Majority preference can be intransitive — A beats B, B beats C, yet C beats A
Voter Preferences (drag to reorder)
Pairwise Majority Matrix
Condorcet's paradox (1785): even with rational individual preferences, majority voting can produce a collective cycle A>B>C>A. This is the core of Arrow's impossibility theorem (1951): no voting system with ≥3 candidates can simultaneously satisfy Pareto efficiency, independence of irrelevant alternatives, and non-dictatorship. The cycle probability approaches 1 as candidates→∞ with random preferences (~8.8% for 3 voters, 3 candidates; grows rapidly).