Majority criterion: Difference between revisions
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The [[Condorcet criterion]] implies the majority criterion. Practically every serious ranked voting method passes the majority criterion. Most [[Cardinal voting|rated voting]] methods fail the majority criterion, such as [[Approval voting|Approval]], [[Score]], and [[STAR voting]], though this is argued to be a good thing in situations where those methods elect a candidate who is well-liked by all voters rather than a candidate who is narrowly preferred by a majority but loathed by the minority.
Example:<blockquote>51 A
25 B>C
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. ▼
▲51 voters prefer A over all others (B and C), therefore A must win by the majority criterion.
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with the likely most general interpretation of "vote ahead of" being "ranked or rated higher than".
=== The majority criterion for rated ballots ===
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.
The difference between the two versions can be seen with this example: <blockquote>51 A:1
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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