Condorcet's method

A Condorcet method (English: /kɒndɔːrˈseɪ/) is any election method that elects the candidate that would win a majority of the vote in all of the head-to-head elections against each of the other candidates, whenever there is such a candidate. A candidate with this property is called the Condorcet winner. Voting methods that always elect the Condorcet winner, when one exists, satisfy the Condorcet criterion.

A Condorcet winner does not always exist in every election because the preference of a group of voters selecting from more than two options can be cyclic—that is, for each candidate it might be possible to select an opponent where the opponent would win a majority of the votes. (This is similar to the game rock-paper-scissors, where each hand shape wins against one other shape and loses against the other). The possibility of such cyclic preferences in a group of voters is known as the Condorcet paradox. Also, the Condorcet winner is not necessarily the utilitarian winner (the one which maximizes social welfare).

Condorcet voting methods are named for the 18th-century French mathematician and philosopher Marie Jean Antoine Nicolas Caritat, the Marquis de Condorcet, who championed such voting systems.

Most Condorcet methods have a single round of voting, in which each voter ranks the candidates from top to bottom. A voter's ranking is often called his or her order of preference, although it may not match his or her sincere order of preference since voters are free to rank in any order they choose and may have strategic reasons to misrepresent preferences. There are many ways that the votes can be tallied to find a winner, and not all will elect the Condorcet winner whenever one exists. The methods that will—the Condorcet methods—can elect different winners when no candidate is a Condorcet winner. Thus the Condorcet methods can differ on which other criteria they satisfy.

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