Arrow's Impossibility Theorem Without Unanimity

Abstract

Arrow's Impossibility Theorem states that any constitution which satisfies Transitivity, Independence of Irrelevant Alternatives (IIA) and Unanimity is a dictatorship. Wilson derived properties of constitutions satisfying Transitivity and IIA for unrestricted domains where ties are allowed. In this paper we consider the case where only strict preferences are allowed. In this case we derive a new short proof of Arrow theorem and further obtain a new and complete characterization of all functions satisfying Transitivity and IIA.