# 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.[1] This is similar to but but more broad than the majority criterion, where the group of candidates can only have one candidate in it. [2]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.[3]

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.

## References

1. "Weak Mutual Majority Criterion for Voting Rules". A voting rule satisfies WMM if whenever some k candidates receive top k ranks from a qualified majority that consists of more than q = k/(k+1) of voters, the rule selects the winner among these k candidates. [...] [It is weaker than] the mutual majority criterion (MM, here for any k the size of majority is fixed q = 1/2).
2. "Collective Decisions and Voting: The Potential for Public Choice". Note that mutual majority consistency implies majority consistency.
3. "Four Condorcet-Hare Hybrid Methods for Single-Winner Elections". Meanwhile, they possess Smith consistency [efficiency], along with properties that are implied by this, such as [...] mutual majority.