Arrow's Theorem and Turing Computability

Abstract

A social welfare function for a denumerable society satisfies {Pairwise Computability} if for each pair (x,y) of alternatives, there exists an algorithm that can decide from any description of each profile on {x,y} whether the society prefers x to y. I prove that if a social welfare function satisfying Unanimity and Independence also satisfies Pairwise Computability, then it is dictatorial. This result severely limits on practical grounds Fishburn's resolution (1970) of Arrow's impossibility. I also give an interpretation of a denumerable "society."

JEL Classification: D71, C69, D89