scispace - formally typeset
Search or ask a question
Journal ArticleDOI

Bounded Rationality and the Choice of Jury Selection Procedures

TL;DR: A new measure of strategic complexity based on level-k thinking is introduced and this measure is used to compare challenge procedures often used in practice and overturn some commonly held beliefs about which jury selection procedures are strategically simple.
Abstract: A peremptory challenge procedure allows the parties to a jury trial to dismiss some prospective jurors without justification. Complex challenge procedures offer an unfair advantage to parties who are better able to strategize. I introduce a new measure of strategic complexity based on “level-k” thinking and use this measure to compare challenge procedures often used in practice. In applying this measure, I overturn some commonly held beliefs about which jury selection procedures are “strategically simple.”

Summary (3 min read)

1. Introduction

  • It is customary to let the parties involved in a jury trial dismiss some of the potential jurors without justification.
  • Jury selection consultancy has become a well-established industry.

1.1. Comparing Strategic Complexity

  • Comparing the strategic complexity of jury selection procedures presents two challenges.
  • The objective is to identify models for which the parties have dominant strategies.
  • All use subject to University of Chicago Press Terms and Conditions (http://www.journals.uchicago.edu/t-and-c).
  • In a report on judges’ practices regarding peremptory challenges, Shapard and Johnson (1994, p. 6) write, “Some judges require that peremptories be exercised [following procedure X]. . . .
  • I show that, contrary to these judges’ beliefs, procedures in which challenges are sequential tend to be strategically simpler than procedures in which challenges are simultaneous: by generating imperfect-information games, simultaneous procedures increase the amount of guesswork needed to determine optimal strategies.

2. Model and Procedures

  • In addition to peremptory challenges, which require no justification, the parties can raise challenges for cause, which must be 6 In contrast, Li (2015) proposes a criterion to compare the incentive properties of different mechanisms that all have dominant strategies.
  • Unlike the divide-and-choose procedure, the divide-and-choose-and-raise-your-hand procedure requires four rounds of backward induction to be solved because of the addition of the inconsequential raise-your-hand action.
  • As explained by Bermant and Shapard (1981, p. 92), the defining feature of a struck procedure “is that the judge rules on all challenges for cause before the parties claim any peremptories.

2.1. The Model

  • The defendant D and the plaintiff P are allowed cD and cP peremptory challenges, respectively.
  • A pair of preferences (RP, RD) is called a preference profile (hereafter, profile), and a quintuple (RP, RD, cP, cD, b) is called a jury selection problem (hereafter, problem).
  • When describing their approach to jury selection, jury consultants often suggest the use of separable (and even additive) preferences relying on some rating or scoring of the individual jurors (Caditz 2014; Leibold 2015).
  • All use subject to University of Chicago Press Terms and Conditions (http://www.journals.uchicago.edu/t-and-c).

2.2. Procedures

  • As attested to by Bermant and Shapard (1981), a wide variety of struck procedures are used by judges.
  • If more than b jurors are left unchallenged, the b impaneled jurors are drawn at random from among the unchallenged jurors.
  • Again, an alternating procedure can be either simultaneous or sequential depending on whether challenges are submitted simultaneously or sequentially in each round.
  • Other than the fact that multiple jurors are selected (instead of a single arbitrator), the one-shotQ procedure is strategically equivalent to the shortlisting procedure proposed by de Clippel, Eliaz, and Knight (2014).

3. Impossibility Results

  • A strategy Î i is is dominant for i given some model - -Í i iS of her opponent if si is a best response to every strategy - -Î .i is S A dominant strategy is a strategy Î * iis that is a best response for i to any strategy - -Î .i is.
  • In other words, a 11 The term “N-struck procedure” emphasizes the fact that, in each round, the parties can challenge any juror in N who has not been challenged yet.
  • All use subject to University of Chicago Press Terms and Conditions (http://www.journals.uchicago.edu/t-and-c).
  • Intuitively, in any N-struck procedure, if −i does not challenge any jurors, then i’s best response is to challenge her ci worst jurors.

4. A Measure of Strategic Complexity

  • Propositions 1 and 2 show that most procedures are not strategically simple in the sense that both parties cannot always follow the simple recommendation of playing a dominant strategy.
  • This does not mean, however, that judges should give up on the idea of using procedures that are as simple as possible.
  • This section and Section 5 show that, although procedures generally fail to feature dominant strategies, not all procedures are equal in terms of strategic complexity.

4.1. Motivating Example

  • Brams and Davis (1978, p. 969) argue that, when the parties have juror-inverse preferences, one-shot procedures raise “no strategic questions of timing: given that each side can determine those veniremen [that is, potential jurors] it believes least favorably disposed to its cause, it should challenge these up to the limit of its peremptory challenges.”.
  • Certainly the one-shotM procedure is not a dominant-strategy procedure.
  • All use subject to University of Chicago Press Terms and Conditions (http://www.journals.uchicago.edu/t-and-c).
  • Therefore, regardless of the jurors whom P believes D will challenge, a best response by P can never include P challenging a juror in {5, . . . , 9}.
  • I then apply this measure in Sections 5 and 6 to compare struck procedures for different assumptions on the problem (RD, RP, cD, cP, b).

4.2. The Dominance Threshold

  • As argued above, first-best procedures are procedures in which each party has a dominant strategy no matter what model she has of her opponent.
  • For each i ∈ {D, P}, eliminate from 0iL the strategies si for which there exist a subgame γ of Γ such that the restriction si|γ of si to γ is not a best response to any s−i|γ in γ.

5. One-Shot Procedures

  • I show that the one-shotQ procedure is strategically simpler than the one-shotM procedure in the following sense: Proposition 3. (i) For every problem, the dominance threshold of the oneshotM procedure is no smaller than the dominance threshold of the one-shotQ procedure.
  • Proposition 6. For any sequential N-struck procedures, if preferences for the outcomes of the procedure are strict, then the dominance threshold is finite and smaller than the depth of the game tree.
  • 22 Again, proposition 6 does not depend on the separability assumption but instead on the assumption that preferences for the outcomes of the procedure are strict.
  • To see why the dominance threshold is infinite in subgame γ*, observe that in γ*, each party wants to free ride on her opponent’s challenge of juror 3.

7. Extension: Incomplete Information

  • Because the lowest dominance threshold for reasonable challenge procedures is 2 (proposition 1), the above comparisons implicitly assume that the parties know each other’s preferences.
  • As these comparisons show, once preferences are known, some procedures lead to simpler strategic interplays than others.
  • To avoid such intricacies, it is useful to assume that 24 For example, identifying the set of i’s level-2 models of −i requires knowing how i believes −i would play a best response if −i assumes that i has a level-1 strategy.
  • But because P’s true preference is RP, following P’s challenge of juror 2, P in fact challenges juror 1, which leaves juror 3 as the effective juror.

Did you find this useful? Give us your feedback

Content maybe subject to copyright    Report

711
[ Journal of Law and Economics, vol. 61 (November 2018)]
© 2018 by e University of Chicago. All rights reserved. 0022-2186/2018/6104-0023$10.00
Bounded Rationality and the Choice
of Jury Selection Procedures
Martin Van der Linden Utah State University
Abstract
A peremptory-challenge procedure allows the parties to a jury trial to dismiss
some prospective jurors without justication. Complex challenge procedures of-
fer an unfair advantage to parties who are better able to strategize. I introduce
a new measure of strategic complexity based on level-k thinking and use this
measure to compare challenge procedures oen used in practice. In applying
this measure, I overturn some commonly held beliefs about which jury selection
procedures are strategically simple.
1. Introduction
It is customary to let the parties involved in a jury trial dismiss some of the
potential jurors without justication. Procedures for dismissal are known as
peremptory- challenge procedures. Such procedures are used in many countries,
including the United States.
1
A variety of procedures are used in practice. ese
procedures dier notably in their strategic complexity. More complex proce-
dures give an unfair advantage to parties who are strategically skilled or can de-
vote ample resources to hiring jury consultants. It is therefore important to iden-
I am grateful to the editor and a referee for useful remarks and suggestions. I am also grateful to
Geir Asheim, Benoit Decerf, Paul Edelman, Hanna Frank, Eun Jeong Heo, Greg Leo, Clayton Mas-
terman, Claudia Rei, Roberto Serrano, Yves Sprumont, Rodrigo Velez, John Weymark, and Myrna
Wooders for helpful discussions and comments. I also thank the participants at presentations at
Aix-Marseille University, Catholic University of Louvain, KU Leuven, Vanderbilt University, the
13th meeting of the Society for Social Choice and Welfare, and the Fih World Congress of the
Game eory Society for their questions and suggestions. I am thankful to the Center for Operations
Research and Econometrics and the Center for Research in Economics for their hospitality during
visits. Support from the Kirk Dornbush summer research grant and National Science Foundation
grant IIS-1526860 is gratefully acknowledged.
1
In Swain v. Alabama (380 U.S. 202 [1965]), the Supreme Court armed that “[t]he right to
challenge a given number of jurors without showing cause is one of the most important of the rights
secured to the accused” (Pointer v. United States, 151 U.S. 396, 408 [1894]). Following Batson v.
Kentucky (476U.S.79[1986]), a party can disqualify a peremptory challenge by her opponent if she
can prove that the challenge was based on race. (Challenges based on gender were later also prohib-
ited following J. E. B. v. Alabama [511 U.S. 127 (1994)].) However, Batson v. Kentucky is notoriously
hard to implement, and judges rarely rule in favor of Batson challenges (Marder 2012; Daly 2016).
This content downloaded from 129.123.124.107 on June 24, 2019 12:19:40 PM
All use subject to University of Chicago Press Terms and Conditions (http://www.journals.uchicago.edu/t-and-c).

712 The Journal of LAW & ECONOMICS
tify the procedures that are strategically simple in order to level the playing eld
among parties. In this paper, I introduce the concept of a dominance threshold,
a new measure of strategic complexity based on level-k thinking, and I use this
measure to compare the complexity of some challenge procedures commonly
used in practice (see Crawford, Costa-Gomes, and Iriberri [2013] for a survey of
the level-k literature).
Fairness is an important issue in jury selection. One feature of a procedure that
impacts fairness is its strategic complexity. If a procedure is complex, parties with
better strategic skills are likely to secure more favorable juries. is is particu-
larly relevant in jury selection in which the parties invest signicant resources for
developing an eective strategy. For example, jury selection consultancy has be-
come a well-established industry.
2
Using strategically simple procedures limits
the impact on the selected jury of dierences in the parties’ ability to strategize or
in their nancial means to hire jury consultants.
1.1. Comparing Strategic Complexity
Comparing the strategic complexity of jury selection procedures presents two
challenges. First, jury selection procedures are indirect mechanisms because the
parties’ actions consist of dismissing jurors rather than revealing their prefer-
ences. Second, in some procedures commonly used in practice, the parties submit
their challenges simultaneously, which induces games of imperfect information.
ese two diculties make it impossible to apply measures of strategic complex-
ity previously developed in the literature (see Section 1.2).
I overcome these diculties by introducing the concept of a dominance thresh-
old. Given some assumption about the strategies her opponent could play—
henceforth, a model of her opponent—a party has a dominant strategy if one of
her strategies is a best response to any strategy of her opponent that is consistent
with her model. e objective is to identify models for which the parties have
dominant strategies. is is accomplished by iteratively eliminating strategies
that are never-best responses. e dominance threshold is the number of rounds
of elimination needed to reach models in which both parties have a dominant
strategy. e dominance threshold measures the complexity of the model of op-
ponents that the parties need in order to have a dominant strategy. For example,
a dominance threshold of 1 corresponds to the parties having a dominant strat-
egy given any model of their opponent. When the dominance threshold is 2, the
parties need to know only that their opponent is a best responder in order to have
a dominant strategy.
2
e widespread use of jury consultants is evidenced by the existence of the American Society of
Trial Consultants and its journal e Jury Expert: e Art and Science of Litigation Advocacy. Jury
consultants explicitly describe how part of their job is concerned with the strategic use of challenges.
Jury consultant Roy Futterman, for example, writes, “Caditz argues that . . . jury selectors pay . . .
little to no attention to the strategic use of strikes [that is, peremptory challenges]. . . . [I]t is a bit of
a reach to say that strategy is barely utilized. In my experience, . . . [jury selection] comes closer to
a long battle of stealth, counter-punches, misdirection, and hand-to-hand combat than a loy aca-
demic experience” (Futterman 2014).
This content downloaded from 129.123.124.107 on June 24, 2019 12:19:40 PM
All use subject to University of Chicago Press Terms and Conditions (http://www.journals.uchicago.edu/t-and-c).

Jury Selection Procedures 713
Many judges appear to share the concern about selecting strategically simple
procedures and have developed procedures that attempt to limit the parties’ abil-
ity to strategize. In a report on judges’ practices regarding peremptory challenges,
Shapard and Johnson (1994, p. 6) write, “Some judges require that peremptories
be exercised [following procedure X]. . . . is approach . . . makes it more di-
cult to pursue a strategy prohibited by Batson (or any other strategy).” “A more
extreme approach to the same end . . . is [procedure Y]. . . . is approach im-
poses maximum limits on counsel’s ability to employ peremptories in a strategic
manner” (Shapard and Johnson [1994], p. 6 n. 6).
Using the dominance threshold as a measure of strategic complexity provides
new insights and challenges some commonly held beliefs about jury selection
procedures. Shapard and Johnson (1994, p. 6) write, “Other judges, for the same
purposes [that is, limiting the parties’ ability to strategize], allow all peremptories
to be exercised aer all challenges for cause, but with the parties making their
choices ‘blind’ to the choices made by opposing parties (in contrast to alternating
‘strikes’ from a list of names of panel members).” I show that, contrary to these
judges’ beliefs, procedures in which challenges are sequential tend to be strategi-
cally simpler than procedures in which challenges are simultaneous: by generat-
ing imperfect-information games, simultaneous procedures increase the amount
of guesswork needed to determine optimal strategies.
I also study the design of maximally simple jury selection procedures. I show
that it is impossible to construct a reasonable procedure that allows the parties to
challenge jurors and always have a dominant strategy. Hence, the smallest achiev-
able dominance threshold is 2. Such a minimal dominance threshold is attained
by a procedure that I call the sequential one-shot procedure, in which the parties
sequentially submit a single list of jurors whom they want to challenge.
1.2. Related Literature
is paper diers from the previous game-theoretic literature on jury selection
procedures in at least two ways (see Flanagan [2015] for a recent review). First,
the literature focuses on subgame-perfect equilibrium as a solution concept (two
exceptions are Bermant [1982] and Caditz [2015]). Subgame perfection requires
a high level of strategic sophistication, especially in complex procedures. By rely-
ing on the concept of a dominance threshold, this paper accounts for the possi-
bility of boundedly rational parties. I show how the dominance threshold, which
measures the amount of common knowledge and rationality needed to have a
dominant strategy, can be used to measure the strategic complexity of a proce-
dure.
Second, most of the literature focuses on the characterization and properties of
equilibria of dierent procedures (see Roth, Kadane, and DeGroot 1977; Brams
and Davis 1978; DeGroot and Kadane 1980; Kadane, Stone, and Wallstrom 1999;
Alpern and Gal 2009; Alpern, Gal, and Solan 2010). When the performance of
procedures is compared, it is typically in terms of their eects on the composition
This content downloaded from 129.123.124.107 on June 24, 2019 12:19:40 PM
All use subject to University of Chicago Press Terms and Conditions (http://www.journals.uchicago.edu/t-and-c).

714 The Journal of LAW & ECONOMICS
of the jury. ese comparisons have yielded few policy recommendations (see,
however, Bermant 1982; Flanagan 2015, sec. 4.2). In contrast, this paper com-
pares procedures with respect to the standard objective of limiting the parties’
ability to strategize. is latter approach enables a clear comparison of some of
the procedures used in practice.
Focusing on strategic complexity also implies that this paper falls short of pro-
viding a full-edged implementation analysis. Bounded rationality has been con-
sidered in implementation theory. Abreu and Matsushima (1992) notably show
that any social choice function can be (virtually) implemented in iteratively un-
dominated strategies. Because the authors do not restrict the number of itera-
tions, the mechanism they propose can, depending on the application, have a
very high dominance threshold.
3
Instead of xing a solution concept and inves-
tigating the social choice functions it allows to be implemented, this paper fo-
cuses on solution concepts themselves. I argue that among a particular class of
solution concepts, the weakest solution concept that enables solving a procedure
is a useful measure of a game’s strategic complexity. A natural subsequent ques-
tion—which is le open—is to determine the best procedure (according to some
outcome-oriented objective) that can be solved by a reasonably weak solution
concept (as in de Clippel, Eliaz, and Knight 2014).
4
is paper also focuses heavily on procedures that are relevant in practice for
jury selection. As a consequence, my analysis incorporates a number of institu-
tional constraints that are specic to jury selection. In particular, I consider only
procedures in which the parties’ actions are limited to challenging some prospec-
tive jurors. Selection procedures based on other action spaces (for example, di-
rect mechanisms) are known to have interesting properties (Barberà and Coelho
2008).
5
For restricted domains, some of those procedures even have dominant
strategies (Barberà, Sonnenschein, and Zhou 1991; Barberà, Massó, and Neme
2005) or can be solved by nitely rational players (Abreu and Matsushima 1992;
de Clippel, Eliaz, and Knight 2014). However, those procedures involve—some-
times complex—action spaces that go beyond the simple challenge of jurors. My
focus on challenge procedures is motivated by the fact that, in the context of jury
selection, the law and legal customs oen specically limit the parties’ actions to
challenges. One contribution of this paper is to show that the few selection pro-
cedures with dominant strategies identied by Barberà, Massó, and Neme (2005)
do not survive conferring the parties with minimal challenge abilities (see also
Van der Linden 2017).
e dominance threshold relates to a recent strand of the literature that com-
3
Another dierence is that Abreu and Matsushima (1992) rely on iteratively undominated strat-
egies, whereas most of this paper deals with iteratively never-best responses. See Section 8 for a dis-
cussion of how my results generalize to iterated undominated strategies.
4
In this respect, it would be useful to develop a parametrized outcome-oriented objective for jury
selection procedures. One could then weigh trade-os between the degree to which a procedure sat-
ises the objective and the procedure’s level of strategic complexity.
5
For a general characterization of mechanisms with a dominance threshold of 2, see Börgers and
Li (2017).
This content downloaded from 129.123.124.107 on June 24, 2019 12:19:40 PM
All use subject to University of Chicago Press Terms and Conditions (http://www.journals.uchicago.edu/t-and-c).

Jury Selection Procedures 715
pares the incentive properties of mechanisms that fail to have dominant strate-
gies.
6
For example, Pathak and Sönmez (2013) and Arribillaga and Massó (2016)
dene comparison criteria for direct games. In indirect games, de Clippel, Eliaz,
and Knight (2014) recommend focusing on procedures that can be solved in two
rounds of backward induction. More generally, this last recommendation sug-
gests using the number of rounds of backward induction needed to solve a proce-
dure as a measure of its complexity.
Measures developed for direct mechanisms are not well suited for the compari-
son of jury selection procedures because those procedures induce indirect games.
In addition, an important question in the choice of a jury selection procedure
is whether challenges should be simultaneous or sequential. Because backward
induction is dened only for perfect-information games, a dierent measure is
therefore required. (When games are modeled in extensive form, any simultane-
ous move implies that the game is of imperfect information.)
7
Unlike previous
measures in the literature, the dominance threshold can be used to compare the
strategic complexity of any pair of games, including indirect games and games of
imperfect information. Although the focus of this paper is the study of jury se-
lection procedures, the dominance threshold applies more generally as a general
measure of strategic complexity.
e paper is organized as follows. Section 2 introduces the model, several ex-
amples of jury selection procedures, and a general class of procedures. In Section
3, I show that most reasonable jury selection procedures do not have dominant
strategies. Section 4 formally introduces the concept of a dominance threshold.
e dominance threshold is then applied to comparing the strategic complexity
of jury selection procedures in Sections 5 and 6. Whereas the previous sections
considered a complete-information setting, Section 7 considers an extension to
situations of incomplete information. In Section 8, I consider further extensions
and discuss some open questions. Proofs are in the Online Appendix.
2. Model and Procedures
I focus on struck procedures. In addition to peremptory challenges, which re-
quire no justication, the parties can raise challenges for cause, which must be
6
In contrast, Li (2015) proposes a criterion to compare the incentive properties of dierent mech-
anisms that all have dominant strategies.
7
Even under complete information, one must be careful to prune game trees before using the
number of rounds of backward induction as a measure of strategic complexity. For example, con-
sider the divide-and-choose procedure for the fair division of a divisible endowment. e procedure
has a dominance threshold of 2 and can be solved in two rounds of backward induction. In contrast,
consider the divide-and-choose-and-raise-your-hand procedure. In this alternate procedure, aer
the endowment has been shared, players sequentially raise or lower their hands, with the show of
hands having no impact on the nal allocation. Unlike the divide-and-choose procedure, the di-
vide-and-choose-and-raise-your-hand procedure requires four rounds of backward induction to
be solved because of the addition of the inconsequential raise-your-hand action. e latter actions
should therefore be pruned before applying the measure of backward-induction complexity. In con-
trast, the dominance threshold is insensitive to the addition of the inconsequential action and does
not require pruning the game tree.
This content downloaded from 129.123.124.107 on June 24, 2019 12:19:40 PM
All use subject to University of Chicago Press Terms and Conditions (http://www.journals.uchicago.edu/t-and-c).

Citations
More filters
Journal ArticleDOI
TL;DR: In this paper, it was shown that even limited veto power implies that the mechanism is not strategy-proof in a large set of domains including the domain of additive preferences and even when probabilistic mechanisms are allowed.
Abstract: Many mechanisms used to select a committee of k members out of a candidates endow voters with some veto power over candidates. Impossibility results are provided showing that, in most cases, even limited veto power implies that the mechanism is not strategy-proof. These impossibilities hold on a large set of domains including the domain of additive preferences and even when probabilistic mechanisms are allowed.

3 citations


Cites result from "Bounded Rationality and the Choice ..."

  • ...14See Van der Linden (2016) for more details and Hylland (1980, Section 4) for similar results....

    [...]

01 Jan 2016
TL;DR: The question in Foster v. Chatman is whether the state habeas court erred when it held that the prosecution's use of peremptory strikes was not a violation of the Batson test as discussed by the authors.
Abstract: Peremptory challenges have existed since the early days of the common law. Many believe that peremptory challenges help prosecutors ensure fair and impartial juries. Prosecutors often, however, use peremptory strikes for discriminatory purposes. The Supreme Court introduced a test in Batson v. Kentucky to evaluate whether peremptory strikes used on potential jurors were based on racial discrimination. Implementing the ambiguous Batson test has proven extremely difficult. Social scientists have found that prosecutors still commonly use race as a factor in selecting juries, and black jurors remain underrepresented relative to their proportion of the population in many jurisdictions, which suggests the Batson test has failed to effectuate its purpose. The question presented in Foster v. Chatman is whether the state habeas court erred when it held that the prosecution’s use of peremptory strikes was not a violation of the Batson test. According

1 citations

Journal ArticleDOI
TL;DR: In particular, the authors showed that even limited veto power makes many mechanisms of interest manipulable, including mechanisms that contain a degenerate lottery in which a committee is chosen for sure and mechanisms that are constructed from extensive game forms with a finite number of strategies.

1 citations

References
More filters
Posted Content
TL;DR: The game-theoretic answer is that all the developers should locate exactly where the natural attractions are as mentioned in this paper, but does not depend on the fraction of lazy tourists or the number of developers (as long as there is more than one).
Abstract: Picture a thin country 1000 miles long, running north and south, like Chile. Several natural attractions are located at the northern tip of the country. Suppose each of n resort developers plans to locate a resort somewhere on the country's coast (and all spots are equally attractive). After all the resort locations are chosen, an airport will be built to serve tourists, at the average of all the locations including the natural attractions. Suppose most tourists visit all the resorts equally often, except for lazy tourists who visit only the resort closest to the airport; so the developer who locates closest to the airport gets a fixed bonus of extra visitors. Where should the developer locate to be nearest to the airport? The surprising game-theoretic answer is that all the developers should locate exactly where the natural attractions are. This answer requires at least one natural attraction at the northern tip, but does not depend on the fraction of lazy tourists or the number of developers (as long as there is more than one).

536 citations


"Bounded Rationality and the Choice ..." refers background in this paper

  • ...In particular, the results hold when i’s level-1 strategies include i’s best responses to probabilistic beliefs about the (pure) level-0 strategy that −i will employ, as in Ho, Camerer, and Weigelt (1998)....

    [...]

  • ...The related concept of a rationality threshold was introduced by Ho, Camerer, and Weigelt (1998)....

    [...]

Journal ArticleDOI
TL;DR: The main result of the paper is a characterization of voting by committees, which is the class of all voting schemes that satisfy voter sovereignty and non-manipulability on the domain of separable preferences.
Abstract: The main result of this paper characterizes voting by committees. There are n voters and K objects. Voters must choose a subset of K. Voting by committees is defined by one monotone family of winning coalitions for each object; an object is chosen if it is supported by one of its winning coalitions. This is proven to be the class of all voting schemes satisfying voter sovereignty and nonmanipulability on the domain of separable preferences. The result is analogous to the characterization of Clarke-Groves schemes in that it exhibits the class of all nonmanipulable schemes on an important domain. Copyright 1991 by The Econometric Society.

322 citations


"Bounded Rationality and the Choice ..." refers background in this paper

  • ...…are known to have interesting properties (Barberà and Coelho 2008).5 For restricted domains, some of those procedures even have dominant strategies (Barberà, Sonnenschein, and Zhou 1991; Barberà, Massó, and Neme 2005) or can be solved by finitely rational players (Abreu and Matsushima 1992; de…...

    [...]

Journal ArticleDOI
Shengwu Li1
TL;DR: In this article, the authors propose a new solution concept: a mechanism is obviously strategy-proof (OSP) if it has an equilibrium in obviously dominant strategies, i.e., a strategy is obviously dominant if and only if a cognitively limited agent can recognize it as weakly dominant.
Abstract: What makes some strategy-proof mechanisms easier to understand than others? To address this question, I propose a new solution concept: A mechanism is obviously strategy-proof (OSP) if it has an equilibrium in obviously dominant strategies. This has a behavioral interpretation: A strategy is obviously dominant if and only if a cognitively limited agent can recognize it as weakly dominant. It also has a classical interpretation: A choice rule is OSP-implementable if and only if it can be carried out by a social planner under a particular regime of partial commitment. I fully characterize the set of OSP mechanisms in a canonical setting, with one-dimensional types and transfers. A laboratory experiment tests and corroborates the theory.

312 citations

Journal ArticleDOI
TL;DR: In this paper, the authors investigate the implementation of social choice functions that map to lotteries over alternatives, and they show that if there are three or more players, any social choice function may be so implemented.
Abstract: The authors investigate the implementation of social choice functions that map to lotteries over alternatives. They require virtual implementation in iteratively undominated strategies. Under very weak domain restrictions, they show that if there are three or more players, any social choice function may be so implemented. The literature on implementation in Nash equilibrium and its refinements is compromised by its reliance on game forms with unnatural features (for example, "integer games") or "modulo" constructions with mixed strategies arbitrarily excluded. In contrast, the authors' results employ finite (consequently "well-behaved") mechanisms and allow for mixed strategies.

288 citations


"Bounded Rationality and the Choice ..." refers background in this paper

  • ...The dominance threshold relates to a recent strand of the literature that com- 3 Another difference is that Abreu and Matsushima (1992) rely on iteratively undominated strategies, whereas most of this paper deals with iteratively never-best responses....

    [...]

  • ...Abreu and Matsushima (1992) notably show that any social choice function can be (virtually) implemented in iteratively undominated strategies....

    [...]

  • ...…properties (Barberà and Coelho 2008).5 For restricted domains, some of those procedures even have dominant strategies (Barberà, Sonnenschein, and Zhou 1991; Barberà, Massó, and Neme 2005) or can be solved by finitely rational players (Abreu and Matsushima 1992; de Clippel, Eliaz, and Knight 2014)....

    [...]

Posted Content
TL;DR: In the case of Chicago Public Schools, this paper showed that the old Chicago matching mechanism is at least as manipulable as any other plausible matching mechanism and that the new mechanism is also manipulably manipulatable.
Abstract: In Fall 2009, officials from Chicago Public Schools changed their assignment mechanism for coveted spots at selective college preparatory high schools midstream. After asking about 14,000 applicants to submit their preferences for schools under one mechanism, the district asked them re-submit their preferences under a new mechanism. Officials were concerned that "high-scoring kids were being rejected simply because of the order in which they listed their college prep preferences" under the abandoned mechanism. What is somewhat puzzling is that the new mechanism is also manipulable. This paper introduces a method to compare mechanisms based on their vulnerability to manipulation. Under our notion, the old mechanism is more manipulable than the new Chicago mechanism. Indeed, the old Chicago mechanism is at least as manipulable as any other plausible mechanism. A number of similar transitions between mechanisms took place in England after the widely popular Boston mechanism was ruled illegal in 2007. Our approach provides support for these and other recent policy changes involving matching mechanisms.

189 citations

Frequently Asked Questions (9)
Q1. What have the authors contributed in "Bounded rationality and the choice of jury selection procedures" ?

This paper introduced the concept of a dominance threshold, a new measure of strategic complexity based on level-k thinking, and used this measure to compare challenge procedures often used in practice. 

If more than b jurors are left unchallenged when the procedure terminates, the b impaneled jurors are drawn at random from the unchallenged jurors. 

The widespread use of jury consultants is evidenced by the existence of the American Society of Trial Consultants and its journal The Jury Expert: The Art and Science of Litigation Advocacy. 

Proposition 6. For any sequential N-struck procedures, if preferences for the outcomes of the procedure are strict, then the dominance threshold is finite and smaller than the depth of the game tree. 

For this subset of profiles, the dominance threshold of any simultaneous N-struck procedure (including alternatingM) is infinite, whereas the dominance threshold of any sequential N-struck procedure (including alternatingQ) is finite. 

Because the authors do not restrict the number of iterations, the mechanism they propose can, depending on the application, have a very high dominance threshold. 

Under complete information, there is a known advantage to being the first to challenge in the alternatingQ procedure, provided that preferences satisfy a mild regularity condition defined in DeGroot and Kadane (1980). 

the measure of strategic complexity defined below relies on the iterated elimination of strategies that are never-best responses in any subgame of an extensive game. 

RD 9. Also suppose that the parties have juror-15 That is, the probability that j is chosen given that i plays jis is 0 for all s−i.