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Optimal Challenges for Selection

Author

Listed:
  • Morris H. Degroot

    (Carnegie-Mellon University, Pittsburgh, Pennsylvania)

  • Joseph B. Kadane

    (Carnegie-Mellon University, Pittsburgh, Pennsylvania)

Abstract

This paper generalizes the problems of optimal selection considered by Roth, Kadane and DeGroot by allowing a set of J items to be chosen by two decision makers, the first of whom has A challenges and the second has B challenges. The two decision makers each have an opportunity to challenge each item before it is accepted, in some arbitrary fixed order. We assume that the decision makers know the utility function of the other side as well as their own over sets of J items, and that they know the subjective distribution, assigned by the other side, of characteristics of potential items that will be observed, as well as their own. Under these conditions the other side's response to each potential item can be predicted with certainty, and backward induction defines an optimal strategy. We study an important special case we call regular, and show that it is never disadvantageous to go first in the regular case. The use of peremptory challenges in jury trials motivates our model. The basic model in which jurors are challenged one at a time is extended to a more general class of problems that includes the group system and the struck jury system.

Suggested Citation

  • Morris H. Degroot & Joseph B. Kadane, 1980. "Optimal Challenges for Selection," Operations Research, INFORMS, vol. 28(4), pages 952-968, August.
    • Handle: RePEc:inm:oropre:v:28:y:1980:i:4:p:952-968
    DOI: 10.1287/opre.28.4.952
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    Cited by:

    1. 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.
    2. Alpern, Steve & Gal, Shmuel & Solan, Eilon, 2010. "A sequential selection game with vetoes," Games and Economic Behavior, Elsevier, vol. 68(1), pages 1-14, January.
    3. 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.
    4. Steve Alpern & Bo Chen, 2017. "Who should cast the casting vote? Using sequential voting to amalgamate information," Theory and Decision, Springer, vol. 83(2), pages 259-282, August.
    5. 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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