Voting Paradoxes
Arrow's Impossibility Theorem & Condorcet Cycles — interactive demo
Voter Groups & Preferences
Each group ranks candidates A, B, C from most to least preferred. Drag sliders to change group sizes.
Pairwise Comparison Matrix (Condorcet)
Preference Graph
Arrow's Impossibility Theorem (1951): No ranked-choice voting system can simultaneously satisfy Unanimity, Independence of Irrelevant Alternatives, and Non-dictatorship. The Condorcet paradox shows that majority preference can be cyclic — A beats B, B beats C, yet C beats A — making collective "rationality" impossible even with perfectly rational voters.