The (sub-)optimality of the majority rule

We consider collective choice from two alternatives. Ex-ante, each agent is uncertain about which alternative she prefers, and may be uncertain about the intensity of her preferences. An environment is given by a probability distribution over utility vectors that is symmetric across agents and neutral across alternatives. In many environments, the majority voting rule maximizes agentsʼ ex-ante expected utilities among all anonymous and dominant-strategy implementable choice rules. But in some environments where the agentsʼ utilities are stochastically correlated, other dominant-strategy choice rules are better for all agents. If utilities are stochastically independent across agents, majority voting is ex-ante optimal among all anonymous and incentive-compatible rules. We also compare rules from an interim-viewpoint. ► We consider collective choice with two alternatives. ► The standard majority rule often maximizes agentsʼ ex-ante expected utility. ► A weak majority rule takes each alternative with probability 1/2 if neither alternative has enough support. ► If the agentsʼ utilities are stochastically correlated, a weak majority rule may perform better than the majority rule. ► We also compare rules from an interim-viewpoint.