguments.
This preference implies that the court places a higher value on pro-gun rights and pro-life
However, if a few justices have very intense preferences one way or the other,
they may bargain with other justices to change their current votes in exchange for their
future support or some comparable incentive. Logically, justices with intense preferences
would first lobby justices with less intense preferences, known as the swing votes. This is
in line with the principle of the lowest hanging fruit. It essentially says that justices will
lobby for those votes that are more easily attained first. This is due to the theory of rising
marginal costs. In our case, as the intensity of a justice’s preference increase, votes
become more ideologically expensive to obtain. Thus, justices with less intense
preferences are easier to sway and more likely to agree to logroll with a justice who has
very intense preferences. These differences in the intensities of the justices’ preferences
can lead to logrolling.
If logrolling occurs, it is possible that y and w will both receive a majority of the
votes, while x and z will only receive a minority of the votes. In other words, if some
justices have very strong preferences concerning anti-gun rights and pro-choice
arguments, they may form a logrolling coalition or voting bloc and win the majority by
capturing the swing votes. The result of such a logroll would be that anti-gun rights and
pro-choice arguments would be preferred to pro-gun rights and pro-life arguments. This
preference again implies a value set on different issues in the eyes of the court, which can
affect future outcomes, by setting a precedent for later cases.
Understandably, all of these preferences can be confusing. The diagrams in
Figures 3.1 and 3.2 are presented to make the logic behind logrolling clearer. There are
nine justices in the Supreme Court. Suppose that each justice votes in each of the two
cases 1 and 2. Let each justice’s preference be represented by a numbered circle. The
number indicates which justice’s preference: Justice 1, Justice 2, […], Justice 9. The size
of the justice’s circle indicates the intensity of his or her preference. The larger the circle,
the more intense his or her preference for that view.
Case 1:
x supporters
y supporters
Case 2:
z supporters
w supporters
Figure 3.1: Possible diagram of votes before logrolling.
Case 1:
x supporters
y supporters
Case 2:
z supporters
w supporters
Figure 3.2: Possible diagram of votes after logrolling.
Focusing on the justices represented by the darker circles, suppose that Justice 9
has a strong preference for y in case 1, but a weaker preference for w in case 2. It is
possible that Justice 9 could arrange a logrolling agreement with Justices 4 and 5, who
each have weak preferences for x in case 1 and stronger preferences for z in case 2.
Likewise, suppose that Justice 7 has a strong preference for w in case 2 and a weaker
preference for y in case 1. Then, it is possible that Justice 7 could arrange a logrolling
agreement with Justices 2 and 3, who each have stronger preferences for x in case 1 and
weaker preferences for z in case 2. Thus, the original outcomes in cases 1 and 2 could be
reversed due to these two possible logrolling agreements. The depth of these logrolling
scenarios will be explored more in Chapter 5.
There are many barriers to accurately model judicial logrolling. The lack of
defined constituencies has been a major difficulty associated with the creation of a model
fitting for judicial logrolling in the Supreme Court. Justices are not supposed to be loyal
to a specific voting region or a political party. This assumption is derived from life-long
appointments that do not require the endorsement of reelection. Most judicial decisions
cannot even be attributed to presidential appointments (O’Brien, 2005). This lends
support to the typical presumption that Supreme Court Justices are free from
constituencies and political party pressures. Yet, it is still possible for logrolling to occur
due to the intense disparities in preference and ideology among the justices, even if the
only defined constituencies are the justices themselves. It is also worth noting that cases
of judicial logrolling less often involve monetary figures and dollar amounts like in the
instance of most legislative bills, rather crucial liberties are often at stake in Supreme
Court rulings. It is likewise difficult to model the interactions among justices, when for
the most part, judicial bargaining occurs behind closed doors. Most of what is known
about judicial decision-making has come from the justices themselves, from papers and
interviews. The law clerks even take an oath of non-disclosure. Thus, we can only project
an approximate picture of how Supreme Court decisions might be made.
This section provides a brief exposition of how the Supreme Court functions as an
institution. It will serve as a compact guide to the Supreme Court, the justices, and how
court decisions are made. This background will be essential to make the details more
vivid later on in the game theory scenarios.
The Supreme Court is an institution in American law. In economics, institutions are
defined as “the rules of the game in a society” or “the humanly devised constraints that
shape human interaction” (North, 1990: 3). Thus, legal institutions like the Supreme
Court “structure incentives in human exchange” and the way that American society
develops (North, 1990: 3). Specifically to the Court, this idea of institutionalization can
be defined as follows:
Institutionalization is a process by which the Court establishes and maintains its
internal procedures and norms and defines and differentiates its role from that of
other political branches. Institutionalization reflects justices’ interactions, vested
interests, and responses to the Court’s distinctive history and changing political
environment. It remains a central force, conditioning judicial behavior (O’Brien,
2005: 104).
The evolution of the Supreme Court as an institution has grown over the years in
accordance with the Court’s rise in importance. Justices not only make collective
decisions on court cases, but also on changes in organizational matters and procedures
(O’Brien, 2005: 127). This shift is relflected in Justice Frankfurter’s statements that court
decisions should ensure inner harmony: “that means not votes but accommodation, the
give-and-take of comradeship, accommodation to the purpose and not mere counting of
heads” (O’Brien, 2005: 128). This comeradeship has been progressively limited as the
Court’s caseload has increased; with institutionalization has come isolation. “A number
of factors isolate the justices. The Court’s members decide together, but each justice
deliberates alone. Their interaction and decision making depend on how each and all of
the nine justices view their roles and common institutional goals” (O’Brien, 2005: 129).
On the other hand, this institutional approach has been denied by Justice Harlan, who has
asserted that “decisions of the Court are not the product of an institutional approach, [...]
[t]hey are the result merely of a tally of individual votes cast after the illuminating
influences of collective debate” (O’Brien, 2005: 129). However, this view seems to
trivialize the give-and-take that other justices openly attribute to their own decisionmaking.
Law clerks have a more central role in Supreme Court decision-making than
might be assumed at first glance. Law clerks offer new perspectives, can create lobbying
opportunities for justices, and act as the gatekeepers to a Supreme Court hearing. For our
purposes, the law clerks’ function as lobbying tools will be the most influential for
Law clerks enable judicial lobbying and thus can facilitate logrolling among
justices. It is well documented that Justice Frankfurter “used his law clerks as flying
squadrons against the law clerks of other Justices and even against the Justices
themselves. Frankfurter, a proselytizer, never missed a chance to line up a vote”
(O’Brien, 2005: 133). Likewise, Justice Brennan “used the informal communications
network among the law clerks to find out other justices’ views. [...] Brennan would then
pitch his points at conference or in draft opinions at particular justices in order to mass
and hold onto a majority” (O’Brien, 2005: 133). The actions of justices like Justice
Frankfurter and Justice Brennan represent attempts to change the vote in their favor. I
propose that actions of this nature support the idea that Supreme Court decisions are not
merely tallies and head counts, but the result of political, or rather judicial, exchange
between justices in accordance with the intensities of their individual preferences.
However, law clerks can also prevent opportunities for justices to interact. It has
been proposed that this stifling of direct debate over time by a more formal process of
draft circulation could lead to less compromise (O’Brien, 2005). I further assert that the
effect of less interaction and compromise among justices, may lead to fewer opportunities
for logrolling to occur.
As gatekeepers, law clerks are responsible for reading all of the filings, writing a
one to two-page summary of the facts and questions presented, as well as making a
recommendation for whether the case should be denied, dismissed, or granted full
consideration (O’Brien, 2005: 135). Since 1972, the majority of the justices have also
shared a pool of clerks and the memoranda that they produce, in addition to personal law
clerks, which again review each circulated memo and make a recommendation of action.4
While this delegation of reading and reporting to the law clerks frees the justices from the
tedium of examining every case, Justice Scalia points out that there may be a “point of
This pool of clerks can be understood as a group of clerks that the justices agree to share. In the past,
some justices have chosen not to join and solely rely on their own personal clerks (O’Brien, 2005).
diminishing returns with law clerks” (O’Brien, 2005: 158). As the Supreme Court’s
caseload has increased over the years, so has the size of its staff and the amount of work
that must be delegated to law clerks. Justices spend a greater portion of their time
supervising and revising. Justice Rehnquist commented that as the nature of the justices’
work has evolved, the justices have less “time and freshness of mind for private study and
reflection... [and] fruitful interchange... indispensable to thoughtful, unhurried decision”
(O’Brien, 2005: 158). This change implies that important cases and issues may be
bypassed in the rushed readings of inexerienced law clerks, fresh out of law school. It
also means that the law clerks are influencing which cases the justices decide on based on
their own recommendations and personal preferences. Thus, not only do the justices’
preferences influence the outcome of a case, but also the intensities of the law clerks’
The Supreme Court grants full hearings to less than 100 of over 9,000 cases on
the docket each year (O’Brien, 2005: 231). In response to this massive caseload,
jurisdictional changes have enlarged the Court’s power of discretionary review and
created new lower appelate courts so that the justices may decide only those cases of
national importance that can adequately be considered in any given term. Justice White
defends this freedom, affirming that “the power to deny cases helps to keep us current”
(O’Brien, 2005: 159).
After a case is granted a hearing, oral arguments are presented and the justices
vote in a private conference to decide on the issues presented. The cases are decided by
majority rule on the basis of a simple tally. These votes are tentative until the
announcement of the official opinion is handed down. After the private conference, the
chief justice or the senior associate justice assigns the responsibility of writing the
Court’s opinion to one of the justices in the majority. Drafts must be circulated to all
justices to facilitate commentary, which is factored into the final revisions. Because the
justices’ votes are tentative, the justices are at liberty to switch their vote and write
separate concurring or dissenting opinions. After the private conference, justices enter
into a competition for influence on the final decision (O’Brien, 2005: 231).
I believe that this bargaining process heightens the possibility of logrolling in the
Supreme Court. Scenarios of trading dissenting and concurring opinions naturally play
out. For example, a justice of the majority opinion may convince a dissenting justice to
withhold his or her dissent by offering to reciprocate the favor in another case. Likewise,
the dissenting justices could sway those justices of the majority with promises of future
support. This sort of logrolling could equally occur in plurality, majority, and unanimous
decisions, since all represent different levels of precedential strength.
The strength of a precedent also depends on how it is written. An opinion should
“convey the political symbolic values of certainty, stability, and impartiality in the law”
(O’Brien, 2005: 232). This is why unanimous decisions hold more weight than plurality
decisions. It is a logical assumption that justices openly compete for votes and attempt to
persuade as many other justices as possible to join one opinion or the other. If no
agreement can be reached, or the case is deemed of minor importance, the court may
issue a per curiam opinion.5 But in general, opinions are seen as “negotiated documents
A per curiam opinion is defined as a decision joined by multiple justices and represents a ruling made by
the court acting as a whole.
forged from ideological divisions within the Court” which “serve as an institutional
justification for a collective decision” (O’Brien, 2005: 233). When decisions are the
product of collective deliberation, threats of concurring or dissenting opinions carry more
weight, especially for unanimous decisions (O’Brien, 2005: 238).
While previous courts under earlier chief justices like Justice Marshall pushed for
compromise and unity in decision-making, later courts like that of Justice Rehnquist act
more as individuals without an emphasis on consensus. It has been proposed that
The trend now is toward less consensus on the Court’s rulings. The justices tend
to be increasingly divided over their decisions. Individual opinions have become
more highly prized than institutional opinions. The Court now functions more like
a legislative body relying simply on a tally of votes to decide cases than like a
collegial body working toward decisions and opinions (O’Brien, 2005: 240).
This trend suggests that logrolling may have been more likely in past Supreme Courts
than in latter Supreme Courts.
Figure 4.1: Concurring behavior of justices. Post-1937 and through the 2003-2004 term.
(O’Brien, 2005: 293).
Figure 4.2: Dissenting behavior of justices. Post-1937 and through the 2003-2004 term.
(O’Brien, 2005: 299).
The rising amount of concurring and dissenting opinions filed also suggests that justices
are not as willing to compromise and trade, as may have been the case previously.
However, just as the legislative body does not rely on a simple tally, it seems premature
to say that judicial decisions have become mere tallies.
The oral argument can also affect the outcome of a case by lending conviction to
a justice’s decision. Justice Brennan admits that often, “how a case shapes up is changed
by oral argument” (O’Brien, 2005: 241). After oral arguments, the justices convene in a
conference on merits, which are essentially kept a “secret, except for revelations in
justices’ opinions, off-the-bench communications, or, when available, private papers”
(O’Brien, 2005: 248). Justice Powell explains,
The integrity of decision making would be impaired seriously if we had to reach
our judgments in the atmosphere of an ongoing town meeting. […] There must be
a candid discussion, a willingness to consider arguments advanced by other
Justices, and a continuing examination and reexamination of one’s own views
(O’Brien, 2005: 248-249).
I propose that these conference discussions are a prime opportunity for logrolling.
However, as the Court has moved away from its emphasis on unity, the
conference discussions have become less instrumental than they once were. It has been
noted that in later courts these conference discussions “now serve only to discover how
the justices line up. There is no longer time for justices to reach agreement and
compromise on opinions for the Court” (O’Brien, 2005: 249). This shift is often
attributed to institutional changes and differences in the chief justices’ styles of
leadership. Experience has shown that,
The result of devoting less time to collective deliberation and consensus building
is more divided decisions and less agreement on the Court’s rulings. Because the
justices no longer have the time or inclination to agree on opinions for the Court,
they file a greater number of separate opinions. The reality of more cases and less
collective deliberation discourages the reaching of compromises necessary for
institutional opinions. Ideological and personal differences in the Court are
reinforced (O’Brien, 2005: 250).
I propose that this trend in the decision-making of the Supreme Court implies that the
possibility for logrolling among justices was probably more likely in the past then in the
contemporary court. This statement also lends to the possible efficiencies of logrolling in
Supreme Court decision-making in so far as it produces more of these institutional
opinions. In the same way that rule of law allowed people to act accordingly, institutional
opinions act as signals to legislators and the people about what is and is not considered
constitutional. The firmer the resolve of a decision, the stronger its precedent. While
precedent can be and is overturned, these institutional opinions are invaluable indicators
for the direction of future opinions.
This movement toward or away from unity is indubitably linked to the chief
justice and his or her style of leadership. The power of opinion assignment has been
noted as the chief justice’s “single most influential function” and an exercise in “judicialpolitical discretion” (O’Brien, 2005: 260). The typical procedure provides that if the chief
justice is in the majority, then he or she will assign the opinion to a fellow justice. On the
other hand, if the chief justice is not within the majority, then the senior associate in the
majority will write or assign the opinion. In the interests of egos, the chief justice will
often choose to self-assign the opinion in turning point cases and unanimous decisions.
The way that an opinion is written can be critical to the final vote. It is not
uncommon for justices to switch votes in response to an opinion or the reassignment of
that opinion (O’Brien, 2005: 262). “The circulation of draft opinions reinforce[s] the
strategic use of tentative votes and the importance of post-conference deliberations for
the Court's decision-making [... and…] provide[s] opportunities for holding on to or
enlarging the majority supporting the decision” (O’Brien, 2005: 258). Justice Blackmun
admits that opinions often require revision,
because other justices say, if you put in this kind of a paragraph or say this, I’ll
join your opinion. So you put it in. And many times the final result is a
compromise. [...] many times the final result it not what the author would have
originally liked to have. But five votes are the answer and that’s what the coached
judgment is. So you swallow your pride and go along with it if you can (O’Brien,
2005: 260).
It is intuitive that justices would participate in strategic behavior and bargaining to obtain
the decision that they prefer. It has been noted that
At conference, a justice may vote with others if they appear to constitute a
majority, even though he or she disagrees with their treatment of a case. The
justice may then bargain and try to minimize the damage, from his or her policy
perspective, of the Court's decision. Alternatively, justices may threaten
dissenting opinions or try to form a voting bloc and thereby influence the final
decision and written opinion (O’Brien, 2005: 257).
Other strategies to influence the drafting of opinions can be as base as emotional appeals
and sometimes even personal threats. It is clear however that sometimes “justices may
not feel that a case is worth fighting over” (O’Brien, 2005: 277). This study will delve
deep into the question posed but unanswered: “[Do] Justices sometimes join an opinion
with which they disagree, perhaps with the hope that in some later case other justices will
reciprocate and not threaten a dissenting vote or opinion” (O’Brien, 2005: 278)? It has
been clearly established that justices bargain for votes within the framework of a case.
Now the question steps into another dimension, asking if votes are traded among different
cases. I advance that the logical answer to this question is yes.
This chapter will build from the basic model of logrolling defined in Chapter 3,
and adapt it to account for the dynamics of Supreme Court decision-making outlined in
Chapter 4. Similar to Thomas Stratmann’s basic preference model of legislative
logrolling, I propose that judicial logrolling can also be modeled in terms of repeated
Prisoners’ Dilemma supergames. It is obvious that justices will not participate in
logrolling if it does not offer them some payoff, in the form of more votes and a stronger
precedent in his or her favor. But the question arises: Why would justices cooperate with
each other and how would such a logroll be coordinated and enforced? I argue that in an
infinite horizon repeated Prisoners’ Dilemma supergame, justices will cooperate and
hence logrolling agreements can be sustained.6
Before proceeding further, it is crucial that a few terms and concepts are defined
for those readers unfamiliar with game theory. Let us begin with a description of a
possible logrolling scenario. For simplicity, let’s assume that we have two justices, call
them Justice A and Justice B. Now suppose that there are two separate court cases, case 1
is about privacy rights and case 2 is in regard to standards of obscenity. Further assume
that Justice A has a strong preference with regard to case 1, but cares little about the
What this entails will be discussed in greater detail later on in the chapter. However, an infinite horizon
simply implies an indefinite end of the game and a supergame is a game obtained by playing numerous
stage games one after the other sequentially.
outcome of case 2. In contrast, Justice B has a strong preference with regard to case 2, but
cares little about the outcome of case 1. Suppose then that Justice A approaches Justice B
about a logrolling agreement, suggesting that if Justice B will join his voting bloc for case
1, then Justice A will promise to join Justice B’s voting bloc for case 2.
In order to make this scenario clearer, we can create a game tree, which can be a
useful tool to show the who, what, and when of a situation. A game tree is composed of
the following elements: (1) decision nodes (vertices), which represent a possible move by
a particular player; (2) branches (edges), which represent the choices available at the
node; and (3) leaves (terminal nodes), which represent all of the possible outcomes.
There is also a root in those trees that do not cycle. The root represents the initial decision
(Binmore, 2007). While it is difficult to exhibit all of the give and take of a particular
logrolling scenario, the reduced form of this example can be expressed in the following
game tree (Figure 5.1).
If the agreement is carried out, then a logroll has occurred and the outcomes of
both cases have been changed. It is important to note that this is a simplified game tree. It
is very possible to expand each piece of this game tree to exhibit numerous scenarios and
possible actions. For instance, consider the first decision node. Any number of things
could influence Justice B’s choice of whether to accept or reject Justice A’s logrolling
Logrolling fails and
the outcomes of both
cases 1 & 2 remain
Logrolling is
successful and the
outcomes of both cases
1 & 2 are changed.
Logrolling fails and
only the outcome of
case 2 is changed.
Justice B votes
as promised.
Justice B
Justice B
Justice B votes
as promised.
No logrolling occurs
and the outcomes of
both cases 1 & 2
remain unchanged.
Justice A votes as
Logrolling fails and
only the outcome of
case 1 is changed.
Justice A cheats.
Justice B agrees.
Justice B declines.
Justice A approaches Justice B about a
logrolling agreement.
Figure 5.1: Reduced game tree of logrolling scenario.
A possible scenario is depicted in Figure 5.2. This expansion of the initial
decision node has an infinite number of possible forms. The game tree in Figure 5.2 only
displays one possibility. Assume that no unanimous decision is initially reached at the
conference discussion. For simplicity, further suppose that the majority opinion is
initially composed of five justices and the minority opinion is composed of four justices.
In addition, assume that Justice A is the swing vote in case 2 and that Justice B is the
swing vote in case 1. Lastly, assume that none of the other justices will negotiate or agree
to logroll.
No reason
to logroll.
A asks B to logroll.
B could agree to
logroll and give A
the majority.
B is in Minority
in case 1
A asks B to logroll. B
could agree to logroll
and increase the strength
of A’s precedent.
B is in Majority
in case 1
B is in Minority
in case 1
A is in Minority
in case 1
No reason
to logroll.
B is in Majority
in case 1
A is in Majority
in case 1
Justice A and Justice B attend the conference discussion
with their briefs prepared by the law clerks.
Figure 5.2: Expansion of a decision node from reduced game tree.
This expansion can be made more intricate by describing possible tactics Justice
A might employ to convince Justice A to agree to such a logroll. For instance, suppose
that Justice A approaches Justice B about a logrolling agreement, when Justice B is of the
majority opinion in case 1. Then an expansion of this portion of the game tree could look
like Figure 5.3. Let Y stand for yes, meaning Justice B accepts, and let N stand for no,
meaning Justice B declines or does not respond positively to Justice A’s action. The bold
trace in Figure 5.3 denotes the outcome displayed in the reduced form.
Court is
trade occurs.
No trade
A bribes B.
A promises to join B’s voting
bloc for case 2, in exchange
for B’s vote in case 1.
A threatens B.
A negotiates with B,
promising to rewrite parts of
the opinion in case 1.
Justice A approaches Justice B.
Justice B is of the majority opinion in case 1.
Figure 5.3: Further expansion of decision node.
Note that in Figure 5.3, a distinction is made between logrolling and bargaining.
Logrolling is an exchange of votes attributed to intense preference. Such an agreement
must occur over many cases jointly, not within an isolated case. Thus, while strategic
bargaining is definitely a way to secure a logrolling agreement, in order for the exchange
to be considered logrolling it must transcend the level of a single case. I have also
included bribery and threats as possible tools for justices to influence the votes of other
justices. This is by no means an endorsement of any claim of the presence of bribery and
corruption in the Supreme Court. It is merely an action, which is economically
convenient to consider. However, as noted in Chapter 4, personal threats have been
documented as a method to bully other justices into reconsidering their votes. Again,
while this is not strictly logrolling, threats could lend to the formation of a logrolling
agreement. These simple expansions demonstrate just how complicated and intricate even
a reduced game tree can become. This should be kept in mind while examining the
extensive forms of the game scenarios to come.
A primary difference between judicial and legislative logrolling is observed in the
second case from Figure 5.2, when Justice A is of the majority opinion and Justice B is of
the minority opinion. Unlike legislative actors, Justice A will still approach Justice B to
arrange a logrolling agreement, because every additional vote in her favor will strengthen
the precedent of her opinion. Thus, the expanded game tree of the second case will play
out similarly to Figure 5.3.
Now that we have explored the intuition behind logrolling agreements, it is
possible to formalize our understanding of judicial logrolling and set up our game.
If the previous reduced logrolling scenario were modeled as a one shot scenario,
then a rational justice would cheat, meaning he or she would not follow through with the
agreement. Following tradition, let Dove be defined as a strategy to cooperate and follow
through with the logrolling agreement and let Hawk be defined as a strategy to cheat and
not vote for the other justice’s voting bloc regardless of the aforementioned agreement.
Since preferences are assumed to be rational and ordinal we can represent this in the
following payoff matrix (Figure 5.4).7 For simplicity, let a ≻ b ≻ c ≻ d . 8
A payoff matrix is a representation of the payoffs attributed to the justices’ choices. Justice A’s payoffs
are in the northeast corners and Justice B’s payoffs are in the southwest corners. The justices’ best
responses are highlighted respectively.
The symbol ≻ means preferred to. For example, a ≻ b means that outcome a is preferred to outcome b.
Justice A
Justice B
Figure 5.4: The Prisoners’ Dilemma. Adapted from (Binmore, 2007: 7).
The socially optimal outcome is (b, b), since b is preferred to c. However, the
Nash equilibrium is at (c, c). A Nash equilibrium is a saddle point. More simply, “A pair
of strategies is a ash equilibrium in a game if and only if each strategy is a best reply to
the other” (Binmore, 2007: 18).9 Thus, in a single dealing, justices will not optimize their
preferences to the same extent that they could have, if they had cooperated. This payoff
matrix demonstrates that in a single dealing the strategy Hawk strictly dominates that of
Dove.10 Hence the result would be that both justices would play Hawk and cheat,
resulting in smaller payoffs than they might have received had they cooperated. The
outcome (c, c) will conceptually represent neither case ending in accord with the justices’
views. On the other hand, had the justices cooperated, the result would be (b, b) and both
cases would result in the desired ruling. The payoffs (a, d) and (d, a) are similar. Let a
represent the gains that a justice receives for attaining the desired vote in the case for
which she had a strong preference and for still being able to vote as she originally wished
A Nash Equilibrium can be found by determining all of the players’ best strategies in response to the other
players’ possible strategies. If a Nash Equilibrium exists, each player will be acting in accordance with
their best response given the other players’ strategies. Several Nash Equilibria can exist. Likewise one or
no Nash Equilibrium can exist dependent on the game at hand.
Strictly dominates means that one strategy, in this case Hawk, is always the best response, no matter what
the other player may choose to do.
in the second case. Then d would represent the loss of the justice that was tricked into
voting one way for the other case, while still losing the vote for the case she had a strong
Thus, it is clear that in a one shot game, logrolling would not occur because both
justices would have an incentive to cheat rather than follow through with the logrolling
agreement. In the following section, we will see that this lack of cooperation cannot
sustain repeated dealings where cooperation becomes the dominant strategy.
Unlike the one-shot Prisoners’ Dilemma, the Supreme Court Justices do not
operate based on single dealings. The same justices will have repeated dealings with each
other over the many years of their life-long appointments. In order to secure a logroll, we
must require an additional assumption of repeated dealings, otherwise the justices will
have little reason to cooperate, as observed previously. Thus, we must consider the case
of many stage games played repeatedly, one after the other. This is called a supergame.
We will assume perfect information. This guarantees that the justices “know
everything they might wish to know about what has happened in the game so far when
they make a move” (Binmore, 2007: 46). Thus, all of the justices participating in
potential logrolling agreements are aware of all of the preceding votes of the other
justices. This is reasonable since official votes are not only tallies in the justices’ minds,
but a matter of public record. In other words, if a justice cheats, the other justices will
By setting up a logrolling scenario as a supergame, we are making the justices’
behavior in each stage game contingent on the stage game before it.11 Thus, the justices’
actions are contingent on the history of play.12 In our case, the justices’ actions can be
defined as S = {s1, s2} for Justice A and T = {t1, t2} for Justice B. Let s1 and t1 represent
cooperating (Dove) and s2 and t2 represent cheating (Hawk). The set of all of the possible
outcomes of the first stage, say the first attempt to logroll, is called Z and is defined as
H = S x T.
The set H contains four elements {h (s1, t1), h (s1, t2), h (s2, t1), h (s2, t2)} each of which
represents a possible history of play for the second stage of the game called Z 2. For
example, the history h (s1, t1) means that Justice A played s1 (Dove) and Justice B played
t1 (Dove) (Binmore, 2007: 321).
Since each stage of the game is dependent on the stage before it, define f: H → S
and g: H → T as functions (Binmore, 2007: 321).13 These functions represent Justice A
and Justice B’s pure strategies respectively. For example, Justice A’s pure strategy is
defined as the pair (s, f), where s is the action Justice A takes at the first stage and f is the
above function representing Justice A’s action at the current stage based on the game’s
history. A pure strategy in a game “specifies an action at each of the information sets at
which it would be his or her duty to make a decision if that information set were actually
By contingent we mean based upon or conditioned by.
Actions are defined as the justices’ pure strategies within a stage game. They should not be confused
with the pure strategies of the repeated game.
We know that f is a function because the result S (Justice A’s action) depends on H (the history of play)
and similarly for g.
reached” (Binmore, 2007: 49-50). The significance of pure strategies is the guarantee that
the justices’ decisions determine the outcome of the game, without chance moves.
f1111 : H → S
f1112 : H → S
f1121 : H → S
f1122 : H → S
h11 h12 h21 h22
h11 h12 h21 h22
h11 h12 h21 h22
h11 h12 h21 h22
f1211 : H → S
f1212 : H → S
f1221 : H → S
f1222 : H → S
h11 h12 h21 h22
h11 h12 h21 h22
h11 h12 h21 h22
h11 h12 h21 h22
f2111 : H → S
f2112 : H → S
f2121 : H → S
f2122 : H → S
h11 h12 h21 h22
h11 h12 h21 h22
h11 h12 h21 h22
h11 h12 h21 h22
f2211 : H → S
f2212 : H → S
f2221 : H → S
f2222 : H → S
h11 h12 h21 h22
h11 h12 h21 h22
h11 h12 h21 h22
h11 h12 h21 h22
Figure 5.5: Justice A’s possible functions. Taken from (Binmore, 2007: 322).
Unfortunately, these strategic forms can become unmanageably large and difficult
to interpret. In an attempt to make the process of determining each justice’s pure
strategies clearer, I have provided the following tables in Figure 5.5, which display the
sixteen possible functions f: H → S. As an aside, since Justice A has two choices for s,
either s1 (Dove) or s2 (Hawk), and sixteen choices of f, he or she will have thirty-two
choices of pure strategies in the second stage of the game Z 2 (Binmore, 2007: 321).14
Since justices’ actions are contingent on the history of the game, it is possible to
expand our previous logrolling scenario from the one shot prisoners’ dilemma to become
a finitely repeated dealings Prisoners’ Dilemma. This new repeated dealings supergame
can be represented by the following payoff matrices (Figure 5.6 and Figure 5.7). For
consistency and simplicity, let a ≻ b ≻ c ≻ d .
Justice A
Justice B
Figure 5.6: Stage game of a repeated Prisoners’ Dilemma. Adapted from (Binmore, 2007:
Thirty-two because, from combinatorics, the number of permutations is 2 ·16 = 32.
Again, since each stage of the game is dependent on the stage before it, let the functions
f: H → S and g: H → T represent Justice A and Justice B’s pure strategies respectively.
Thus, the payoffs in Figure 5.7 are the sums of the payoffs in the final stage and all of the
preceding payoffs incurred from past actions at each stage of the game.
Justice B
Justice A
b + f(h)
a + f(h)
b + g(h)
d + g(h)
d + f(h)
c + f(h)
a + g(h)
c + g(h)
Figure 5.7: Final stage of repeated Prisoners’ Dilemma. Adapted from (Binmore, 2007:
The unique set up of the finitely repeated dealings prisoners’ dilemma supergame
lends itself to cooperation among the justices, and thus to the possibility of logrolling.
The justices are more likely to cooperate with each other in the case of repeated dealings
for fear of retaliation from the other justices. In the context of our logrolling scenario,
suppose that Justice A and Justice B were to enter into a logrolling agreement. If Justice
A cheats on the first agreement, then his or her credibility is tarnished. This makes the
probability less likely for Justice B, or any other justices that are aware of Justice A’s
cheating, to enter into another logrolling agreement with Justice A. But this backlash
would be against Justice A’s best interests, since, in the long run, cooperation and
successful logrolling will yield higher payoffs than cheating. The conclusion is that
logrolling agreements will be made and kept by rational justices who fear the retaliation
that would follow cheating.
But in the final stage, there is no fear of retaliation. In terms of our logrolling
scenario, the end of the game would be when Justice A or Justice B retire. Thus, the last
stage game would be the last possible logrolling agreement between Justice A and Justice
B. Then the final stage becomes equivalent to the one-shot Prisoners’ Dilemma outlined
earlier where Hawk strongly dominates Dove. Hence, the final stage is a subgame-perfect
equilibrium in which both justices always cheat, violating the agreement and preventing
the possibility of successful logrolling.
Suppose that there are n stages to our game, such that the final stage is denoted as
Z n. Then this outcome is also true for the next to last stage game, denoted Z
(n – 1)
Logically, the worst punishment the other justice can inflict on a cheating justice in the
final stage is to cheat. But since it has already been observed that the justices will cheat in
the final stage regardless, there is no retaliation for cheating in the next to last stage.
Thus, for the next to last stage game, Hawk will again strongly dominate Dove and the
last two logrolling agreements will fail (Binmore, 2007: 322).
What is gained from this model of the Prisoners’ Dilemma with finitely repeated
dealings is that cooperation is possible. However, it is important to note that a justice’s
reputation and the trust of his or her colleagues may be more valuable than cheating in
the end. This will be explored more in depth at the end of this section.
A final refinement of our logrolling supergame, and a possibly more accurate
depiction of the conditions of the Supreme Court, is a repeated dealings Prisoners’
Dilemma with an infinite horizon. This implies that the Prisoners’ Dilemma is repeated
an indefinite number of times.
The payoffs in this game are based upon the probability of the game continuing to
the next stage. For simplicity, let this probability be defined as p such that 0 < p < 1. The
probability that the game will continue at the nth stage is (p)n, so there is no value of n for
which the game is guaranteed to end. However, note that the limit of (p)n is zero as n
approaches infinity. This implies that the probability that the game will actually have
infinite repetitions is zero (Binmore, 2007: 322).
This set up is appealing to consider because with an indefinite number of dealings
it is possible for the justices to cooperate forever, or as long as they both serve as a
member of the Court. This is because the justices are unable to anticipate the final stage
of the game. The set up of this game easily supports the possibility of logrolling, since
justices expect to receive higher payoffs in indefinitely repeating games when they follow
through with the logrolling agreements that they make with other justices.
In reality, Supreme Court Justices generally retire at the end of a defined term.
However, this decision may not be announced early enough for other justices to adjust
their actions accordingly. There are also instances where justices may fall ill or die while
in office. In exceptional cases, justices may even be in the middle of a logrolling
agreement when an unexpected event leaves a justice unable to fulfill his or her end of
the bargain. The point is that this game model is a feasible representation of possible
judicial interaction and logrolling scenarios among the Supreme Court Justices.
So for the remainder of this study, our logrolling game scenario will be modeled
in the form of an infinite horizon repeated dealings Prisoners’ Dilemma unless otherwise
noted. However, this distinction from the finitely repeated Prisoners’ Dilemma will only
be noticeable in the final two stages of the game, which is extraneous with respect to
most of the cases that will be discussed in depth later in the case studies.
5. 2
There are other strategies beyond the standard Hawk and Dove approaches. The
most accessible are named Grim and Tit-for-Tat or Tat-for-Tit (Binmore, 2007). We will
continue under the assumption that justices make decisions on whether to logroll based
on perfect information. Therefore, the justices’ actions will depend on more than the
payoffs, but also what the justices know about the other justices’ strategies and past
The Grim strategy is often used to explain how acts of collusion can withstand the
conditions of a duopoly (Binmore, 2007: 25). A justice playing according to the Grim
strategy will play Dove as long as the other justice reciprocates by playing Dove in return
(Binmore, 2007: 325). The Grim strategy is a potentially appealing strategy for the
justices in our logrolling scenario as an infinite horizon repeated Prisoners’ Dilemma,
since it guarantees cooperation and thus successful logrolling agreements by
implementing credible threats of retaliation for cheating.
For example, if Justice A is acting in under the Grim strategy, then he or she will
initially cooperate and fulfill her logrolling agreements. Now suppose that Justice B plays
Hawk at some point in the game and cheats on their logrolling agreement. Then the Grim
strategy requires that Justice A retaliate against Justice B by playing Hawk and cheating
for the remainder of the game. There is no return to cooperation after a justice acting in
accordance with the Grim strategy has been betrayed. A payoff matrix for an intermediate
stage of a repeated Prisoners’ Dilemma is displayed in Figure 5.8, which offers a clear
comparison of the payoffs associated with Hawk, Dove, and Grim strategies.
Justice A
Justice B
Figure 5.8: Playing Grim in stage game of a repeated Prisoners’ Dilemma. Adapted from
(Binmore, 2007: 24).
Note that more than one Nash equilibrium exists in the repeated Prisoners’
Dilemma: one at (Grim, Grim) and one at (Hawk, Hawk). By the definition of the
justices’ preferences, it is obvious that the Nash equilibrium (b, b) resulting from both
justices playing Grim is preferred to the Nash equilibrium (c, c) resulting from both
justices playing Hawk. The Pareto-efficient Nash equilibrium is also at (b, b), since b is
preferred to c. In its weakest form, an outcome is Pareto-efficient “when there is no other
feasible agreement that all the players prefer” (Binmore, 2007: 20). It is clear that playing
Grim therefore offers justices participating in logrolling agreements an efficient and
preference maximizing strategy.
A justice who adopts either the Tit-for-Tat or the Tat-for-Tit strategy always does
next time what the other justice did last time. The difference between the two strategies is
defined by the first action of the game. A justice playing Tit-for-Tat is considered “nice”
because he or she will begin by playing Dove. In contrast, a justice playing Tat-for-Tit is
said to be “nasty” because he or she will begin by playing Hawk in an attempt to cheat
the other justice (Binmore, 2007: 328).
The Tit-for-Tat and the Tat-for-Tit strategies are more forgiving than the Grim
strategy, which offers no return from (Hawk, Hawk) and a sub-optimal outcome if one
justice cheats. The result is that those justices who adopt the Tit-for-Tat and the Tat-forTit strategies “end up cycling through the same sequence of states forever” (Binmore,
2007: 328). However, if both justices adopt the Tit-for-Tat strategy, then they will
continue to cooperate throughout the entire game (Binmore, 2007: 333).
The payoff matrix for the Tit-for-Tat and the Tat-for-Tit strategies, in addition to
the previously mentioned strategies, are displayed in Figure 5.9. Again, let a ≻ b ≻ c ≻ d .
The restricted strategic form in Figure 5.9 demonstrates that there are often many Nash
equilibria made possible by numerous strategies. Note that within the context of our
infinite horizon repeated Prisoners’ Dilemma, the justices are best off if they cooperate,
and, in effect, logroll. So, it is in both of the justices’ best interest to form logrolling
coalitions and keep their promises according to the agreements set beforehand. This fact
is important because it is clear that logrolling can maximize the justices’ personal
preferences. However, it is still unclear if maximizing the justices’ preferences leads to a
higher social welfare or not. This issue and the possible implications of judicial logrolling
will be explored in more detail in Chapter 7.
Justice A
Justice B
Tit-for-Tat Tat-for-Tit
Figure 5.9: A restricted strategic form. Adapted from (Binmore, 2007: 332).
This section provides a nice summing up of why the justices would cooperate and
how to represent the payoffs that they receive for their cooperation.
A payoff region is defined as “the set of all payoff profiles that can occur in a
game under various hypotheses about what the players are allowed to do” (Binmore,
2007: 199). A cooperative payoff region is composed a “convex combination of the
payoff pairs in the game’s payoff table” (Binmore, 2007: 200). The payoff region for our
judicial logrolling example is shown below in Figure 5.10. Again, let a ≻ b ≻ c ≻ d .
(d, a)
(b, b)
(c, c)
(a, d)
Figure 5.10: Payoff regions. Adapted from (Binmore, 2007: 333).
Note that the cooperative payoff region of a one-shot Prisoners’ Dilemma is
represented by the lighter shaded region, while the darker shaded region is the set of all
possible Nash equilibria for our infinitely repeated Prisoners’ Dilemma. These payoff
regions easily indicate that the payoffs associated with cooperation are larger than those
payoffs associated with cheating in our repeated game of judicial logrolling. The
significance of these payoff regions is described by the folk theorem, which states that:
The set of all Nash equilibrium outcomes of an indefinitely repeated game
consists of all points in the cooperative payoff region of the stage game at which
all players get their security levels or more (Binmore, 2007: 334).
The importance of this statement for judicial logrolling is, again, that by cooperating the
justices could maximize their own preferences. The folk theorem emphasizes that there is
no external enforcement agency to guarantee cooperation, since all actors, including the
government, must have incentives to make them act a certain way. However, in infinitely
repeated games, like in the case of our judicial logrolling scenario, justices can enter into
self-policing contracts. Justices will cooperate because they fear the retaliation that will
be dealt to them if they cheat on a logrolling agreement. Thus, judicial logrolling could
be maintained without an external authority. Instead, the justices will essentially police
themselves. This is possible because of the assumption that justices have perfect
In Chapter 4, the Supreme Court was described as an institution, which operated
in accordance with the institutional rules agreed upon by majority vote. As an institution,
the Supreme Court behaves like a very small elite society. Every society must have some
form of a social contract. The social contract can be defined as the “organizing principle
of society” in the form of “a tacit agreement” to which all of the justices are a part that
somehow regulates the justices interactions, and, in our specific case, how a logrolling
agreement is carried out (Binmore, 2007: 341). It is important to note that “the individual
does not enter into social contract for the purpose of imposing constraints on himself” but
rather “[h]e enters into agreement with others to secure the benefits of behavioral
limitation on their part” (Buchanan, 1975: 107). A justice would enter into a logrolling
agreement with the other justices under the assumption that the social contract will be
upheld and the other justices will follow through, meaning they will not cheat. Social
contracts can also refer to many actions and issues such as the taboo, which could affect
the way that the justices may vote in particular cases.
The goal of this study requires that the social contract, or more appropriately the
institutional contract, of the Supreme Court be self-policing, as mentioned above.15 For
the social contract to be self-policing, it must be in the justices’ best interests to act in
accordance with the terms of the agreement. We have already established that this is the
case for judicial logrolling with indefinitely repeating dealings. Thus, logrolling
agreements would be self-policing in the Supreme Court. The justices essentially police
each other by means of reciprocity. Basically, if you help me, then I will help you.
However, if you hurt me, then I will hurt you.
Of course there are other reasons that justices may follow through with their
logrolling agreements. A justice may place a high value on the status of his reputation
among the other justices. Likewise, justices may maintain “ideological commitments to
integrity and honesty” (North, 1990: 55). Furthermore, a justice may feel that he or she
has a duty to follow through with the agreements and promises they make. This concept
of duty was proposed by Immanuel Kant, who argued that “duty is the cement that holds
societies together” (Binmore, 2007: 342). Justices could also cooperate on the basis of
fairness. It is important to consider all of these motivations for judicial logrolling. While
we assume people are rational, that does not necessitate that they always act rationally.
A social contract is an agreement made among a particular subset of actors. In the case of the Supreme
Court, the justices act as an institution. This was discussed in more detail in Chapter 4. Thus, the term
institutional contract is more appropriate for our particular setting.
The purpose of this section is to employ the principles of game theory to map out
actual Supreme Court cases where I suspect that logrolling could have influenced the
Court’s final ruling. The analysis of these case studies should solidify the possibility of
logrolling among Supreme Court Justices and offer a more concrete illustration of what
this logrolling really entails. As a disclaimer, I am not suggesting that logrolling is the
definitive explanation for any particular case.
Given the interminable list of Supreme Court rulings, I have selected only one
group of decisions, which have overturned or established new precedents. I have chosen
to focus on two issues under the Equal Protection Clause and the Civil Rights Act of
1964. I could have easily chosen other areas of law such as obscenity or decisions on
abortion. However, I believe that these areas of law remain very blurry and can be
difficult to define and compare due to the specific nature of each decision.
There are also instances when the same justice has ruled differently on an identical
issue in separate cases. These discrepancies in voting behavior could point to the
possibility of logrolling among Supreme Court justices. While I do not specifically
address these cases, a few examples may be found in the line of cases following Booth v.
Maryland, 482 U.S. 496 (1987), including South Carolina v. Gathers, 490 U.S. 805
(1989), and then Payne v. Tennessee, 501 U.S. 808 (1991). In each ruling, Justice White
switched his vote, siding with each of the opposing sides of the debate. These sorts of
inconsistencies could very well indicate the presence of logrolling. My hope is that these
scenarios will add life to the game theoretic models that were defined in Chapter 5 and
further illustrate that logrolling could occur behind closed doors.
There are few issues of more importance than the guarantee of our civil rights and
liberties. In the Supreme Court, the doctrine of stare decisis plays a crucial role in the
justices’ decisions. The policy of stare decisis requires the court to stand by precedent.
According to the courts, the significance of stare decisis is
only for what it decides – for the “what,” not for the “why,” and not for the
“how.” Insofar as precedent is concerned, stare decisis is important only for the
decision, for the detailed legal consequence following a detailed set of facts
(United States Internal Revenue Service v. Osborne, 76 F.3d 306, 96-1 U.S. Tax
Case (9th Cir. 1996)).
The relevance of stare decisis for this study concerns the strength of precedence. The
more votes a logrolling coalition can obtain, the more resistant that precedent will be to
being overturned the next time a similar issue arises. The strongest precedents are
obviously forged by unanimous decisions. This is especially true in the 1950’s cases on
desegregation and public schools.
The Fourteenth Amendment is divided into five sections. It emerged from the
rumble of the Civil War. For the purposes of this study we only require Section 1, which
is stated as follows.
Section 1. All persons born or naturalized in the United States, and subject to the
jurisdiction thereof, are citizens of the United States and of the State wherein they
reside. No State shall make or enforce any law which shall abridge the privileges
or immunities of citizens of the United States; nor shall any State deprive any
person of life, liberty, or property, without due process of law; nor deny to any
person within its jurisdiction the equal protection of the laws (United States
Constitution: Fourteenth Amendment, 1868).
The Equal Protection Clause found in the Fourteenth Amendment is a bedrock of
American society and the way that all of its members view each other. Issues of civil
rights most often rely on this promise of Equal Protection, which provides that “no state
shall […] deny to any person within its jurisdiction the equal protection of the laws.” The
Equal Protection Clause is essentially the force behind the United States declaration that
“all men are created equal.”
In 1951, the National Association for the Advancement of Colored People
(NAACP) set forth the argument that the existence of legal segregation in elementary
schools was “tantamount to legalizing a racial caste system harmful to blacks” (Farber,
2003: 60). Brown v. Board of Education, 347 U.S. 483 (1954), is one of the single most
important decisions in the history of the Supreme Court. It is also a unanimous decision,
without a single concurrence. On May 17, 1954, Chief Justice Warren read the decision
of the unanimous Court:
We come then to the question presented: Does segregation of children in public
schools solely on the basis of race, even though the physical facilities and other
“tangible” factors may be equal, deprive the children of the minority group of
equal educational opportunities? We believe that it does. (Farber, 2003: 79).
This landmark decision overturned the previous standard of separate but equal
established in Plessy v. Ferguson, 163 U.S. 537 (1896). Justice Harlan’s dissent in Plessy
v. Ferguson, 163 U.S. 537 (1896), vehemently admonished the Court for their decision.
He claimed that “in view of the Constitution, in the eye of the law, there is in this country
no superior, dominant, ruling class of citizens. There is no caste here. Our Constitution is
color-blind, and neither knows nor tolerates classes among citizens. In respect of civil
rights, all citizens are equal before the law” (Farber, 2003: 65). In the spirit of Justice
Harlan’s famous dissent, Brown v. Board of Education, 347 U.S. 483 (1954), proclaimed
that “Separate educational facilities are inherently unequal.”
This case is noteworthy within the context of judicial logrolling because of the
intensity of preferences and the significance of such an important decision. Scholars have
noted that “[i]n extraordinary cases all the justices may sign an opinion to emphasize
their agreement” (O’Brien, 2005: 233). As negotiated documents, Supreme Court
decisions require a certain level of collective bargaining, both in the drafting and the
resulting division of votes. It has been documented that Chief Justice Warren “wanted a
unanimous ruling because Brown would inevitably engender resistance” (O’Brien, 2005:
252). In order to achieve a unanimous decision, Justice Warren employed various
strategies. "On especially controversial cases, one strategy may be simply to confer but
not to vote. Forcing a vote may sharply divide the justices and foreclose negotiations"
(O’Brien, 2005: 252). When Brown v. Board of Education, 347 U.S. 483 (1954), was first
discussed in conference, Justice Warren prevented an initial vote and instead emphasized
the moral issue at stake. Without Justice Warren’s persistence and use of authority, the
ruling would probably have been six to three or five to four, rather than unanimous
(O’Brien, 2005: 252).
I pose that Justice Warren and other justices could have employed promises in the
form of a logrolling agreement to secure such an outcome. I have no means to justify the
specifics of such a claim nor do I wish to present these statements as facts. These
hypothetical details are merely possible scenarios. I am only proposing that logrolling
could be a possible strategy in order to win a unanimous victory, not that it was or is.
Because of the importance of Brown v. Board of Education, 347 U.S. 483 (1954), threats
of concurring or dissenting opinion would have carried more weight.
This intuitively implies that justices would be able to bargain whether he or she
would publish a concurring opinion or a dissent with those justices who favored Brown to
receive favors in future cases. This idea is not that far fetched, and in the case of whether
the arrangement was with Justice Warren or some other justice is irrelevant to the
purpose of this study. This is especially pertinent in light of later cases that do include
concurrences from some of the same justices. For instance, Justice Frankfurter added a
concurring opinion to the unanimous ruling to reaffirm Brown v. Board of Education, 347
U.S. 483 (1954), in Cooper v. Aaron, 358 U.S. 1 (1958).
Suppose a similar situation to Brown v. Board of Education, 347 U.S. 483 (1954).
Let Justice Warren have intense preferences about the outcome of the case and assume
that he is the leader of the Pro-Desegregation majority, which includes every justice
except Justice Frankfurter. Suppose Justice Frankfurter threatens to file a concurring
opinion that would belittle an important element of the majority opinion. Justice
Frankfurter is aware of the strong preferences involved and knows that Justice Warren
will bargain to ensure a unanimous decision in favor of desegregation. Consider the
extensive form of a possible game displayed in Figure 6.1 below.
(P, f )
No Logroll
Majority with
(P - C, 0)
for Logroll
No Logroll
Majority with
(P - D, 0)
(P, f )
No Logroll
Majority with
(P - C, 0)
for Logroll
No Logroll
(P, 0)
No Logroll
Majority with
(P - D, 0)
for Logroll
for Logroll
Threaten Concurrence
Threaten Dissent
Figure 6.1: Possible extensive form of Brown logroll. The heavy traces represent the
possible outcomes if a successful logrolling agreement were to be carried out.
The payoffs for each player are denoted as the outcomes of each terminal node in
the order (Justice Warren, Justice Frankfurter). Each entry in the payoff vector signifies
the payoff to that particular player. For convenience, define P as the payoff Justice
Warren receives if he gets to write the opinion for a unanimous landmark precedent.
Then (P – C) represents the weakened payoff associated with a precedent originating
from a ruling that included a concurring opinion. Likewise, (P – D) represents the
weakened payoff associated with a precedent originating from a ruling that included a
dissenting opinion. Now, define f as the payoff for Justice Frankfurter in the form of
future support from Justice Warren as part of the logrolling agreement. In addition,
assume that a payoff of zero represents the case when no change among the votes occurs,
meaning Justice Frankfurter receives no extra benefits. It is clear that it is in all of the
justices’ best interest to logroll in order to maximize their preferences and hence the
number of votes in line with their own preferences.
Following the decision in Brown v. Board of Education, 347 U.S. 483 (1954), it
became clear that limiting the number of racial minorities a university admitted would
violate the Equal Protection Clause and thus be unconstitutional. Further standards were
defined in Loving v. Virginia, 388 U.S. 1 (1967), a case concerning interracial marriage.
In a unanimous decision, the Court established that distinctions made on the basis of race
were “odious to a free people whose institutions are founded upon the doctrine of
equality” and were subject to “the most rigid scrutiny” under the Equal Protection Clause
(Farber, 2003: 184). By strict scrutiny, the Court is referring to the standard that says that
racial classifications “must by justified by a compelling government interest and must be
‘necessary […] to the accomplishment’ of their legitimate purpose” (Farber, 2003: 187).
The Court also held that, regardless of the “equal application” of the statute to both
whites and blacks, there was “patently no legitimate overriding purpose independent of
invidious racial discrimination which justifies this classification” (Farber, 2003: 183184). It is important to note the Court’s statement on prejudice, that such private “biases
may be outside the reach of the law, but the law cannot, directly or indirectly, give them
effect” (Farber, 2003: 186). This statement is very similar to the public choice
perspective that was explored earlier in Chapter 2, which emphasized the equal treatment
of unequals (Buchanan, 1975).
Following Loving v. Virginia, 388 U.S. 1 (1967), the practice of racial quotas
would be “unconstitutional regardless of whether heightened scrutiny is triggered merely
by the use of a racial classification, or alternatively by only those racial classifications
that disadvantage a racial minority” (Farber, 2003: 240). This led to two distinct
approaches to racial classification: (1) racial classification is never justified; or (2) racial
classification is sometimes justified to aid a disadvantaged minority. These approaches to
racial criteria lead to new questions about the place of affirmative action in our schools
and universities. The Court was confronted with a new side of racial classification,
specifically, reverse discrimination.
Regents of the University of California v. Bakke, 438 U.S. 265 (1978), posed this
very question. Allan Bakke, a white man, was rejected twice after applying for admission
to the University of California Medical School at Davis. He argued that his qualifications
surpassed those of qualified minorities, who were admitted on the basis of the university's
affirmative action program. The program was meant to assure a certain number of spots
for minorities in order to break down previous barriers to which minority students had
been subjected. There was no clear majority opinion. In a split decision, four justices
asserted that the university’s racial quota system violated the Civil Rights Act of 1964,
while another four justices claimed that no conflict existed. Justice Powell was the
deciding vote, agreeing with the first argument that the racial quotas were in violation. In
this matter, the Court ordered that Bakke be admitted to the medical school. However, on
the issue of whether racial quotas violate the Equal Protection Clause, Justice Powell
sided with the second group of justices. He claimed that while the strict use of racial
quotas was unconstitutional, the use of race as one of many criteria for admission was
The Court’s ruling was no doubt meant to forward the goal of equality by aiding
Bakke and minority interests simultaneously. Justice Powell held that “remedying a
societal discrimination was too amorphous a ‘concept of injury that may be ageless in its
reach into the past’” (Farber, 2003: 243). Justice Powell agreed that “the attainment of a
diverse student body” was a “constitutionally sufficient purpose” (Farber, 2003: 243). He
defined that purpose as follows: “The diversity that furthers a compelling state interest
encompasses a far broader array of qualifications and characteristics of which racial or
ethnic origin is but a single though important element” (Farber, 2003: 243). Thus, race
should be considered as a “plus” but “does not insulate the individual from comparison
with all other candidates for the favorable seats. […] This kind of program treats each
applicant as an individual in the admissions process” (Farber, 2003: 243).
As the deciding vote for both parts of the case, it is interesting to consider Justice
Powell’s role within the context of logrolling. A possible scenario could emerge where
both voting blocs are competing for Justice Powell’s vote in their favor. The breakdown
of the voting blocs is shown in Figure 6.2 below. In an obvious oversimplification, let us
call these voting groups Pro-Racial Quotas (Justices Brennan, White, Marshall, and
Blackmun) and Anti-Racial Quotas (Justices Burger, Stewart, Rehnquist, and Stevens).
Figure 6.2: Votes in Regents of the University of California v. Bakke (1978). Sorted by
ideology. The heavy trace around particular justices indicates that they voted with the
majority. Adapted from (Oyez Project, 2008).
Then suppose that one or more of the justices in the Pro-Racial Quota group
approach Justice Powell about a logrolling agreement in regards to the vote on the Civil
Rights Act of 1964. The Pro-Racial Quota voting bloc promises Justice Powell its future
support in another case for which Justice Powell has more intense preferences. Likewise,
suppose the Anti-Racial Quota voting bloc approaches Justice Powell about a logrolling
agreement in regards to the Equal Protection Clause. The extensive form of a possible
representation of this scenario is represented in Figure 6.3. The payoffs for each player
are denoted as the outcomes of each terminal node in the order (Pro-Racial Quota, AntiRacial Quota, Justice Powell). Each entry in the payoff vector signifies the payoff to that
particular player. For convenience, define v as the payoff of Justice Powell’s additional
vote to the voting blocs and define f as the payoff of the voting bloc or blocs’ future
support to Justice Powell. In addition, assume that a payoff of zero represents the case
when no change among the votes occurs. It is clear that it is in all of the justices’ best
interest to logroll in order to maximize their preferences and hence the number of votes in
line with their own preferences.
One Logroll
(0, v, f )
No Logroll
(0, 0, 0)
Two Logrolls
(v, v, 2f )
One Logroll
(v, 0, f)
No Logroll
(0, 0, 0)
One Logroll
(v, 0, f )
No Logroll
(0, 0, 0)
Don’t Approach
Anti-Racial Quotas
Don’t Approach
Anti-Racial Quotas
No Logroll
(0, 0, 0)
Don’t Approach
Pro-Racial Quotas
Figure 6.3: Possible extensive form of Bakke logroll. The heavy trace represents the
outcome if two successful logrolling agreements were carried out.
In this Chapter, it has been demonstrated that logrolling could feasibly be used in
order to strengthen precedent in accordance with the justices’ preferences, thereby
maximizing the justices preferences and hence their utility. However, the question arises
whether judicial logrolling is beneficial to society. This is the topic of the next chapter.
The possibility of judicial logrolling has been established. However, the
implications of logrolling in the Supreme Court are still unclear. Vote trading can
obviously change the outcomes of Supreme Court rulings and alter the precedents that
these holdings establish. In the judicial setting, logrolling has the potential to not only
determine the majority vote, but to actually strengthen a precedent incrementally, one
vote at a time. But this leads to the question of who benefits and who loses in judicial
It is clear that the justices themselves can benefit as they maximize the number of
votes in accordance with their own preferences and in effect strengthen the institutional
opinion in their favor. Scholars assert that
the Court must provide definitive statements of the law. More than a mere
agreement on the result is needed; without a majority rationale for the result, the
Supreme Court abdicates its responsibility to the institutions and parties
depending on it for direction (Plurality Decisions and Judicial Decisionmaking,
1981: 1128).
If society is indifferent as to what these precedents are, then judicial logrolling can offer a
higher level of legal stability. This stability can be attributed to the increased unity in
opinion writing that logrolling makes possible as justices vote for opinions that they do
not feel strongly about to secure votes for those cases for which they do have intense
preferences. As the standards of our legal institutions become more determined and
resistant to change, the law becomes a more reliable “guide to human interaction” (North,
1990: 3). In this way, “Institutions reduce uncertainty by providing a structure to
everyday life” (North, 1990: 3). Our legal institutions shape the interactions of
individuals within the context of society and the opportunities available to each
individual. If institutional change is minimal, few if any of these interactions and
opportunities will change.
But society is rarely indifferent as to what these stable institutions dictate. While
stability can be effective in minimizing uncertainty, it can also result in a stagnant system
of social norms that do not necessarily treat everyone equally. Doctrines of distributive
justice and moral institutions can be just as stable, if not more stable, than those of justice
and rule of law that were discussed earlier in Chapter 2. For instance, it is difficult to
support statutes prescribing racial segregation because they are stable or that we should
discriminate because we always have in the past. While stability can be efficient,
tradeoffs emerge as liberties are sacrificed for increased certainty.
It is reasonable to assume that institutions must also be malleable. They must
evolve as society evolves. Institutional change is the “feedback process by which human
beings perceive and react to changes in the opportunity set” (North, 1990: 7). But this
does not mean that logrolling could not act as a propellant of institutional change. As we
discussed in our game theory scenario based on Brown v. Board of Education, 347 U.S.
483 (1954), logrolling agreements could also form the foundation of institutional change.
Many of the changes in our legal institutions have been the result of strong unified
precedents based on landmark Supreme Court cases. Logrolling agreements could be
used as a tool to ensure that important precedents like those in regard to desegregation in
Brown v. Board of Education, 347 U.S. 483 (1954), are strong enough to command
enforcement and create new social norms. Hopefully, for the better.
There are other possible costs and benefits associated with judicial logrolling.
Scholars have questioned why vote trading in the Supreme Court should or should not be
objectionable (Hasen, 2000: 1347-1348). Some of these studies focus on whether vote
trading would undermine judicial legitimacy (Caminker, 1997; Hasen, 2000: 1347). It is
also argued that the application of efficiency analysis to the question of judicial logrolling
is inappropriate because legal principle is not immeasurable, in contrast to preference
satisfactions (Caminker, 1997; Hasen, 2000: 1348). However, it seems that even without
numbers, it is invaluable to attempt to understand the dynamics of a topic as provocative
as judicial logrolling. It is also helpful to note that preferences are not just numbers and
dollars. The benefits are abstract, just as the costs are not quantifiable.
In sum, judicial logrolling has the potential to both stifle and encourage
institutional change, whether for society’s good or its detriment is unclear and depends on
each decision and what values are important. The same institutional change can aid one
group and harm another. Therefore, while justices can potentially maximize their own
preferences through the practice of judicial logrolling, the payoffs for society are unclear.
In conclusion, judicial logrolling has been established as a possible strategy for
the justices of the Supreme Court. In the course of this study, the Supreme Court has been
examined both as an institution and as a group of individuals seeking to maximize their
individual preferences. By modeling the justices’ decisions in a game theoretic setting, it
was possible to explore how logrolling could take place in the Supreme Court and why
justices would even participate in such an arrangement. This study proposes that the
dynamics of judicial logrolling in the Supreme Court are best modeled as an infinite
horizon repeated Prisoners’ Dilemma. This model allows for cooperation and thus
logrolling to occur within the constructs of perfect information.
While a great deal of controversy exists in regards to the gains and losses of such
a strategy, judicial logrolling does fit with the public choice model of voters as vote
maximizing actors. This political exchange in the form of vote trading across different
decisions has the potential to change the outcomes of crucial Supreme Court rulings and
hence change our legal institutions and how individuals and groups interact in society.
While studies have attempted to measure the effects of judicial logrolling, most
have been restricted to district courts and issues of female justices. This is
understandable, as logrolling is a difficult element to model without defined
constituencies. Future studies should consider an empirical model following Thomas
Stratmann and his work in legislative logrolling. It would also be beneficial to expand the
simple case studies and scenarios that I have considered within this study. The answer to
if Supreme Court Justices logroll may not be empirical. It may only be found between the
lines of the justices’ journals and could even stay behind closed doors forever. All that I
suppose is that judicial logrolling could happen in the Supreme Court. There is still much
to learn about judicial logrolling and its effects. I leave the proof up to these studies.
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