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Condorcet paradox

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A paradox of intransitive preferences arising from the aggregation of individual transitive preferences under majority rule. Its simplest manifestation is in a group of three voters choosing among three alternatives x, y, and z, the first voter preferring the three alternatives in the order xyz, the second yzx, and the third zxy. In a majority vote, x is preferred to y by a majority of two to one (the first and third voters preferring the alternatives in that order), and similarly y is preferred to z by a majority, and z is preferred to x by a majority. Also called a cyclic majority or the paradox of voting. See also Arrow's impossibility theorem. [Named after the French philosopher and mathematician Marie Jean Antoine Nicolas de Caritat Condorcet (1743–94) who discovered it in 1785]

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