Arrow's impossibility theorem - Wikipedia

Abstraction: No ranked voting rule simultaneously satisfies Pareto, non-dictatorship, and IIA

Key points:

• Arrow proved in 1950: any ranked voting rule with 3+ alternatives must violate at least one of Pareto efficiency, non-dictatorship, or independence of irrelevant alternatives (IIA)
• IIA requires that the social preference between A and B not change when a third option C is introduced — the spoiler effect problem
• Condorcet methods uniquely minimize spoiler frequency among ranked rules; spoilers occur only in cyclic preference cycles, which are rare in practice
• Black's median voter theorem (1951) shows Arrow's three conditions are all compatible when voters have single-peaked preferences on a left-right spectrum
• Rated/cardinal voting systems (score, approval voting) are not subject to Arrow's theorem — Arrow later acknowledged this was a meaningful distinction
• Gibbard's theorem still applies to rated systems: no voting game has a single always-dominant strategy

Connections: Kenneth Arrow · Social Choice Theory · Voting Theory

Source: http://en.wikipedia.org/wiki/Arrow's_impossibility_theorem