Mutual majority criterion: Difference between revisions
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; 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]]
; Systems which fail:
: [[Black]], [[Borda]], [[Dodgson]], [[Minmax]], [[Sum of Defeats]]
== Notes ==
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
49 B
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.
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
25 B
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.
[[Category:Voting system criteria]]
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