A necessary and sufficient condition for Wilson's impossibility theorem with strict non-imposition

Yasuhito Tanaka ()

Economics Bulletin, 2003, vol. 4, issue 17, pages 1-8

Abstract: Wilson's impossibility theorem (Wilson(1972)) about Arrovian social welfare functions (Arrow(1963)) states that there exists a dictator or an inverse-dictator for any non-null social welfare function which satisfies the conditions of unrestricted domain, non-imposition and independence of irrelevant alternatives (IIA). Among these conditions IIA is very strong and controversial. We will show that, under the condition of strict non-imposition which is stronger than non-imposition, IIA can be replaced by weaker condition. We call this condition "monotonicity". We will also show that under strict non-imposition it is necessary and sufficient condition for Wilson's theorem, that is, it is equivalent to dictatorship or inverse-dictatorship of Arrovian social welfare functions under unrestricted domain and strict non-imposition.

Keywords: monotonicity; strict non-imposition; Wilson's impossibility theorem (search for similar items in EconPapers)
JEL-codes: D7 (search for similar items in EconPapers)
Date: 2003-03-31
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