Social preference under twofold uncertainty

Abstract

We investigate the conflict between the ex ante and ex post criteria of social welfare in a novel axiomatic framework of individual and social decisions, which distinguishes between a subjective and an objective source of uncertainty. This framework permits us to endow the individuals and society not only with ex ante and ex post preferences, as is classically done, but also with interim preferences of two kinds, and correspondingly, to introduce interim forms of the Pareto principle. After characterizing the ex ante and ex post criteria, we present a first solution to their conflict that amounts to extending the former as much possible in the direction of the latter. Then, we present a second solution, which goes in the opposite direction, and is our preferred one. This solution combines the ex post criterion with an objective interim Pareto principle, which avoids the pitfalls of the ex ante Pareto principle, and especially the problem of "spurious unanimity" discussed in the literature. Both solutions translate the assumed Pareto conditions into weighted additive utility representations, and both attribute common individual probability values only to the objective source of uncertainty.

Bayesian social aggregation with almost‐objective uncertainty

“…Thus, the scope of application of Restricted Pareto* will shift as the information available to the agents changes. As noted by Mongin and Pivato (2020, Section 6, p. 649), different agents might “spuriously” assign the same probabilities to the cells of a partition because they receive different information. This can lead Restricted Pareto* to make recommendations that are obviously incorrect in light of the aggregate information of the entire group.…”

“…And for all , we have for both individuals, as shown in Figure 1(f). So, Restricted Pareto* leads society to the wrong answer 16 Mongin and Pivato. refer to this phenomenon as “complementary ignorance.” 17…”

“…In the models of Mongin and Pivato (2020) and Pivato (2022), these sources of common-belief uncertainty were either exogenous, or the asymptotic outcome of a learning process. In the first paper, there is an exogenous distinction between two sources of uncertainty: one "subjective" and one "objective."…”

“…However, while it escapes from the spurious unanimity diagnosed by Mongin, the Restricted Pareto axiom of Gilboa, Samet, and Schmeidler is still susceptible to another form of spurious unanimity, which Mongin and Pivato (2020, Section 6) call “complementary ignorance.” Agents might “agree” about the probabilities of certain events—and unanimously prefer one act over another—only because they have different private information. Restricted Pareto will then require the social preferences to agree with these unanimous individual preferences, even when this contradicts the preference that all agents would have if they had adequately pooled their private information (see Section 6 for details).…”

“…The specification of collective beliefs is an epistemic problem, whereas the specification of the SWF is an ethical problem; there is no reason that these two problems should be solved by the same theorem 3 . For this reason, Mongin and Pivato (2020) and Pivato (2022) have recently introduced weak Pareto axioms, which entail a utilitarian SWF, but do not impose any constraints on collective beliefs. They thus concentrate on the ethical problem, leaving the epistemic problem to be solved later by other methods.…”