Sen's Theorem: Geometric Proof, New Interpretations

Abstract

Sen's classic social choice result supposedly demonstrates a conflict between Pareto and even minimal forms of liberalism. By providing the first direct mathematical proof of this seminal result, we underscore a significantly different interpretation: rather than conflicts among rights, Sen's result occurs because the liberalism assumption negates the assumption that voters have transitive preferences. This explanation enriches interpretations of Sen's conclusion by including radically new kinds of societal conflicts, it suggests ways to sidestep these difficulties, and it explains earlier approaches to avoid the difficulties.