Arrow's impossibility theorem

Proof all ranked voting rules have spoilers

Arrow's impossibility theorem is a key result in social choice theory, proved by American economist Kenneth Arrow. It shows that no group decision-making procedure based on ordinal utilities (citizens' orderings of different alternatives) can satisfy the requirements of rational choice. Specifically, no such rule can satisfy independence of irrelevant alternatives, the principle that a choice between two alternatives A and B should not depend on the quality of some third, unrelated option, C. The result is often cited in discussions of voting rules, where it shows no ranked voting rule can eliminate the spoiler effect.

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