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A Bayesian Model of Voting in Juries

Author

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  • John Duggan

    (University of Rochester)

  • Cesar Martinelli

Abstract

We take a game-theoretic approach to the analysis of juries by modelling voting as a game of incomplete information. Rather than the usual assumption of two possible signals (one indicating guilt, the other innocence), we allow jurors to perceive a full spectrum of signals. Given any voting rule requiring a fixed fraction of votes to convict, we characterize the unique symmetric equilibrium of the game, and we consider the possibility of asymmetric equilibria: we give a condition under which no asymmetric equilibria exist and show that, without under which no asymmetric equilibria exist and show that, without it, asymmetric equilibria may exist. We offer a condition under which unanimity rule exhibits a bias toward convicting the innocent, regardless of the size of the jury, and we exhibit an example showing this bias can be reversed. And we prove a "jury theorem" for our general model: as the size of the jury increases, the probability of a mistaken judgment goes to zero for every voting rule, except unanimity rule; for unanimity rule, we give a condition under which the probability of a mistake is bounded strictly above zero, and we show that, without this condition, the probability of a mistake may go to zero.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • John Duggan & Cesar Martinelli, 1998. "A Bayesian Model of Voting in Juries," Wallis Working Papers WP14, University of Rochester - Wallis Institute of Political Economy.
  • Handle: RePEc:roc:wallis:wp18
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    File URL: http://www.wallis.rochester.edu/WallisPapers/wallis_18.pdf
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    References listed on IDEAS

    as
    1. Kyle Bagwell & Robert Staiger, 1997. "Collusion Over the Business Cycle," RAND Journal of Economics, The RAND Corporation, vol. 28(1), pages 82-106, Spring.
    2. Timothy Feddersen & Wolfgang Pesendorfer, 1997. "Voting Behavior and Information Aggregation in Elections with Private Information," Econometrica, Econometric Society, pages 1029-1058.
    3. repec:cup:apsrev:v:82:y:1988:i:02:p:567-576_08 is not listed on IDEAS
    4. Matsui Akihiko & Matsuyama Kiminori, 1995. "An Approach to Equilibrium Selection," Journal of Economic Theory, Elsevier, pages 415-434.
    5. repec:cup:apsrev:v:94:y:2000:i:02:p:395-406_22 is not listed on IDEAS
    6. Myerson, Roger B., 1998. "Extended Poisson Games and the Condorcet Jury Theorem," Games and Economic Behavior, Elsevier, vol. 25(1), pages 111-131, October.
    7. Hao Li & Sherwin Rosen & Wing Suen, 2001. "Conflicts and Common Interests in Committees," American Economic Review, American Economic Association, pages 1478-1497.
    8. Hao Li & Sherwin Rosen & Wing Suen, 2001. "Conflicts and Common Interests in Committees," American Economic Review, American Economic Association, pages 1478-1497.
    9. repec:cup:apsrev:v:90:y:1996:i:01:p:34-45_20 is not listed on IDEAS
    10. Duggan, John & Martinelli, Cesar, 2001. "A Bayesian Model of Voting in Juries," Games and Economic Behavior, Elsevier, pages 259-294.
    11. Feddersen, Timothy J & Pesendorfer, Wolfgang, 1996. "The Swing Voter's Curse," American Economic Review, American Economic Association, pages 408-424.
    12. repec:cup:apsrev:v:82:y:1988:i:04:p:1231-1244_19 is not listed on IDEAS
    13. Wit, Jorgen, 1998. "Rational Choice and the Condorcet Jury Theorem," Games and Economic Behavior, Elsevier, vol. 22(2), pages 364-376, February.
    14. Timothy Feddersen & Wolfgang Pesendorfer, 1996. "Convicting the Innocent: The Inferiority of Unanimous Jury Verdicts," Discussion Papers 1170, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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