Extending the Condorcet Jury Theorem to a general dependent jury |
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Authors: | Bezalel Peleg Shmuel Zamir |
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Institution: | 1. Center for the Study of Rationality, The Hebrew University of Jerusalem, Jerusalem, Israel
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Abstract: | We investigate necessary and sufficient conditions for the existence of Bayesian-Nash equilibria that satisfy the Condorcet Jury Theorem (CJT). In the Bayesian game G n 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??, ?? i (that is, a strategy that is independent of the size n ?? i of the jury), such that ?? = (?? 1, ?? 2, . . . , ?? n . . .) satisfies the CJT, then by McLennan (Am Political Sci Rev 92:413?C419, 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?=?(X 1, X 2, . . . , X n , . . .) 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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