Social preference under twofold uncertainty

We investigate the conflict between the ex ante and ex post criteria of social welfare in a new framework of individual and social decisions, which distinguishes between two sources of uncertainty, here interpreted as being objective and subjective, respectively. This framework makes it possible to endow the individuals and society not only with ex ante and ex post preferences, as is usually done, but also with interim preferences of two kinds, and correspondingly, to introduce interim forms of the Pareto principle. After characterizing the two social welfare criteria, we present two compromises between them, one based on the ex ante criterion and absorbing as much as possible of the ex post criterion (Theorem 1), the other based on the ex post criterion and absorbing as much as possible of the ex ante criterion (Theorem 2). Both solutions translate the assumed Pareto conditions into weighted additive utility representations, as in Harsanyi’s Aggregation Theorem, and both attribute to the individuals common probability values on the objective source of uncertainty, and different probability values on the subjective source. We discuss these solutions in terms of the by now classic spurious unanimity argument and a novel informational argument labeled complementary ignorance. The paper complies with the standard economic methodology of basing probability and utility representations on preference axioms.