The (sub-)optimality of the majority rule

Schmitz, Patrick W. and Tröger, Thomas (2011): The (sub-)optimality of the majority rule.

Abstract

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 agents' ex-ante expected utilities among all anonymous and dominant-strategy implementable choice rules. But in some environments where the agents' 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.

• Item Type: MPRA Paper
• Language: English
• Keywords: majority rule
• Subjects: D - Microeconomics > D7 - Analysis of Collective Decision-Making > D72 - Political Processes: Rent-Seeking, Lobbying, Elections, Legislatures, and Voting Behavior

References

Badger, W.W. (1972), "Political Individualism, Positional Preferences, and Optimal Decision-Rules" in Probability Models of Collective Choice Making, edited by R.G. Niemi and H.F. Weisberg, Merrill Publishing, Columbus, Ohio.

Barbera, S. (1979), "Majority and Positional Voting in a Probabilistic Framework", Review of Economic Studies 46, 379-389.

Barbera, S., and M.O. Jackson (2004), "Choosing How to Choose: Self-Stable Majority Rules and Constitution", The Quarterly Journal of Economics 119, 1011-1048.

Barbera, S., and M.O. Jackson (2006), "On the Weights of Nations: Assigning Voting Weights in a Heterogeneous Union," Journal of Political Economy 114, 317-339.

Bergemann, D., and S. Morris (2005), "Robust Mechanism Design," Econometrica 73, 1771-1813.

Borgers, T. (2004), "Costly Voting," American Economic Review 94, 57-66.

Borgers, T., and P. Postl (2009), "Efficient Compromising," Journal of Economic Theory 144, 2057-2076.

Buchanan, J.M. and Tullock, G. (1962), The Calculus of Consent, Ann Arbor: University of Michigan Press.

Casella, A. (2005), "Storable Votes," Games and Economic Behavior 51, 391-419.

Chung, K.-S. and J. Ely (2007), "Foundations of Dominant Strategy Mechanisms," Review of Economic Studies 74, 447-476.

Curtis, R.B. (1972), "Decision Rules and Collective Values in Constitutional Choice," in Probability Models of Collective Choice Making, edited by R.G. Niemi and H.F. Weisberg, Merrill Publishing, Columbus, Ohio.

Fishburn, P.C. (1970), Utility Theory for Decision Making, John Wiley, New York.

Gibbard, A. (1977), "Manipulation of Schemes that Mix Voting with Chance," Econometrica 45, 665-681.

Harsanyi, J. (1955), "Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparisons of Utility," Journal of Political Economy 63, 309-321.

Holmstrom, B., and R. Myerson (1983), "Efficient and Durable Decision Rules with Incomplete Information," Econometrica 51, 1799-1819.

Jackson, M. and H. Sonnenschein (2007), "Overcoming Incentive Constraints by Linking Decisions," Econometrica 75, 241-258.

Ledyard, J. (1978), "Incentive Compatibility and Incomplete Information," Journal of Economic Theory 18, 171-189.

Karni, E. (1985), Decision Making under Uncertainty: The Case of State-Dependent Preferences, Harvard University Press.

Krasa, S., and M. Polborn (2009), "Is Mandatory Voting Better than Voluntary Voting?," Games and Economic Behavior 66, 275-291.

May, K. (1952), "A set of independent necessary and sufficient conditions for simple majority rule," Econometrica 20, 680-684.

Messner, M. and M. Polborn (2004), "Voting on Majority Rules," Review of Economic Studies 71, 115-132.

Milgrom, P., and R.Weber (1982), "A Theory of Auctions and Competitive Bidding," Econometrica 50, 1089-1122.

Rae, D. (1969), "Decision Rules and Individual Values in Constitutional Choice," American Political Science Review 63, 40-56.

Schoeld, N.J. (1972), "Ethical Decision Rules for Uncertain Voters," British Journal of Political Science 2, 193-207.

Taylor, M. (1969), "Proof of a Theorem on Majority Rule," Behavioral Science 14, 228-31.