Voting paradox

The voting paradox is a situation noted by the Marquis de Condorcet in the late 18th century, in which collective preferences can be cyclic, even if the preferences of individual voters are not. This appears paradoxical, as it contradicts intuitive ideas of what should happen.

This is best illustrated by an example. Suppose we have three candidates, A, B and C, and that there are three voters with preferences as follows (candidates being listed in decreasing order of preference):

Voter 1: A B C

Voter 2: B C A

Voter 3: C A B

The majority view of the voters in this situation is that B is better than C, who is better than A, who is better than B, who is better than C, etc.

See also: Arrow's Impossibility Theorem, Condorcet's method, Smith set, voting system.