Condorcet winner

The Condorcet candidate (a.k.a. Condorcet winner) is the person who would win a two-candidate election against each of the other candidates in a plurality vote. For a set of candidates, the Condorcet winner is always the same regardless of the voting system in question. A voting system satisfies the Condorcet criterion (English pronunciation: /kɒndɔːrˈseɪ/) if it always chooses the Condorcet winner when one exists. Any voting method conforming to the Condorcet criterion is known as a Condorcet method.

A Condorcet winner will not always exist in a given set of votes, which is known as Condorcet's voting paradox. When voters identify candidates on a 1-dimensional left-to-right axis and always prefer candidates closer to themselves, a Condorcet winner always exists. Real political positions are multi-dimensional, however, which can lead to circular societal preferences with no Condorcet winner.

These terms are named after the 18th-century mathematician and philosopher Marie Jean Antoine Nicolas Caritat, the Marquis de Condorcet.

The Condorcet criterion implies the majority criterion; that is, any system that satisfies the former will satisfy the latter. Because of this, Arrow's impossibility theorem shows that any method which satisfies the Condorcet criterion will not satisfy independence of irrelevant alternatives. This means that removing some losing candidates from an election may result in a different Condorcet winner.

The Condorcet criterion is also incompatible with the later-no-harm criterion, the participation criterion, and the consistency criterion.

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