Majority criterion: Difference between revisions

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{{Definition| If one candidate is preferred by a majority (more than 50%) of voters, then that candidate must win}}

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The [[mutual majority criterion]], which is sometimes simply called the majority criterion, generalizes the constraint to sets of candidates.

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== Example ==

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The [[Condorcet criterion]] implies the majority criterion. ~~Practically every serious ranked voting method passes the majority criterion.~~

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<blockquote>51 A

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Example:

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51 A

25 B>C

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24 C>B</blockquote>51 voters out of 100 prefer A over all others (B and C), therefore A must win by the majority criterion.

24 C>B

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== Complying methods ==

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51 voters out of 100 prefer A over all others (B and C), therefore A must win by the majority criterion.

Practically every serious ranked voting method passes the majority criterion, with the notable exception of [[Borda]].

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== Weaker forms of the criterion ==

== Related forms of the criterion ==

=== Stronger forms ===

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The [[mutual majority criterion]], which is sometimes simply called the majority criterion, generalizes the constraint to sets of candidates.

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The [[Condorcet criterion]] implies the majority criterion.

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=== Weaker forms of the criterion ===

Some voting methods (most [[rated voting]] methods) pass a weaker form of the majority criterion, which only requires that a majority be able to force their 1st choice to win by coordinating and voting strategically. Note that it is not always the case that the majority will have the ability to safely vote strategically I.e. if they're unsure as to whether there is or who their collective 1st choice is.

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=== Majority criterion for rated ballots ===

==== Majority criterion for rated ballots ====

There are some Cardinal systems which are designed to fulfil Majoritarianism not Utilitarianism. The majority criterion for rated ballots is a weaker, separate criterion which says that a candidate given a perfect (maximal) rating by a majority of voters must win if no other candidate received a perfect rating from that majority.

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49 B:5</blockquote>If the highest score is a 5, then the majority criterion for rated ballots allows either A or B to win. This is in contrast to the regular majority criterion, which requires A to win. Arguably, the majority criterion for rated ballots is more appropriate in the context of rated ballots, since a voter who doesn't give their 1st choice a perfect score is essentially choosing not to use all of their voting power, and thus their preference need not be (or even perhaps, shouldn't) be maximally respected or enforced.

== Notes ==

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For both the majority and [[mutual majority criterion]], the size of the majority may either be an absolute majority of all voters, or an absolute majority of voters who have any preference between the candidates, depending on how it's defined. For example:

== Notes ==

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For both the majority and [[~~Mutual majority criterion|~~mutual majority criterion]], the size of the majority may either be an absolute majority of all voters, or an absolute majority of voters who have any preference between the candidates, depending on how it's defined. For example:

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The very minimum a voting method must do in order to be considered "majoritarian" is to pass the majority criterion for at least the two-candidate case.

=== Independence of irrelevant alternatives ===

The majority criterion implies failure of the [[Independence of irrelevant alternatives]] criterion; see [[Condorcet's paradox]] for an example.

[[Category:Voting theory]]