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.