Mutual majority criterion: Difference between revisions

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The mutual majority criterion is implied by the [[Smith criterion]].

Example for candidates A, B, C, D and E (scores are shown for each candidate, with the implicit ranked preferences in parentheses, and the unscored candidates assumed to be ranked last):<blockquote>17 A:10 B:9 C:8 (A>B>C >D=E)

17 B:10 C:9 A:8 (B>C>A >D=E)

18 C:10 A:9 B:8 (C>A>B >D=E)

49 D:10 E:10 (D>E >A=B=C)</blockquote>A, B, and C are preferred by a mutual majority, because a group of 52 voters (out of 100), an absolute majority, scored all of them higher than (preferred them over) all other candidates (D and E).

; Systems which pass

: [[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]], any [[:Category:Smith-efficient Condorcet methods|Smith-efficient Condorcet method]], [[:Category:Condorcet-IRV hybrid methods|Condorcet-IRV hybrid methods]]

:[[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]], any [[:Category:Smith-efficient Condorcet methods|Smith-efficient Condorcet method]], most [[:Category:Condorcet-IRV hybrid methods|Condorcet-IRV hybrid methods]]

; Systems which fail

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

: most [[Cardinal voting|rated methods]] (such as [[Approval voting]], [[Score|Score voting]], and [[STAR|STAR voting]]), [[Black]], [[Borda]], [[Dodgson]], [[Minmax]], [[Sum of Defeats]]

== Alternative Definitions ==