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单词 Condorcet paradox
释义
Condorcet paradox

Statistics
  • A voting paradox noted by the Marquis de Condorcet in an essay published in 1785. For example, suppose there are three candidates, A, B, and C, and three voters whose preferences are as follows:

    Preference

    First

    Second

    Third

    Voter 1:

    A

    B

    C

    Voter 2:

    B

    C

    A

    Voter 3:

    C

    A

    B

    A is preferred to B by a majority of voters and B is preferred to C by a majority. However, it is also the case that C is preferred to A by a majority.


Economics
  • The observation that the preference order resulting from pairwise majority voting can be intransitive. Assume there are three options x, y, and z, and three individuals A, B, and C. Assume the individuals rank the alternatives as follows (preferred option given first): A: x, y, z; B: y, z, x; and C: z, x, y. If a vote is taken over the pair x and y then x will win with a majority of two votes against one. Similarly, y will defeat z, and z will defeat x. The preference order obtained from the voting process is cyclical, and therefore intransitive. The Condorcet paradox was an early example of Arrow’s impossibility theorem. See also collective choice.


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