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Condorcet method: Difference between revisions
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{{Wikipedia}}
Any election method conforming to the [[Condorcet criterion]] - that is, one which always elects the [[beats-all winner]], a candidate who can beat any other candidate in a runoff, if one exists - is known as a '''Condorcet method'''. The name comes from the 18th century mathematician and philosopher [[Marquis de Condorcet]], although the method was previously described by [[Ramon Llull]] in the 13th century. Many Condorcet advocates agree that a further criterion that Condorcet methods should pass is the [[Smith criterion]], which means the Condorcet method will always elect someone from the [[Smith set]] when there is no beats-all winner (usually due to the [[Condorcet paradox]]).▼
'''Condorcet''' is sometimes used to refer to the family of Condorcet methods as a whole.▼
==Simple explanation==▼
If one candidate is preferred by more voters than all other candidates (when [[pairwise counting|compared one-on-one]]), that candidate is the [[Condorcet Criterion|Condorcet Winner]], abbreviated as CW. This can be determined through use of ranked or rated ballots (i.e. if a voter ranks or rates one candidate higher than another). On rare occasions, there is no Condorcet winner (because of either [[pairwise counting#Terminology|ties]] in the head-to-head matchups or the [[Condorcet paradox]]). In that case it is necessary to use some "tiebreaking" or cycle resolution/completion procedure; a very common standard for a Condorcet method's tiebreaking procedure is that it should be [[Smith-efficient]], that is, always elect someone from the [[Smith set]], the smallest group of candidates that win all their [[head-to-head matchup|head-to-head matchups]] against all candidates not in the group.▼
== Example ==
{{Image frame|width=500|content=Suppose the voters had been polled on their preferences among the candidates, and the following preferences in head-to-head matchups are produced between French Fries (FF), Hamburger (H), and Cookies (C)
(FF>C shows the number of voters who prefer FF over C, for example):
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|caption=Example of finding the Condorcet winner|border=|max-width=}}
▲Any election method conforming to the [[Condorcet criterion]] - that is, one which always elects the [[beats-all winner]], a candidate who can beat any other candidate in a runoff, if one exists - is known as a '''Condorcet method'''. The name comes from the 18th century mathematician and philosopher [[Marquis de Condorcet]], although the method was previously described by [[Ramon Llull]] in the 13th century. Many Condorcet advocates agree that a further criterion that Condorcet methods should pass is the [[Smith criterion]], which means the Condorcet method will always elect someone from the [[Smith set]] when there is no beats-all winner (usually due to the [[Condorcet paradox]]).
▲'''Condorcet''' is sometimes used to refer to the family of Condorcet methods as a whole.
▲==Simple explanation==
▲If one candidate is preferred by more voters than all other candidates (when [[pairwise counting|compared one-on-one]]), that candidate is the [[Condorcet Criterion|Condorcet Winner]], abbreviated as CW. This can be determined through use of ranked or rated ballots (i.e. if a voter ranks or rates one candidate higher than another). On rare occasions, there is no Condorcet winner (because of either [[pairwise counting#Terminology|ties]] in the head-to-head matchups or the [[Condorcet paradox]]). In that case it is necessary to use some "tiebreaking" or cycle resolution/completion procedure; a very common standard for a Condorcet method's tiebreaking procedure is that it should be [[Smith-efficient]], that is, always elect someone from the [[Smith set]], the smallest group of candidates that win all their [[head-to-head matchup|head-to-head matchups]] against all candidates not in the group.
==Casting ballots==
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