The relationship between Arrow's and Wilson's theorems on restricted domains (Q2070578)

This article discusses variations of Arrow's theorem on variable domains. Domains are characterized in terms of properties like being Cartesian and Pareto complete. A basic domain possesses both the Cartesian and the Pareto complete properties. When every social welfare function that is Pareto optimal and satisfies binary independence is dictatorial, a domain is classified as ARROW. By substituting non-imposition for Pareto optimality and adding to dictatorship the possibilities of anti-dictatorship or nullity, a WILSON domain is obtained. If the two WILSON conditions lead to, instead of dictatorship, anti-dictatorship or nullity, the result of Pareto optimality, anti-Pareto optimality or nullity, the domain is classified as MALAWSKY-ZHOU. General conditions on domains for the validity of each of these three variants of Arrow's theorem and their intersections are presented. The existence and the non-existence of such domains are also proven.