Mutual majority criterion: Difference between revisions
Copy over definition from the Woodall's method article, and attribute confusing usage of the term "Majority" to Woodall (with reference)
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(Copy over definition from the Woodall's method article, and attribute confusing usage of the term "Majority" to Woodall (with reference)) |
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== Alternative Definitions ==
It can be stated as follows:
It can be stated as follows:{{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.}}▼
{{definition|A mutual majority (MM) is a set of voters comprising a majority of the voters, who all prefer some same set of candidates to all of the other candidates. That set of candidates is their MM-preferred set.
A generalized form that also encompasses [[Rated voting|rated voting]] methods: <blockquote>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.</blockquote>Note that the logical implication of the mutual majority criterion is that a candidate from the '''smallest''' set of candidates preferred by the same absolute majority of voters over all others must win; this is because if, for example, 51 voters prefer A over B, and B over C, with the other 49 voters preferring C, then not only is (A, B) a set of candidates preferred by an absolute majority over all others (C), but candidate A is also a candidate preferred by an absolute majority over all others (B and C), and therefore A must win in order to satisfy the criterion.▼
If a MM vote sincerely, then the winner should come from their MM-preferred set.
A voter votes sincerely if s/he doesn't vote an unfelt preference, or fail to vote a felt preference that the balloting system in use would have allowed hir to vote in addition to the preferences that she actually does vote.
To vote an unfelt preference is to vote X over Y if you prefer X to Y.
To vote an unfelt preference is to vote X over Y if you don't prefer X to Y.}}
or more simply,
▲
A generalized form that also encompasses [[Rated voting|rated voting]] methods: {{definition|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.}}
▲
It is sometimes simply (and confusingly) called the '''Majority criterion.''' This usage is due to Woodall.<ref name="Woodall 1994 Properties">{{cite journal | last=Woodall |first=D. |title=Properties of preferential election rules | journal=Voting matters | issue=3 | pages=8–15 | year=1994 | url=http://www.votingmatters.org.uk/ISSUE3/P5.HTM}}</ref>
== Notes ==
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49 C</blockquote>Despite B being preferred by an absolute majority over C, and the only candidate preferred by any voters in that absolute majority over or equally to B being A (with no voters in the majority preferring anyone over A), the mutual majority criterion doesn't guarantee that either A or B must win. It has been argued that to avoid the [[Chicken dilemma]], C must win here (and C would win in some mutual majority-passing methods, such as [[IRV]], which is often claimed to resist the chicken dilemma), but methods that do so have a spoiler effect, since if A drops out, B must win by the majority (and thus mutual majority) criterion. All major [[:Category:Defeat-dropping Condorcet methods|defeat-dropping Condorcet methods]] elect B here, since they have the weakest pairwise defeat.
By analogy to the majority criterion for
==References==
<references />
[[Category:Voting system criteria]]
[[Category:Majority-related concepts]]
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