Social welfare with net utilities

We consider a society facing a binary choice, in an environment in which differences in utility are comparable across individuals. In such an environment, net utility is the difference between the utility that an individual attains from one alternative, and the utility she attains from the other alternative. A social welfare ordering is a preference relation over net utility profiles. We show that a social welfare ordering satisfies a collection of standard normative axioms if and only if it is representable by a collective utility function defined by the sums of a given power of net individual utilities.