Condorcet method: Difference between revisions
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{{Wikipedia}}{{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):
FF>H:51, FF>C:60
H>FF:49, H>C:70
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 (due to the [[Condorcet paradox]]).▼
C>FF:40, C>H:20
If for each pair of candidates, we subtract the number of votes preferring the second candidate over the first from the number of votes preferring the first to the second, then we'll know which one won the head-to-head matchup.
(Margins)
<p style="border: 5px dotted green;">FF>H:2 (Win), FF>C:20 (Win)</p>
H>FF:-2, H>C:20 (Win)
C>FF:-20, C>H:-50
The Condorcet winner (if one exists) will be the candidate who got a majority of votes (as indicated by the positive margin) in all of their head-to-head matchups.
FF (French Fries) is the CW here.
▲|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 (due to the [[Condorcet paradox]]).
'''Condorcet''' is sometimes used to refer to the family of Condorcet methods as a whole.
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