On Hierarchical Dictators
at the Andrew Young School of Policy Studies

On Hierarchical Dictators (pdf)

by Yongsheng Xu
July 2003

Keywords: hierarchical dictators, social welfare function, domain restriction, strong Pareto, weak Pareto, independence of irrelevant alternatives

This paper explores implications of a social welfare function satisfying the Strong Pareto Principle (SPP) and Independence of Irrelevant Alternatives (IIA) under various domain restrictions. It is shown that, for certain domain restrictions, any social welfare function satisfying SPP and IIA must be hierarchically dictatorial: there exists a dictator; when the dictator is indifferent between two social states x and y, there exists another individual whose strict preference over x and y is preserved by the social preference; and when these two individuals are indifferent between x and y, there exists a third individual whose strict preference over x and y is
preserved by the social preference; and so on.

Comments and questions regarding this paper may be directed to Yongsheng Xu at yxu3@gsu.edu.