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

TL;DR

This paper introduces a new class of aggregation rules called relative fair aggregation rules for preference aggregation under uncertainty, combining utilitarianism, egalitarianism, and normalization to address classical concerns.

Contribution

It characterizes these rules using two novel axioms and a new method of outcome randomization within the Savage framework, advancing the theory of collective decision-making.

Findings

Proposes relative fair aggregation rules based on normalized utilities.

Develops two axioms: weak preference for mixing and restricted certainty independence.

Provides a characterization of these rules within the preference aggregation framework.

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.