Informative voting and condorcet jury theorems with a continuum of types

Abstract

We consider a model of information aggregation in which there are two possible states of the world and agents receive private signals from the set of probability measures over the binary state space – the unit interval. For a reasonably general set of signal densities, a unique symmetric Bayesian Nash equilibrium in responsive strategies exists and voting is informative in this equilibrium. Asymptotic analysis shows that society makes the correct decision almost surely as population size grows. In contrast to findings of Feddersen and Pesendorfer (1998) in the finite signal space case and Duggan and Martinelli (1999) in an alternative model in which the signal space is a continuum, this result holds for unanimity rule. The key to the efficiency of unanimity rule is that there are perfectly informative (or at least nearly perfectly informative) signals. A corollary to the asymptotic efficiency result is that for all rules the collective performs better than a single agent's dictatorship for large but finite populations. This need not be true for arbitrary population sizes.