Condorcet method

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摘自维基百科
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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. Voting methods that always elect the Condorcet winner (when one exists) are the ones that satisfy the Condorcet criterion.

It is 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).

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.[citation needed]

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. But this method cannot reveal a voting paradox in which there is no Condorcet winner and a majority prefer an early loser over the eventual winner. 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.[citation needed]

Ramon Llull devised the earliest known Condorcet method in 1299.[1] It was equivalent to Copeland’s method in cases with no pairwise ties.

Summary
The concise rule that defines a Condorcet method can be stated in a single sentence:

“If more voters mark their ballots that they prefer Candidate A over Candidate B for office than the number of voters who mark their ballots to the contrary, then Candidate B is not elected.”

Because of the possibility of the Condorcet paradox, it is possible, but unlikely, that this objective cannot be realized in a specific election. This is sometimes called a Condorcet cycle or just cycle and can be thought of as Candidate Rock beating Candidate Scissors, Candidate Scissors beating Candidate Paper, and Candidate Paper beating Candidate Rock. It is only in how the various Condorcet methods resolve such a cycle is how they effectively differ. If there is no cycle, all Condorcet methods elect the same candidate and are operationally equivalent.

Each voter ranks the candidates in order of preference (top-to-bottom, or best-to-worst, or 1st, 2nd, 3rd, etc.). The voter may be allowed to rank candidates as equals, to express indifference between them. To save time, candidates omitted by a voter may be treated as if the voter ranked them at the bottom.

For each pairing of candidates (as in a round-robin tournament) count how many votes rank each candidate over the other candidate. Thus each pairing will have two totals: the size of its majority and the size of its minority.

For most Condorcet methods, those counts usually suffice to determine the complete order of finish. They always suffice to determine whether there is a Condorcet winner. Additional information may be needed in the event of ties. Ties can be pairings that have no majority, or they can be majorities that are the same size; these ties will be rare when there are many voters. Some Condorcet methods may have other kinds of ties; for example, it would not be rare for two or more candidates to win the same number of pairings, when there is no Condorcet winner.