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arXiv · 2505.03232

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

Leo Kurata·Kensei Nakamura
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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.

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Leo Kurata, Kensei Nakamura. 2025-05-06. Collective decisions under uncertainty: efficiency, ex-ante fairness, and normalization. https://arxiv.org/abs/2505.03232

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