Mutual majority criterion

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 says that if a majority of voters like a group of candidates more than all of the other candidates, then one of the candidates in the group must win. This is similar to but but more broad than the majority criterion, where the group of candidates can only have one candidate in it. The Droop proportionality criterion is a more broad form of the mutual majority criterion, which also applies to multi-winner elections.
The Schulze method, ranked pairs, instant-runoff voting, Nanson's method, and Bucklin voting pass this criterion. All Smith-efficient Condorcet methods pass the mutual majority criterion.
The plurality vote, approval voting, range voting, the Borda count, and minimax fail this criterion.
Voting methods which pass the majority criterion but fail mutual majority can have a spoiler effect, since if a minority-preferred candidate wins, and all of the candidates preferred by the majority, except for one, leave the election, then the remaining majority-preferred candidate will win instead.