Condorcet's Voting Paradox
Three voters each rank candidates A, B, and C in a different order. Pair them up head-to-head: a majority prefers A over B, and a majority prefers B over C. Surely, then, a majority prefers A over C? Can a group's collective preferences form a cycle — A beats B, B beats C, and C beats A — even though every individual voter's own ranking is perfectly consistent?
Reveal the answer
Yes — it's not just possible, it's unavoidable in some elections. With voters ranking A>B>C, B>C>A, and C>A>B, majorities exist for A over B, B over C, and C over A all at once: a cycle with no overall winner. The Marquis de Condorcet described this in his 1785 essay on the mathematics of majority decisions, launching the formal study of voting systems and foreshadowing Kenneth Arrow's 20th-century proof that no ranked voting system can fully escape this kind of paradox.