🤖 AI Summary
This paper addresses the preference aggregation problem in collective decision-making under uncertainty, overcoming classical limitations of Harsanyi’s utilitarianism—namely, its tension among efficiency, ex ante fairness, and utility normalization. We propose a *relative fairness aggregation rule*: individual utilities are normalized to the [0,1] interval, and the social choice minimizes a weighted sum of these normalized utilities, thereby unifying utilitarian and egalitarian principles. Methodologically, we introduce two novel axioms—*weak mixture preference* and *restricted independence of deterministic alternatives*—enabling, for the first time within the Savage framework, the integration of objective randomization. Our rule subsumes relative utilitarianism and the Rawlsian maximin as special cases. We fully characterize this class of rules, proving that it guarantees both Pareto efficiency and ex ante fairness simultaneously. The result establishes a new axiomatic foundation and mechanism design paradigm for social choice under uncertainty. (149 words)
📝 Abstract
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.