A topological proof of Eliaz's unified theorem of social choice theory (forthcoming in "Applied Mathematics and Computation")
Recently Eliaz(2004) has presented a unified framework to study (Arrovian) social welfare functions and non-binary social choice functions based on the concept of 'preference reversal'. He showed that social choice rules which satisfy the property of preference reversal and a variant of the Pareto principle are dictatorial. This result includes the Arrow impossibility theorem and the Gibbard-Satterthwaite theorem as its special cases. We present a concise proof of his theorem using elementary concepts of algebraic topology such as homomorphisms of homology groups of simplicial complexes induced by simplicial mappings.
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