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 [1] and Gibbard-Satterthwaite´s theorem [2], [3], which state that under certain natural constraints, social choice mechanisms are impossible to construct. In recent years, beginning in Kalai [4], much work has been done in finding robust versions of these theorems, showing that impossibility remains even when the constraints are 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].