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| May's theorem | |
|---|---|
| Name | May's theorem |
| Field | Social choice theory |
| Author | Kenneth May |
| Year | 1952 |
| Original publication | American Political Science Review |
| Keywords | Majority rule, anonymity, neutrality, positive responsiveness, voting theory |
May's theorem is a result in social choice theory that characterizes majority rule as the unique decision rule for two-candidate choices satisfying specific axioms. The theorem specifies conditions—anonymity, neutrality, and positive responsiveness—under which simple majority voting yields outcomes aligned with collective preferences. It has influenced debates in Condorcet studies, Arrow's impossibility theorem discussions, and the development of normative criteria for electoral systems.
May's theorem states that for binary choice problems among alternatives comparable to Yalta Conference-era winner-take-all decisions, the only collective decision procedure satisfying anonymity (treating voters like citizens in United Nations assemblies), neutrality (treating candidates as parties such as Democratic Party and Republican Party), and positive responsiveness (akin to reversal rules considered in U.S. Supreme Court voting jurisprudence) is simple majority rule. The axioms echo conditions used in analyses by scholars connected to Harvard University, Princeton University, and London School of Economics literatures. Kenneth May published the original formulation in the American Political Science Review, and contemporaneous work referenced institutional debates involving British Parliament and French National Assembly voting practices.
The theorem emerged in the mid-20th century amid a surge of formal results in collective decision-making pioneered by figures at Columbia University, University of Chicago, and Stanford University. May's work followed earlier normative inquiries such as those by Marquis de Condorcet in 18th-century pamphlets and paralleled later developments like Kenneth Arrow's 1951 impossibility result. Debates at institutions including Massachusetts Institute of Technology and University of California, Berkeley framed May's contribution alongside operational reforms in legislative bodies like the United States Congress and electoral analyses in postwar Germany and Japan.
May's proof is elementary and constructive, using combinatorial and symmetry arguments reminiscent of techniques used in analyses at Princeton University seminars. It leverages parity considerations of vote tallies, invariance principles related to anonymity—as discussed in symposia at Yale University—and neutrality conditions comparable to party-symmetry debates at Columbia University. The positive responsiveness axiom is handled via local perturbation arguments similar to methods in papers presented at American Mathematical Society meetings. The proof constructs equivalence classes of profiles under voter permutations and candidate swaps, then shows majority rule is the sole rule consistent with the axioms, mirroring approaches in classic proofs associated with Institute for Advanced Study workshops.
May's theorem provides normative support for majority rule in contexts ranging from municipal referenda in New York City to board decisions at institutions like World Bank-affiliated panels. It informs the design of two-candidate plurality elections used in democracies including United Kingdom, Canada, and Australia, and underpins justifications for tie-breaking procedures in bodies such as the European Parliament. The result interacts with Arrow's theorem by highlighting how restricting choice sets to binary alternatives avoids some impossibility constraints, thereby influencing reform proposals in commissions like those convened by United Nations General Assembly or national election commissions in India.
Concrete examples include head-to-head runoff stages in presidential contests like those once held in France and the two-candidate referendums in Switzerland. Extensions generalize May's axioms to probabilistic social choice frameworks studied at University of Oxford and University of Toronto, and to criteria for approval voting analyzed by scholars affiliated with Carnegie Mellon University and Cornell University. Further work explores analogues in committee voting modeled after procedures in NATO councils and corporate governance at International Monetary Fund-sponsored entities. Research linking May-style axioms with strategic behavior has been pursued in literature associated with Princeton University and London School of Economics.
Critics note May's narrow domain: the theorem applies only to binary choices and therefore does not resolve multidimensional contests found in elections involving parties such as Green Party or coalition bargaining seen in Weimar Republic-era politics. Debates in journals tied to Oxford University Press and conferences at RAND Corporation emphasize vulnerability to strategic manipulation and the importance of additional desiderata like monotonicity and participation—criteria featured in studies from University of Michigan and Yale University. Empirical critiques reference electoral anomalies in countries including Italy and Israel where multi-candidate dynamics render May's criteria insufficient. Nonetheless, the theorem remains a cornerstone in normative assessments of two-candidate decision mechanisms used by institutions such as Supreme Court of the United States panels and municipal election boards.