We formulate the problem of deciding which preference domains admit a non-dictatorial Arrovian Social Welfare FUnction as one of verifying the feasibility of an integer linear program. Many of the known results about the presence or absence of Arrovian social welfare functions, impossibility theorems in social choice theory, and properties of 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 and give a polyhedral characterization of Arrovian social welfare functions on single-peaked domains.
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