Extending the Condorcet Jury Theorem to a general dependant jury
|Speaker:||Shmuel Zamir, The Hebrew University of Jerusalem|
|Date:||Friday 11 November 2011|
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". si (that is, a strategy that is independent of the size n ≥ i of the jury), such that sn = (s 1,s 2, . . . ,s n . . .) satisfies the CJT, then by LcLennan (1998) there exists a Bayesian-Nash equilibrium which also satisfies the CJT. We translate the CJT condition on the sequence 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.