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

نویسنده

  • Yasuhito Tanaka
چکیده

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. I wish to thank anonymous referees for their very valuable comments. This research has been supported by a grant from the Zengin Foundation for Studies on Economics and Finance in Japan. Citation: Tanaka, Yasuhito, (2003) "A necessary and sufficient condition for Wilson's impossibility theorem with strict non−imposition." Economics Bulletin, Vol. 4, No. 17 pp. 1−8 Submitted: December 18, 2002. Accepted: March 31, 2003. URL: http://www.economicsbulletin.com/2003/volume4/EB−02D70020A.pdf

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تاریخ انتشار 2003