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

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  • Bezalel Peleg
  • Shmuel Zamir

Abstract

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.

Suggested Citation

  • Bezalel Peleg & Shmuel Zamir, 2009. "On Bayesian-Nash Equilibria Satisfying the Condorcet Jury Theorem: The Dependent Case," Discussion Paper Series dp527, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
  • Handle: RePEc:huj:dispap:dp527
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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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    References listed on IDEAS

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    3. 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.
    4. Jean-François Laslier & Jörgen Weibull, 2008. "Committee decisions: Optimality and Equilibrium," Working Papers halshs-00121741, HAL.
    5. Duggan, John & Martinelli, Cesar, 2001. "A Bayesian Model of Voting in Juries," Games and Economic Behavior, Elsevier, vol. 37(2), pages 259-294, November.
    6. Roger B. Myerson, 1998. "Population uncertainty and Poisson games," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(3), pages 375-392.
    7. 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.
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    9. Wit, Jorgen, 1998. "Rational Choice and the Condorcet Jury Theorem," Games and Economic Behavior, Elsevier, vol. 22(2), pages 364-376, February.
    10. Daniel Berend & Luba Sapir, 2007. "Monotonicity in Condorcet’s Jury Theorem with dependent voters," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 28(3), pages 507-528, April.
    11. Daniel Berend & Jacob Paroush, 1998. "When is Condorcet's Jury Theorem valid?," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 15(4), pages 481-488.
    12. Berg, Sven, 1993. "Condorcet's jury theorem revisited," European Journal of Political Economy, Elsevier, vol. 9(3), pages 437-446, August.
    13. 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 289-297, June.
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