Mutual majority criterion

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The mutual majority criterion is a criterion used to compare voting systems. It is also known as the majority criterion for solid coalitions and the generalized majority criterion.

The criterion states: If there is a subset S of the candidates such that more than half of the voters strictly prefer every member of S to every candidate outside of S, and this majority votes sincerely, then the winner must come from S.

This is similar to but more strict than the majority criterion, where the requirement applies only to the case that S contains a single candidate.

Methods that pass: The Schulze method, ranked pairs, instant-runoff voting, Nanson's method, Bucklin voting.

Methods that fail: plurality, approval voting, range voting, the Borda count, minimax.