研究

Chambers and Echenique (in J Econ Theory 189:105086, 2020) characterised quadratic(-plus-linear) social welfare functions using Status Quo Independence and Eventual Linearity. We show that Status Quo Independence implies the latter condition at every status quo, making it redundant. Under continuity and normalisation, Status Quo Independence solely yields a unique quadratic-plus-linear decomposition: The proof separates the even and odd parts of the social welfare function into the parallelogram equation and Jensen's equation. Eventual Linearity alone is insufficient because it leaves the even component unrestricted.

Every even function $U:\mathbb{R}^n\to\mathbb{R}$ automatically satisfies EL. Indeed, if $U$ is even, then $\delta_{\mathbf{0}}(x)=U(x)-U(-x)=0$ for every $x\in\mathbb{R}^n$, so the EL-additivity holds at $w=\mathbf{0}$ for every pair $x,y\in\mathbb{R}^n$. Thus, EL imposes no restriction within the class of even functions.

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.

This paper studies preference aggregation under ambiguity when agents have incomplete preference relations due to imprecise beliefs. We introduce the “dual” of the Pareto principle, which respects unanimity among individuals, including those with unexpressed opinions. Our first theorem shows that, in most cases, this principle leads to a dictatorial rule in taste aggregation. We argue that this stems from the problem of spurious unanimity, even when the individuals have the same prior set. By weakening the above principle to avoid respecting spurious unanimity, the second theorem characterizes novel belief-aggregation rules, under which society does not discard any combination of plausible priors.

This paper studies preference aggregation under risk. In our model, each agent has an incomplete preference relation represented by a set of expected utility functions. The classical Pareto principle is silent on agreement involving indecisiveness. To examine the implications of respecting such agreement, we introduce the Paretian principle that can be applied when some individuals reserve their judgment. Our main result shows that, under this principle, for each combination of individuals’ utility functions, there exists a corresponding social utility function constructed as a weighted sum of the individual ones. These aggregation rules guarantee natural properties that the standard Pareto principle fails to ensure.

We prove that a mixture preorder on any mixture space admits a mixture-preserving multi-representation if and only if its graph is closed in the weak topology generated by all real-valued mixture-preserving functions. This answers the question left open by McCarthy, Mikkola, and Thomas (2021). Leonetti (2025, Theorem 2.6) states the corresponding result for simple lotteries, but his proof relies on an incorrect assertion about weakly convergent nets. We refute this assertion for every infinite outcome set using a net of lotteries, each supported on at most two points. We provide a valid proof using the finest locally convex topology as an auxiliary tool, while retaining the original weak closedness assumption. The result for simple lotteries then yields the corresponding representation theorem on arbitrary mixture spaces.