Equally-distributed equivalent utility, ex post egalitarianism and utilitarianism

We provide an axiomatization of expected equally-distributed equivalent-utility social welfare functions in the context of Harsanyi's impartial observer theorem. For this family of social welfare functions, we show what additional axiom is necessary and sufficient for the observer to exhibit aversion to ex post inequality. We also relate this axiomatization to our axiomatization in a companion paper of generalized utilitarian social welfare functions. Given certain richness assumptions, the only social welfare functions that belong to both families are the utilitarian.