Consequences of the Condorcet Jury Theorem for Beneficial Information Aggregation by Rational Agents

The Condorcet Jury Theorem pertains to elections in which the agents have common preferences but diverse information. We show that, whenever "sincere" voting leads to the conclusions of the Theorem-decisions superior to those that would be made by any individual based on private information, and asymptotically correct decisions as the population becomes large--there are also Nash equilibria with these properties, and in symmetric environments the equilibria may be taken to be symmetric. These conclusions follow from a simple property of common interest games: a mixed strategy profile of a (symmetric) common interest game that is optimal in the set of (symmetric) mixed strategy profiles is a Nash equilibrium