Condorcet method

A Condorcet method (pronkɒndɔrˈseɪ; kɔ̃dɔʁsɛ) is an election method that elects the candidate who wins a majority of the vote in every head-to-head election against each of the other candidates, that is, a candidate preferred by more voters than any others, whenever there is such a candidate. A candidate with this property, the pairwise champion or beats-all winner, is formally called the Condorcet winner. The head-to-head elections need not be done separately; a voter's choice within any given pair can be determined from the ranking. Some elections may not yield a Condorcet winner because voter preferences may be cyclic—that is, it is possible (but rare) that every candidate has an opponent that defeats them in a two-candidate contest.(This is similar to the game rock paper scissors, where each hand shape wins against one opponent and loses to another one). The possibility of such cyclic preferences is known as the Condorcet paradox. However, a smallest group of candidates that beat all candidates not in the group, known as the Smith set, always exists. The Smith set is guaranteed to have the Condorcet winner in it should one exist. Many Condorcet methods elect a candidate who is in the Smith set absent a Condorcet winner, and is thus said to be "Smith-efficient". The Condorcet winner is also usually but not necessarily the utilitarian winner (the one that 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 systems. However, Ramon Llull devised the earliest known Condorcet method in 1299. It was equivalent to Copeland's method in cases with no pairwise ties. Condorcet methods may use preferential ranked, rated vote ballots, or explicit votes between all pairs of candidates. Most Condorcet methods employ a single round of preferential voting, in which each voter ranks the candidates from most (marked as number 1) to least preferred (marked with a higher number).