Condorcet Paradox

The Condorcet paradox (also called the voting paradox) is the discovery, made by the Marquis de Condorcet in 1785, that majority voting over three or more alternatives can produce cyclic social preferences even when every individual voter holds perfectly consistent, transitive preferences. If voter 1 prefers A to B to C, voter 2 prefers B to C to A, and voter 3 prefers C to A to B, then A beats B by majority, B beats C by majority, and C beats A by majority — a cycle with no winner. The paradox is the founding observation of Social Choice Theory and was generalized by Kenneth Arrow into the full impossibility result that bears his name. The paradox reveals that majority voting has no stable equilibrium in the general case: the outcome depends on the order in which alternatives are considered, making it vulnerable to agenda manipulation by whoever controls the sequence of votes.