Mutual majority criterion: Difference between revisions

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The '''Mutual majority criterion''' is a criterion for evaluating [[voting system]]s. It applies to [[ranked ballot]] elections. It can be stated as follows:

~~:''~~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.''

{{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.}}

[Merge: The mutual majority criterion says that 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.]

This is often called '''Majority criterion for solid coalitions''' or simply '''Majority criterion'''.

Systems which pass:

; Systems which pass:

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: [[Borda-Elimination]], [[Bucklin voting|Bucklin]], [[Coombs]], [[IRV]], [[Kemeny-Young]], [[Nanson (original)]], [[Raynaud|Pairwise-Elimination]], [[Ranked Pairs]], [[Schulze method|Schulze]], [[Smith//Minimax|Smith//Minmax]], [[Descending Solid Coalitions]], [[Majority Choice Approval]]

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; Systems which fail:

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[[Borda-Elimination]], [[Bucklin voting|Bucklin]], [[Coombs]], [[IRV]], [[Kemeny-Young]], [[Nanson (original)]], [[Raynaud|Pairwise-Elimination]], [[Ranked Pairs]], [[Schulze method|Schulze]], [[Smith//Minimax|Smith//Minmax]], [[Descending Solid Coalitions]], [[Majority Choice Approval]]

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: [[Black]], [[Borda]], [[Dodgson]], [[Minmax]], [[Sum of Defeats]]

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Systems which fail:

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[[Black]], [[Borda]], [[Dodgson]], [[Minmax]], [[Sum of Defeats]]

[[Category:Voting system criteria]]