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.
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[change | change source]
- "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).
- "Collective Decisions and Voting: The Potential for Public Choice".
Note that mutual majority consistency implies majority consistency.
- "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.