The (sub-)optimality of the majority rule

• Published in: Games and economic behavior Vol. 74; no. 2; pp. 651 - 665
• Main Authors: Schmitz, Patrick W., Tröger, Thomas
• Format: Journal Article
• Language: English
• Published: Duluth Elsevier Inc 01.03.2012; Academic Press
• Subjects: Collective behaviour; Correlated values; Correlation; Decision theory; Game theory; Majority rule; Mechanism design; Principal-agent theory; Probability; Stochastic processes; Studies; Utilitarianism; Utility functions; Utility theory; Voting; Voting behaviour; Majority rule; Mechanism design; D72; Utilitarianism; D82; Correlated values
• ISSN: 0899-8256; 1090-2473
• DOI: 10.1016/j.geb.2011.08.002

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.