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On Bayesian-Nash Equilibria Satisfying the Condorcet Jury Theorem: The Dependent Case

  • Bezalel Peleg
  • Shmuel Zamir

We investigate sufficient conditions for the existence of Bayesian-Nash equilibria that satisfy the Condorcet Jury Theorem (CJT). In the Bayesian game Gn among n jurors, we allow for arbitrary distribution on the types of jurors. In particular, any kind of dependency is possible. If each juror i has a constant strategy, h, si (that is, a strategy that is independent of the size n.i of the jury), such that s =(s 1,s 2, . . . ,sn . . .) satisfies theCJT, then byMcLennan (1998) there exists a Bayesian-Nash equilibrium that also satisfies the CJT. We translate the CJT condition on sequences of constant strategies into the following problem: (**) For a given sequence of binary random variables X = (X1,X2, ...,Xn, ...) with joint distribution P, does the distribution P satisfy the asymptotic part of the CJT ? We provide sufficient conditions and two general (distinct) necessary conditions for (**). We give a complete solution to this problem when X is a sequence of exchangeable binary random variables.

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File URL: http://ratio.huji.ac.il/sites/default/files/publications/dp527.pdf
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File URL: http://link.springer.com/article/10.1007/s00355-011-0546-1
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Paper provided by The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem in its series Discussion Paper Series with number dp527.

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Length: 30 pages
Date of creation: Dec 2009
Date of revision:
Publication status: Published in Social Choice and Welfare, 39 (2012) 91-125 as "Extending the Condorcet Jury Theorem to a generalized jury".
Handle: RePEc:huj:dispap:dp527
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  1. John Duggan & Cesar Martinelli, 1998. "A Bayesian Model of Voting in Juries," Wallis Working Papers WP14, University of Rochester - Wallis Institute of Political Economy.
  2. Roger B. Myerson, 1994. "Population Uncertainty and Poisson Games," Discussion Papers 1102, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  3. Daniel Berend & Luba Sapir, 2007. "Monotonicity in Condorcet’s Jury Theorem with dependent voters," Social Choice and Welfare, Springer, vol. 28(3), pages 507-528, April.
  4. Jean-François Laslier & Jörgen Weibull, 2008. "Committee decisions: Optimality and Equilibrium," Working Papers halshs-00121741, HAL.
  5. Franz Dietrich & Christian List, 2002. "A Model of Jury Decisions Where All Jurors Have the Same Evidence," Economics Papers 2002-W23, Economics Group, Nuffield College, University of Oxford.
  6. 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.
  7. Wit, Jorgen, 1998. "Rational Choice and the Condorcet Jury Theorem," Games and Economic Behavior, Elsevier, vol. 22(2), pages 364-376, February.
  8. Daniel Berend & Jacob Paroush, 1998. "When is Condorcet's Jury Theorem valid?," Social Choice and Welfare, Springer, vol. 15(4), pages 481-488.
  9. Ladha, Krishna K., 1995. "Information pooling through majority-rule voting: Condorcet's jury theorem with correlated votes," Journal of Economic Behavior & Organization, Elsevier, vol. 26(3), pages 353-372, May.
  10. Nitzan, Shmuel & Paroush, Jacob, 1982. "Optimal Decision Rules in Uncertain Dichotomous Choice Situations," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 23(2), pages 289-97, June.
  11. Berg, Sven, 1993. "Condorcet's jury theorem revisited," European Journal of Political Economy, Elsevier, vol. 9(3), pages 437-446, August.
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