Social Decision Rules Which Are Simple Games

Abstract

A simple game social decision rule is defined by the condition that under it an alternative x is socially preferred to another alternative y iff all individuals belonging to some winning coalition unanimously prefer x to y. This chapter provides a characterization for the class of social decision rules that are simple games as well as for the subclass that are strong simple games and derives Inada-type necessary and sufficient conditions for transitivity and quasi-transitivity under the rules belonging to the class.