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Yasuhito Tanaka
''A necessary and sufficient condition for Wilson's impossibility theorem with strict non-imposition''
( 2003, Vol. 4 No.17 )
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: inverse monotonicity
JEL: D7 - Analysis of Collective Decision-Making: General
Manuscript Received : Mar 27 2003 Manuscript Accepted : Mar 31 2003

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