A Bayesian Model of Voting in Juries

John Duggan and Cesar Martinelli ()

No 9904, Working Papers from Centro de Investigacion Economica, ITAM

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.

Date: 1999-06
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http://ftp.itam.mx/p ... /martinelli/9904.pdf First version, 1998-11 (application/pdf)

Related works:
Working Paper: A Bayesian Model of Voting in Juries (1998)
Journal Article: A Bayesian Model of Voting in Juries (2001)
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