Condorcet Paradox & Voting Methods

Explore how different voting systems can choose different winners

Voter Groups

Group 1: 33 voters — prefers A > B > C

A > B > C

Group 2: 33 voters — prefers B > C > A

B > C > A

Group 3: 34 voters — prefers C > A > B

C > A > B

Head-to-Head Matrix

vs	A	B	C

⚠ Condorcet Cycle detected! A beats B, B beats C, but C beats A — no majority winner exists.

Voting Method Results

Condorcet Paradox: Named after the Marquis de Condorcet (1785), this paradox shows that majority preferences can be cyclic even when individual preferences are rational and transitive. Arrow's Impossibility Theorem (1951) generalizes this: no voting system with 3+ candidates can simultaneously satisfy unanimity, independence of irrelevant alternatives, and non-dictatorship. Plurality takes the most first-choice votes; instant-runoff eliminates the lowest and redistributes; Borda count scores by rank position; Condorcet winner beats all others one-on-one.