Mutual majority criterion: Difference between revisions
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It can be stated as follows:{{definition|If there is a majority of voters for which it is true that they all rank a set of candidates above all others, then one of these candidates must win.}} |
It can be stated as follows:{{definition|If there is a majority of voters for which it is true that they all rank a set of candidates above all others, then one of these candidates must win.}} |
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A generalized form that also encompasses [[Rated voting|rated voting]] methods: <blockquote>If a majority of voters unanimously vote a given set of candidates above a given rating or ranking, and all other candidates below that rating or ranking, then the winner must be from that set.</blockquote> |
A generalized form that also encompasses [[Rated voting|rated voting]] methods: <blockquote>If a majority of voters unanimously vote a given set of candidates above a given rating or ranking, and all other candidates below that rating or ranking, then the winner must be from that set.</blockquote>Note that the logical implication of the mutual majority criterion is that a candidate from the '''smallest''' set of candidates preferred by the same absolute majority of voters over all others must win; this is because if, for example, 51 voters prefer A over B, and B over C, with the other 49 voters preferring C, then not only is (A, B) a set of candidates preferred by an absolute majority over all others (C), but candidate A is also a candidate preferred by an absolute majority over all others (B and C), and therefore A must win in order to satisfy the criterion. |
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It is sometimes simply (and confusingly) called the '''Majority criterion.''' |
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== Notes == |
== Notes == |
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