Mutual majority criterion: Difference between revisions
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10 C(>A=B) </blockquote>The last line "10 C(>A=B)" should be read as "these 10 voters prefer C as their 1st choice and are indifferent between A and B."
Even though candidate A is preferred by the (same) majority of voters in [[Pairwise counting|pairwise matchups]] against B (51 vs. 49) and C (51 vs. 10), candidate A technically is not preferred by an absolute majority (i.e. over half of all voters), and C would beat A in some mutual majority-passing methods, such as [[Bucklin]]. A "mutual plurality" criterion might make sense for these types of situations where a [[plurality]] of voters prefer a set of candidates above all others, and everyone in that set [[Pairwise counting|pairwise beats]] everyone outside of the set; this mutual plurality criterion implies the mutual majority criterion (because a majority is a plurality, and anyone who is preferred by an absolute majority over another candidate is guaranteed to pairwise beat that candidate, thus all candidates in the mutual majority set pairwise beat all other candidates). The [[Smith criterion]] implies this mutual plurality criterion (because the Smith criterion implies that someone from the smallest set of candidates that can pairwise beat all others must win, and this smallest set must be a subset of any set of candidates
1 E>A>B
1 F>A>B
2 B
1 G>C>B
1 H>C>B
1 I>C>B</blockquote>B is ranked above all other candidates by 2 voters, which is more voters than any other set of candidates (in this case, the singletons (D), (E), (F), (G), (H) and (I)), yet after a few eliminations this reduces to<blockquote>3 A>B
2 B
3 C>B</blockquote>and B is eliminated first, despite pairwise dominating everyone else (i.e. being the [[Condorcet winner]]). This is an example of the [[Center squeeze]] effect.
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. Example: <blockquote>26 A>B
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