Universally selection-closed families of social choice functions

Abstract

In this thesis, we introduce a new notion of consistency for families of social choice functions, called selection-closedness. This concept requires that every member of a family of social choice functions that are to be employed by a society to make its choice from an alternative set it faces, should choose a member of the given family, when it is also employed to choose the social choice function itself in the presence of other rival such functions along with the members of the initial family. We show that a proper subset of neutral social choice functions is universally selection-closed if and only if it is a subset of the set of dictatorial and anti-dictatorial social choice functions. Finally, we introduce a weaker version of selection-closedness and conclude that a “rightextendable scoring correspondence” is strict if and only if the set consisting of its singleton valued refinements is universally weakly selection-closed.