Wilson's theorem for economic environments and continuous social preferences
\textit{R. Wilson} [J. Econ. Theory 5, 478-486 (1972)] proved a generalization of Arrow's impossibility theorem for finite sets of alternatives and agents: every non-imposed and non-null (not all alternatives equivalent) social welfare function that satisfies Arrow's independence axiom is dictatorial or inversely dictatorial. The Pareto criterion is not required. Other authors proved this result for sets of alternatives consisting of allocations of strictly positive commodity bundles and with a finite set of agents with selfish individual preferences. In the present paper it is proved that, after adding an assumption on the continuity of individual preferences, the result also holds in the closure of the positive orthant and with an infinite society. It follows as a corollary that some individual gets a zero vector if the social preference is non-null and non-imposed.
scientific article; zbMATH DE number 4119890