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 Elections and Parties Series Democracy Representative democracy History of democracy Referenda Liberal democracy Representation Voting Voting systems Ideology Elections Elections by country Elections by calender Electoral systems Politics Politics by country Political campaigns Political science Political philosophy Related topics Political parties Parties by country Parties by name Parties by... The voting paradox is a situation noted by the Marquis de Condorcet in the late 18th century, in which collective preferences can be cyclic (i. ...

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. The Democracy Series Liberal democracy History of democracy Representative democracy Representation Voting Voting systems Elections Elections by country Elections by calender Politics Politics by country Political campaigns Political science Political philosophy Political parties Parties by country Parties by name Parties by ideology Voting systems are methods (algorithms) for groups of... Any election method conforming to the Condorcet criterion is known as a Condorcet method. ...

Complying methods

Black, Smith/IRV, Copeland, minimax, Nanson's method, Smith/minimax, ranked pairs and variations (maximize affirmed majorities, maximum majority voting), and Schulze comply with the Condorcet criterion. Copelands method is a Condorcet method in which the winner is determined by finding the candidate with the most pairwise victories. ... The Borda count can be combined with an Instant Runoff procedure to create hybrid election methods that are called Nanson method and Baldwin method. ... Ranked Pairs (RP) or Tideman (named after Nicolaus Tideman) is a voting method that selects a single winner using votes that express preferences. ... Maximize Affirmed Majorities (MAM) is a voting method developed by Stephen Eppley that selects a single winner using votes that express preferences. ... Maximum majority voting (MMV) is a voting method that selects a single winner using votes that express preferences. ... The Schulze method is a voting system developed in 1997 by Markus Schulze that selects a single winner using votes that express preferences. ...

Approval voting, Range voting, Borda count, plurality voting, and instant-runoff voting do not. Approval voting is a voting system used for elections, in which each voter can vote for as many or as few candidates as the voter chooses. ... Range voting, or average voting, or cardinal ratings is a voting system used for single or multiple-seat elections. ... The Borda count is a voting system used for single-winner elections in which each voter rank-orders the candidates. ... The first-past-the-post electoral system is a voting system for single-member districts, variously called first-past-the-post (FPTP or FPP), winner-take-all, plurality voting, or relative majority. ... When the single transferable vote voting system is applied to a single-winner election it is sometimes called instant-runoff voting (IRV), as it is much like holding a series of runoff elections in which the lowest polling candidate is eliminated in each round until someone receives majority vote. ...

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. But instant-runoff voting allows each voter to rank the candidates, yet it still does not comply. A simple example will prove that IRV fails to comply with the Condorcet criterion. The first-past-the-post electoral system is a voting system for single-member districts, variously called first-past-the-post (FPTP or FPP), winner-take-all, plurality voting, or relative majority. ... Approval voting is a voting system used for elections, in which each voter can vote for as many or as few candidates as the voter chooses. ...

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. So according to the Condorcet criteria, B should win. By contrast, according to the rules of IRV, B is ranked first by the fewest voters and is eliminated, and C wins with the transferred votes from B; in plurality voting A wins with the most first choices.

See also

• Condorcet method