# Bounded Rationality and the Choice of Jury Selection Procedures

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## 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.
- 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.

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##### Citations

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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....

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1 citations

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##### References

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)....

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

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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…...

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312 citations

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....

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

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...…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)....

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189 citations

##### Related Papers (5)

##### Frequently Asked Questions (9)

###### Q2. How many jurors are left unchallenged when the procedure terminates?

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

###### Q3. What is the common use of jury consultants?

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.

###### Q4. What is the dominance threshold for a sequential N-struck 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.

###### Q5. What is the dominance threshold of a sequential N-struck procedure?

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.

###### Q6. Why does the author limit the number of iterations?

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.

###### Q7. What is the advantage of being the first to challenge in the alternating Q procedure?

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).

###### Q8. What is the definition of the measure of strategic complexity?

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.

###### Q9. What is the probability that j is chosen given that i plays jis?

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.