Wilson's theorem for economic environments and continuous social preferences
type: Item
instance of: scholarly article
title: Wilson's theorem for economic environments and continuous social preferences
zbMATH Open document ID: 0683.90009
DOI: 10.1007/BF00446988
author: Donald E. Campbell
published in: Social Choice and Welfare
publication date: 1989-01-01T00:00:00Z
review text: \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.
reviewed by: Claus Weddepohl
Mathematics Subject Classification ID: 91B14
zbMATH DE Number: 4119890
zbMATH Keywords: continuous social preferences
zbMATH Keywords: Arrow's impossibility theorem
zbMATH Keywords: infinite society
MaRDI profile type: Publication
cites work: Social choice and individual values
cites work: Existence of equilibrium actions and of equilibrium. A note on the 'new' existence theorems
cites work: The Existence of Social Welfare Functions
cites work: Social welfare functions for economic environments with and without the Pareto principle
cites work: Q3223417
cites work: Arrovian theorems with private alternatives domains and selfish individuals
cites work: Can equity be purchased at the expense of efficiency? An axiomatic inquiry
cites work: Arrow's theorem for economic environments and effective social preferences
cites work: Social choice in economic environments
cites work: On the existence of maximal elements
full work available at URL: https://doi.org/10.1007/bf00446988
OpenAlex ID: W2043328461
description: scientific article; zbMATH DE number 4119890