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Condorcet paradox
 

 

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.

 

Reference: Oxford Press Dictonary of Economics, 5th edt.