We provide an axiomatization of generalized utilitarian social welfare functions in the context of Harsanyi’s impartial observer theorem. To do this, we reformulate Harsanyi’s problem such that lotteries over identity (accidents of birth) and lotteries over outcomes (life chances) are independent. We show how to accommodate (ﬁrst) Diamond’s critique concerning fairness and (second) Pattanaik’s critique concerning diﬀering attitudes toward risk. In each case, we show what separates them from Harsanyi by showing what extra axioms return us to Harsanyi. Thus we provide two new axiomatizations of Harsanyi’s utilitarianism.
Grant, Simon; Kajii, Atsushi; Polak, Ben; and Safra, Zvi, "Generalized Utilitarianism and Harsanyi’s Partial Observer Theorem" (2006). Cowles Foundation Discussion Papers. 1870.