Nonasymptotic Condorcet and Anti-Condorcet Jury Theorems under Strategic Voting

Abstract

The nonasymptotic Condorcet jury theorem states that, under certain conditions, group decision-making by simple majority voting can decide more efficiently than single-person decision-making, in terms of having a higher probability of choosing the better alternative. Wit (1998) showed that the nonasymptotic Condorcet jury theorem holds under strategic voting in the basic model in which each member receives a binary signal. We examine the robustness of the nonasymptotic Condorcet jury theorem shown by Wit (1998) with respect to the assumptions of information structure. We show two results. The first result is that the nonasymptotic Condorcet jury theorem holds robustly in a general signal model with finite signals for binary states when the strongest signals for each state are realized with probability larger than 1/2. The second result is that the nonasymptotic Condorcet jury theorem may not hold when the strongest signal that indicates a particular state is realized with probability less than 1/2. We provide a sufficient condition for this anti-Condorcet jury theorem with respect to the prior probability and the likelihoods of signals.