Majority criterion

The majority criterion is a criterion for evaluating voting systems. It can be most simply thought of as "if a majority prefers a candidate as their unique 1st choice (i.e. they prefer this candidate above all other candidates), then the majority's 1st choice must win."

The mutual majority criterion, which is sometimes simply called the majority criterion, generalizes the constraint to sets of candidates.

The Condorcet criterion implies the majority criterion. Practically every serious ranked voting method passes the majority criterion. Most rated voting methods fail the majority criterion, such as Approval, Score, and STAR voting, though this is argued to be a good thing in situations where those methods elect a candidate who is well-liked by all voters rather than a candidate who is narrowly preferred by a majority but loathed by the minority.

It can be stated as follows:

If a majority of the voters vote a given candidate X ahead of everybody else, then X must win.

with the likely most general interpretation of "vote ahead of" being "ranked or rated higher than".

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