Mutual majority criterion: Difference between revisions
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; 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]] |
: [[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]] |
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; Systems which fail: |
; Systems which fail: |
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: [[Black]], [[Borda]], [[Dodgson]], [[Minmax]], [[Sum of Defeats]] |
: [[Black]], [[Borda]], [[Dodgson]], [[Minmax]], [[Sum of Defeats]] |
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== Notes == |
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The mutual majority criterion doesn't apply to situations where there are two largest "sides" if enough voters are indifferent to the two sides. <blockquote>51 A>C |
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49 B |
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10 C</blockquote>Even though A and B are the two candidates with the most dedicated support, with A [[Pairwise counting#Terminology|pairwise beating]] B and C, A technically is not preferred by a majority, and C would beat A in some mutual majority-passing methods, such as [[Bucklin]]. [[Smith criterion|Smith-efficiency]] implies both the mutual majority criterion and the election of one of the largest side's candidates (A) in these types of scenarios. |
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Likewise, if there are some losing candidates ranked above the mutual majority set of candidates by some voters in the majority, this voids the criterion guarantee. <blockquote>26 A>B |
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25 B |
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49 C</blockquote>It has been argued that to avoid the Chicken dilemma, C must win here. But methods that do so create a spoiler effect, since if A drops out, B must win by the mutual majority criterion. |
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[[Category:Voting system criteria]] |
[[Category:Voting system criteria]] |