Interpreting Arrow’s Impossibility Theorem

Arrow’s Impossibility Theorem is commonly understood to invoke a dictatorship that is somehow lurking within our voting arrangements. The theorem has been described as proving that “any constitution that respects transitivity, independence of irrelevant alternatives and unanimity is a dictatorship”. But the theorem is really not about dictatorship. It is more appropriately understood as being about the spoiler problem, about the possibility that the presence of a candidate who cannot win the election himself may, nevertheless, violate the “independence of irrelevant alternatives” by switching the outcome of the election between two other candidates. The theorem becomes that no electoral system is guaranteed to avoid the spoiler problem altogether, regardless of the options and regardless of voter preferences.