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A Bayesian Model of Voting in Juries

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  • Duggan, John
  • Martinelli, Cesar

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.
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Suggested Citation

  • Duggan, John & Martinelli, Cesar, 2001. "A Bayesian Model of Voting in Juries," Games and Economic Behavior, Elsevier, vol. 37(2), pages 259-294, November.
  • Handle: RePEc:eee:gamebe:v:37:y:2001:i:2:p:259-294
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    References listed on IDEAS

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    1. Timothy Feddersen & Wolfgang Pesendorfer, 1997. "Voting Behavior and Information Aggregation in Elections with Private Information," Econometrica, Econometric Society, vol. 65(5), pages 1029-1058, September.
    2. repec:cup:apsrev:v:82:y:1988:i:02:p:567-576_08 is not listed on IDEAS
    3. Feddersen, Timothy J & Pesendorfer, Wolfgang, 1996. "The Swing Voter's Curse," American Economic Review, American Economic Association, vol. 86(3), pages 408-424, June.
    4. repec:cup:apsrev:v:94:y:2000:i:02:p:395-406_22 is not listed on IDEAS
    5. Myerson, Roger B., 1998. "Extended Poisson Games and the Condorcet Jury Theorem," Games and Economic Behavior, Elsevier, vol. 25(1), pages 111-131, October.
    6. Hao Li & Sherwin Rosen & Wing Suen, 2001. "Conflicts and Common Interests in Committees," American Economic Review, American Economic Association, vol. 91(5), pages 1478-1497, December.
    7. repec:cup:apsrev:v:90:y:1996:i:01:p:34-45_20 is not listed on IDEAS
    8. Duggan, John & Martinelli, Cesar, 2001. "A Bayesian Model of Voting in Juries," Games and Economic Behavior, Elsevier, vol. 37(2), pages 259-294, November.
    9. repec:cup:apsrev:v:82:y:1988:i:04:p:1231-1244_19 is not listed on IDEAS
    10. Wit, Jorgen, 1998. "Rational Choice and the Condorcet Jury Theorem," Games and Economic Behavior, Elsevier, vol. 22(2), pages 364-376, February.
    11. 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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