Manipulated Electorates and Information Aggregation

We study the aggregation of dispersed information in elections in which turnout may depend on the state. State-dependent turnout may arise from the actions of a biased and informed "election organizer." Voters are symmetric ex ante and prefer policy a in state α and policy b in state β, but the organizer prefers policy a regardless of the state. Each recruited voter observes a private signal about the unknown state but does not learn the turnout. First, we characterize how the outcomes of large elections depend on the turnout pattern across states. In contrast to existing results for large elections, there are equilibria in which information aggregation fails whenever there is an asymmetry in turnout; information aggregation is only guaranteed in all equilibria if turnout is state independent. Second, when the turnout is the result of costly voter recruitment by a biased organizer, the organizer can ensure that its favorite policy a is implemented with high probability independent of the state as the voter recruitment cost vanishes. Moreover, information aggregation will fail in all equilibria. The critical observation is that a vote is more likely to be pivotal for the decision if turnout is smaller, leading to a systematic bias of the decision toward the low-turnout state.