Social rationality, separability, and equity under uncertainty

Harsanyi (1955) proved that, in the context of uncertainty, social rationality and the Pareto principle impose severe constraints on the degree of priority for the worst-off that can be adopted in the social evaluation. Since then, the literature has hesitated between an ex ante approach that relaxes rationality (Diamond, 1967) and an ex post approach that fails the Pareto principle (Hammond, 1983; Broome, 1991). The Hammond-Broome ex post approach conveniently retains the separable form of utilitarianism but does not make it explicit how to give priority to the worst-off, and how much disrespect of individual preferences this implies. Fleurbaey (2010) studies how to incorporate a priority for the worst-off in an explicit formulation, but leaves aside the issue of ex ante equity in lotteries, retaining a restrictive form of consequentialism. We extend the analysis to a framework allowing for ex ante equity considerations to play a role in the ex post evaluation, and find a richer configuration of possible criteria. But the general outlook of the Harsanyian dilemma is confirmed in this more general setting.