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Generalized Binary Constitutions and the Whole Set of Arrovian Social Welfare Functions

Nicolas Gabriel Andjiga, Issofa Mouyouwou and Joël Moulen

Annales d'Economie et de Statistique, 2011, issue 101-102, pages 187-202

Abstract: Arrow’s theorem [1963] states that a social welfare function (SWF) that simultaneously completeness, transitivity, independence of irrelevant alternatives (IIA) and Pareto principle is necessarily dictatorial in the sense that the social decision on any pair of candidates coincides with the strict preference of a fixed individual, the Arrow’s dictator. When individual preferences are weak orders, no further description is provided on the social outcome as soon as the Arrow’s dictator is indifferent on a pair of candidates. We provide in the present paper another proof of the Arrow’s theorem using generalized binary constitutions. Moreover we completely characterize the set of Arrovian SWFs, those are complete and transitive SWFs that satisfy IIA and the Pareto principle.

Date: 2011
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