Arrow's impossibility theorem
Basic assumptions

Arrow's theorem assumes as background that non-degenerate ranked social choice rules satisfy:

Arrow's original statement of the theorem included the assumption of nonperversity, i.e. increasing the rank of an outcome should not make them lose. However, this assumption is not needed or used in his proof, except to derive the weaker Pareto efficiency axiom, and as a result is not related to the paradox. While Arrow considered it an obvious requirement of any proposed social choice rule, ranked-choice runoff (RCV) fails this condition. Arrow later corrected his statement of the theorem to include runoffs and other perverse voting rules.
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