Collective decisions under uncertainty: efficiency, ex-ante fairness, and normalization

Abstract

This paper studies preference aggregation under uncertainty in the multi-profile framework and characterizes a new class of aggregation rules that address classical concerns about Harsanyi's (1955) utilitarian rules. Our aggregation rules, which we call relative fair aggregation rules, are grounded in three key ideas: utilitarianism, egalitarianism, and the 0--1 normalization of individual utilities. These rules are parameterized by a set of weight vectors over individuals and evaluate each ambiguous alternative by taking the minimum weighted sum of 0--1 normalized utility levels over the weight set. For the characterization, we propose two novel axioms -- weak preference for mixing and restricted certainty independence -- developed by using a new method of objectively randomizing outcomes within the Savagean setting. Additional results clarify how these axioms capture the utilitarian and egalitarian attitudes of the rules.