Arrow's impossibility theorem

Proof all ranked voting rules have spoilers

Arrow's impossibility theorem is a key result in social choice, discovered by Kenneth Arrow, showing that no ranked voting rule can behave rationally. Specifically, any such rule violates independence of irrelevant alternatives (IIA), the idea that a choice between and should not depend on the quality of a third, unrelated option . The result is most often cited in election science and voting theory, where is called a spoiler candidate. In this context, Arrow's theorem can be restated as showing that no ranked voting rule can eliminate the spoiler effect.

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