Independence and Social Choice

Abstract

A new version of independence (I⁺) is proposed for social welfare functions based on the following notion of agreement. Two weak orders and ' on a finite set S agree on a pair {x,y}, denoted by

if |_{x,y} = '|_{x,y} and [z ^* x and z ^* y for some z in S] if and only if [z' (')^* x and z' (')^* y for some z' in S]. The last part says that x and y are strictly under z with respect to exactly when x and y are strictly under z' with respect to '. The idea is that there may be an alternative that is preferred over x and y and one should keep track of this additional information. There exist nondictatorial social welfare functions that satisfy (I⁺) and Pareto allowing one to avoid the Arrow paradox. In fact, our main result is a description of the social welfare functions that satisfy (I⁺), Pareto, and nondictatorship.