An Algebraic Proof of a Robust Social Choice Impossibility Theorem

An important element of social choice theory are impossibility theorems, such as Arrow's theorem and Gibbard-Satterthwaite's theorem, which state that under certain natural constraints, social choice mechanisms are impossible to construct. In recent years, beginning in Kalai'01, much work has been done in finding \text it{robust} versions of these theorems, showing that impossibility remains even when the constraints are \text it{almost} always satisfied. In this work we present an Algebraic scheme for producing such results. We demonstrate it for a variant of Arrow's theorem, found in Dokow and Holzman [5].