May's theorem

May's theorem states that, for choosing between two alternatives, simple majority rule is the unique voting method satisfying anonymity, neutrality, and positive responsiveness.

Simple majority rule: A voting rule that selects the alternative receiving more votes, with a tie when the totals are equal. This is the rule May's theorem characterizes uniquely.
Pairwise majority rule: A comparison rule that selects the option preferred by more voters in each pairwise contest. With two alternatives, this is the majority rule characterized by May's theorem.
Arrow's impossibility theorem: A theorem showing that no ranked voting system with at least three alternatives satisfies a specified set of fairness conditions. May's positive result depends on having only two alternatives.
Kenneth May: A Canadian-American economist and political scientist known for formal work on voting theory. May published the theorem's original characterization of majority rule in 1952.
Anonymity (voting): A voting property under which permuting voters' identities does not change the outcome. May's theorem requires the outcome to depend on votes, not who casts them.
Voting profile: A collection of voters' expressed preferences over a set of alternatives. The theorem evaluates outcomes across all possible preference profiles.
Gibbard–Satterthwaite theorem: A theorem showing that every non-dictatorial, unrestricted deterministic voting rule with at least three alternatives can be manipulated strategically. It addresses strategic incentives that May's axioms do not cover.
International Economic Review: An economics journal established in 1960 and published by the University of Pennsylvania and Osaka University. May's theorem is sometimes confused with later work published in this journal; the original appeared earlier.
Neutrality (social choice): A voting property under which swapping the names of alternatives swaps the outcome correspondingly. This rules out methods that favor one of the two alternatives by name.
Vote-count vector: A vector recording how many voters support each alternative in a two-option election. Anonymity reduces the relevant information to the counts for each side.

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Condorcet paradoxCompared with: Its two-option result highlights why adding a third option changes the aggregation problem.