Information Aggregation in Poisson-Elections

The modern Condorcet jury theorem states that under weak conditions, when voters have common interests, then elections will aggregate information when the population is large, in any responsive and symmetric equilibrium. Here, we study the performance of large elections with population uncertainty. We find that the modern Condorcet jury theorem holds if and only if the expected number of voters is independent of the state. If the expected number of voters depends on the state, then additional equilibria exist in which information is not aggregated. The main driving force is that, everything else equal, voters are more likely to be pivotal if the population is small. We provide conditions under which the additional equilibria are stable. We show that the Condorcet jury theorem also fails if abstention is allowed or if there is aggregate uncertainty due to the presence of noise voters. The presence of noise voters simplifies the analysis.