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Example Condorcet method voting ballot. Blank votes are equivalent to ranking that candidate last. A Condorcet method (English: / k ɒ n d ɔːr ˈ s eɪ /; French: [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, whenever there is such a candidate.
The Condorcet criterion implies the majority criterion since a candidate ranked first by a majority is clearly ranked above every other candidate by a majority. When a Condorcet winner exists, this candidate is also part of the smallest mutual majority set, so any Condorcet method passes the mutual majority criterion and Condorcet loser in ...
To find the Condorcet winner, every candidate must be matched against every other candidate in a series of imaginary one-on-one contests. In each pairing, each voter will choose the city physically closest to their location. In each pairing the winner is the candidate preferred by a majority of voters.
A voting system complying with the Condorcet loser criterion will never allow a Condorcet loser to win. A Condorcet loser is a candidate who can be defeated in a head-to-head competition against each other candidate. [11] (Not all elections will have a Condorcet loser since it is possible for three or more candidates to be mutually defeatable ...
Result: L loses against all other candidates and, thus, is Condorcet loser. However, the candidates A, B and C form a cycle with clear defeats. L benefits from that since it loses relatively closely against all three and therefore L's biggest defeat is the closest of all candidates. Thus, the Condorcet loser L is elected Minimax winner. Hence ...
If there is a candidate who is preferred over the other candidates, when compared in turn with each of the others, the ranked-pairs procedure guarantees that candidate will win. Therefore, the ranked-pairs procedure complies with the Condorcet winner criterion (and as a result is considered to be a Condorcet method). [3]
The Marquis de Condorcet viewed elections as analogous to jury votes where each member expresses an independent judgement on the quality of candidates. Candidates differ in terms of their objective merit, but voters have imperfect information about the relative merits of the candidates.
Here is an example of an electorate in which there is no Condorcet winner: There are four candidates: A, B, C and D. 40% of the voters rank D>A>B>C. 35% of the voters rank B>C>A>D. 25% of the voters rank C>A>B>D. The Smith set is {A,B,C}. All three candidates in the Smith set are majority-preferred over D (since 60% rank each of them over D).