Mutual majority criterion: Difference between revisions
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== Notes ==
The smallest mutual majority set can be found by looking for the [[Smith set]], and then checking with the original ballots whether there are enough voters who helped all of the candidates in the Smith set pairwise beat candidates not in the Smith set to constitute an absolute majority. If there aren't, there is no mutual majority set. If there are, then all candidates in the Smith set constitute a subset of the mutual majority set; proceed to ignore all voters except for those in this majority, and now check for the smallest group of candidates who have at least an absolute majority of voters preferring them above all others not in the group.
Voting methods which pass the majority criterion but not the mutual majority criterion (some ranked methods fall under this category, notably [[FPTP]]) possess a spoiler effect, since if all but one candidate in the mutual majority drops out, the remaining candidate in the mutual majority is guaranteed to win, whereas if nobody had dropped out, a candidate not in the mutual majority might have won. ▼
▲Voting methods which pass the majority criterion but not the mutual majority criterion (some ranked methods fall under this category, notably [[FPTP]]) possess a spoiler effect, since if all but one candidate in the mutual majority drops out, the remaining candidate in the mutual majority is guaranteed to win, whereas if nobody had dropped out, a candidate not in the mutual majority might have won. This is also why [[:Category:Sequential loser-elimination methods|Sequential loser-elimination methods]] whose base methods pass the majority criterion pass the mutual majority criterion.
The mutual majority criterion doesn't apply to situations where there are large "sides" if enough voters are indifferent to the large sides. Example: <blockquote>51 A>C
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