Condorcet criterion
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The Condorcet candidate or Condorcet winner of an election is the candidate who, when compared in turn with each of the other candidates, is preferred over the other candidate. Mainly because of Condorcet's voting paradox, a Condorcet winner will not always exist in a given set of votes.
The Condorcet criterion for a voting system is that it chooses the Condorcet winner when one exists. Any method conforming to the Condorcet criterion is known as a Condorcet method.
It is named after the 18th century mathematician and philosopher Marie Jean Antoine Nicolas Caritat, the Marquis de Condorcet.
[edit] Complying methods
Black, Copeland, Kemeny-Young, minimax, Nanson's method, Smith/minimax, ranked pairs and Schulze comply with the Condorcet criterion.
Approval voting, Range voting, Borda count, plurality voting, and instant-runoff voting do not.
[edit] Commentary
Non-ranking methods such as plurality and approval cannot comply with the Condorcet criterion because they do not allow each voter to fully specify their preferences.
Instant-runoff voting is an example of a method which allows each voter to rank all the candidates, but does not comply with the Condorcet criterion. Consider, for example, the following vote count of preferences with three candidates {A,B,C}:
499: A>B>C 498: C>B>A 3: B>C>A
In this case, B is preferred to A by 501 votes to 499, and B is preferred to C by 502 to 498, hence B is preferred to both A and C. B must then win according to the Condorcet criterion. Using the rules of IRV, B is ranked first by the fewest voters and is eliminated, and then C wins with the transferred votes from B.
