May's theorem
Social Choice theory on voting
In social choice theory, May's theorem, also called the general possibility theorem, says that majority vote is the unique ranked social choice function between two candidates that satisfies the following criteria:
Anonymity: the decision rule treats each voter identically (one vote, one value). Who casts a vote makes no difference; the voter's identity need not be disclosed.
Neutrality: the decision rule treats each alternative or candidate equally (a free and fair election).
Decisiveness: if the vote is tied, adding a single voter (who expresses an opinion) will break the tie.
Positive response: If a voter changes a preference, MR never switches the outcome against that voter. If the outcome the voter now prefers would have won, it still does so.
Ordinality: the decision rule relies only on which of two outcomes a voter prefers, not how much.
This can be replaced by strategyproofness, i.e. every person's dominant strategy is to honestly disclose their preferences.
The theorem was first published by Kenneth May in 1952.[1]
Various modifications have been suggested by others since the original publication.
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