← Back to Voting Theory

Arrow's Theorem

Fairness Criteria

Toggle criteria to see which methods satisfy them. Try to find a method that satisfies all five!

Arrow's Impossibility Theorem (1951) proves that no ranked voting system with 3+ candidates can simultaneously satisfy all five fairness criteria. The only system satisfying criteria 1, 3, 4, and 5 is a dictatorship -- where one voter's preference always determines the outcome. Democracy is, mathematically, impossible to make perfectly fair.