voters' paradox
A problem (not strictly a paradox) in assessing majority preference, published by Edward John Nanson (1850–1936) in Transactions and Proceedings of the Royal Society of Victoria, 1882, but anticipated by Condorcet . Suppose three citizens A, B, C, vote to rank three policies x, y, z . The results are: A: x > y > z ; B: y > z > x ; C: z > x > y . Then two citizens (a majority) prefer x to y, and two (a majority) prefer y to z, but a majority also prefers z to x . Each voter is consistent but the ‘social choice’ is inconsistent. This illustrates the difficulty of extracting a social choice from individual preferences. See also Arrow's theorem.

Philosophy dictionary. . 2011.

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