On social welfare functionals: Representation theorems and equivalence classes

We substantially weaken the traditional unrestricted domain assumption and give axiomatic characterizations of social welfare functionals representable by utility functions of the form W(u(⋅)), where u=(u1,…,un) is a utility profile specifying a concrete welfare situation, and W is a real-valued function belonging to a particular class. Also we consider general equivalence relations on the utility space and obtain representation theorems on utility equivalence classes.