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

Bezalel Peleg and Shmuel Zamir ()

Discussion Paper Series from The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem

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.

Pages: 30 pages
Date: 2009-12
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Published in Social Choice and Welfare, 39 (2012) 91-125 as "Extending the Condorcet Jury Theorem to a generalized jury".

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