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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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File URL: http://www.sciencedirect.com/science/article/B6WFW-458NM3G-2/2/32b3de632cc885a2badcf8cfe4affdec
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Bibliographic Info

Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 37 (2001)
Issue (Month): 2 (November)
Pages: 259-294

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Handle: RePEc:eee:gamebe:v:37:y:2001:i:2:p:259-294

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Web page: http://www.elsevier.com/locate/inca/622836

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References

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  1. Roger B. Myerson, 1994. "Extended Poisson Games and the Condorcet Jury Theorem," Discussion Papers 1103, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  2. 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.
  3. John Duggan & Cesar Martinelli, 1999. "A Bayesian Model of Voting in Juries," Working Papers 9904, Centro de Investigacion Economica, ITAM.
  4. Feddersen, Timothy J & Pesendorfer, Wolfgang, 1996. "The Swing Voter's Curse," American Economic Review, American Economic Association, vol. 86(3), pages 408-24, June.
  5. Hao Li & Sherwin Rosen & Wing Suen, 2000. "Conflicts and Common Interests in Committees," Econometric Society World Congress 2000 Contributed Papers 0341, Econometric Society.
  6. Wit, Jorgen, 1998. "Rational Choice and the Condorcet Jury Theorem," Games and Economic Behavior, Elsevier, vol. 22(2), pages 364-376, February.
  7. 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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