Integer Programming and Social Choice

We characterize the class of Arrovian Social Welfare Functions as integer solutions to a collection of linear inequalities. Many of the known results about impossibility, Arrovian Social Welfare Functions, properties of the majority rule etc., can be derived in a simple and unified way from this integer program. We characterize those preference domains that admit a non-dictatorial, neutral Arrovian Social Welfare Function. We characterize the class of anonymous and monotnic rules in terms of majority rule and give a polyhedral characterization of all Arrovian Social Welfare Functions on single-peaked domains. We then show how the approach can be used to derive results about social choice functions as well.