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Optimal Peremptory Challenges in Trials by Juries: A Bilateral Sequential Process

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  • Arthur Roth
  • Joseph B. Kadane
  • Morris H. Degroot

Abstract

This paper explores optimal strategies for the use of peremptory challenges in jury trials where the prospective jurors are examined and then either challenged or seated, one by one. We assume that the lawyers for each side do not necessarily agree about the probability that each prospective juror will vote for conviction, but that the assessment of each side is available to the other. The strategies we develop are optimal noncooperative sequential strategies in the sense that each side maximizes its expected utility at each stage under the assumption that both sides will continue to use these optimal strategies in all future decisions. Under certain regularity conditions we show that it is optimal to be the first side to decide whether to challenge any prospective juror. Necessary and sufficient conditions are given for an optimal strategy to be reversible, which means that it does not matter to either side whether it decides first or second. Specifically, the optimal strategy is reversible if the two sides always agree about the probability that each prospective juror will vote for conviction. We give an algorithm based on backward induction for finding the optimal strategies and discuss simple examples.

Suggested Citation

  • Arthur Roth & Joseph B. Kadane & Morris H. Degroot, 1977. "Optimal Peremptory Challenges in Trials by Juries: A Bilateral Sequential Process," Operations Research, INFORMS, vol. 25(6), pages 901-919, December.
    • Handle: RePEc:inm:oropre:v:25:y:1977:i:6:p:901-919
    DOI: 10.1287/opre.25.6.901
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    Cited by:

    1. Joseph Kadane & Christopher Stone & Garrick Wallstrom, 1999. "The Donation Paradox for Peremptory Challenges," Theory and Decision, Springer, vol. 47(2), pages 139-155, October.
    2. Bloom, David E & Cavanagh, Christopher L, 1986. "An Analysis of the Selection of Arbitrators," American Economic Review, American Economic Association, vol. 76(3), pages 408-422, June.
    3. Steven J. Brams & Todd R. Kaplan, 2004. "Dividing the Indivisible," Journal of Theoretical Politics, , vol. 16(2), pages 143-173, April.
    4. Steve Alpern & Shmuel Gal, 2009. "Analysis and design of selection committees: a game theoretic secretary problem," International Journal of Game Theory, Springer;Game Theory Society, vol. 38(3), pages 377-394, November.
    5. Lehmann, Jee-Yeon & Smith, Jeremy, 2011. "Attorney empowerment in Voir Dire and the racial composition of juries," MPRA Paper 36338, University Library of Munich, Germany.
    6. Alfredo Di Tillio & Marco Ottaviani & Peter Norman Sørensen, 2021. "Strategic Sample Selection," Econometrica, Econometric Society, vol. 89(2), pages 911-953, March.
    7. Francis X. Flanagan, 2015. "Peremptory Challenges and Jury Selection," Journal of Law and Economics, University of Chicago Press, vol. 58(2), pages 385-416.

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