Harsanyi's impartial observer must consider two types of lotteries: imaginary identity lotteries (“accidents of birth”) that she faces as herself and the real outcome lotteries (“life chances”) to be faced by the individuals she imagines becoming. If we maintain a distinction between identity and outcome lotteries, then Harsanyi-like axioms yield generalized utilitarianism, and allow us to accommodate concerns about different individuals' risk attitudes and concerns about fairness. Requiring an impartial observer to be indifferent as to which individual should face similar risks restricts her social welfare function, but still allows her to accommodate fairness. Requiring an impartial observer to be indifferent between identity and outcome lotteries, however, forces her to ignore both fairness and different risk attitudes, and yields a new axiomatization of Harsanyi's utilitarianism.