A Condorcet method is any election method that elects the candidate that would win by majority rule in all pairings against the other candidates, whenever one of the candidates has that property. A candidate with that property is called a Condorcet winner (named for the 18th-century French mathematician and philosopher Marie Jean Antoine Nicolas Caritat, the Marquis de Condorcet, who championed such outcomes). A Condorcet winner doesn't always exist because majority preferences can be like rock/paper/scissors: for each candidate, there can be another that is preferred by some majority (this is known as Condorcet paradox).
Voting methods that always elect the Condorcet winner (when one exists) are the ones that satisfy the Condorcet criterion.
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/her order of preference, although it may not match his/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 ways 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.
The Robert's Rules method for voting on motions and amendments is also a Condorcet method even though the voters do not vote by expressing their orders of preference. There are multiple rounds of voting, and in each round the vote is between two of the alternatives. The loser (by majority rule) of a pairing is eliminated, and the winner of a pairing survives to be paired in a later round against another alternative. Eventually only one alternative remains, and it is the winner. This is analogous to a single-winner tournament; the total number of pairings is one less than the number of alternatives. Since a Condorcet winner will win by majority rule in each of its pairings, it will never be eliminated by Robert's Rules. A considerable portion of the literature on social choice theory is about the properties of this method since it is widely used and is used by important organizations (legislatures, councils, committees, etc.). It is not practical for use in public elections, however, since its multiple rounds of voting would be very expensive for voters, for candidates, and for governments to administer.
Ramon Llull devised the earliest known Condorcet method in 1299. His method did not have voters express orders of preference; instead, it had a round of voting for each of the possible pairings of candidates. (This was more like the Robert's Rules method except it was analogous to a round-robin tournament instead of a single-elimination tournament.) The winner was the alternative that won the most pairings.
Read more about Condorcet Method: Summary, Definition, Example: Voting On The Location of Tennessee's Capital, Circular Ambiguities, Two-method Systems, Single-method Systems, Related Terms, Condorcet Ranking Methods, Comparison With Instant Runoff and First-past-the-post (plurality), Potential For Tactical Voting, Evaluation By Criteria, Use of Condorcet Voting, Other Considerations
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