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

This paper studies preference aggregation under uncertainty in the multi-profile framework introduced by Sprumont (2018, 2019) and characterizes a new class of aggregation rules that can address classical concerns about Harsanyi's (1955) utilitarian rules. Our class of aggregation rules, which we call relative fair aggregation rules, is grounded in three key ideas: utilitarianism, egalitarianism, and the 0--1 normalization. These rules are parameterized by a set of weights over individuals. Each ambiguous alternative is evaluated by computing the minimum weighted sum of the 0--1 normalized utility levels within that weight set. For the characterization, we propose two novel key axioms -- weak preference for mixing and restricted certainty independence -- developed using a new method of objectively randomizing outcomes even within the fully uncertain Savagean framework. Furthermore, we show that relative utilitarian aggregation rules can be identified from the above class by imposing an axiom stronger than restricted certainty independence, and that the Rawlsian maximin version can be derived by considering strong preference for mixing instead.