Arrow's Impossibility Theorem and Ranked-Choice Voting

Arrow's impossibility theorem, proved by Kenneth Arrow in 1950, examines ranked-choice group decision procedures. Under a ranked-choice group decision procedure, choices are evaluated through ranking. The theorem shows that no such procedure can satisfy all of a set of reasonable fairness conditions. In other words, it is impossible for a ranked-choice system to meet every single one of these reasonable conditions together.

This finding can be surprising to an ordinary reader who might assume that a collective decision process could easily satisfy a standard set of reasonable fairness conditions. Arrow's theorem reveals that when group decisions rely on ranked choices, trade-offs are unavoidable, and at least one condition from the set must be left unsatisfied.

Importantly, this limitation does not apply to rated voting systems. Kenneth Arrow's 1950 proof focuses exclusively on ranked-choice group decision procedures. For anyone studying group decision making, this means that while ranked-choice procedures cannot satisfy all of the reasonable fairness conditions at once, rated voting systems remain outside the reach of this impossibility theorem.