spectral aggregation

This study addresses how to aggregate individual preferences—each focused on distinct quantiles of outcome distributions, such as downside risk, typical performance, or upside potential—into collectively Pareto-efficient decisions. The authors develop a quantile preference model and employ an axiomatic approach combined with spectral weighting analysis to characterize social aggregation rules over general and elliptically contoured distribution domains. Their main contributions include a spectral support theorem showing that Pareto-consistent aggregation can only assign positive weight to quantiles already represented in society; an equivalence between representative-quantile aggregation and dictatorial mechanisms; and a full characterization of necessary and sufficient conditions for finite or threshold-based Pareto efficiency, along with the associated reducible structures.

When multiple evaluators rank items, how can the optimal aggregation rule be automatically selected? Existing methods exhibit complementary strengths and weaknesses, and impossibility theorems preclude any rule from simultaneously satisfying all desirable axiomatic properties. Method: We propose a consistency-driven, data-adaptive framework for aggregation rule selection, optimizing for maximal pairwise (or triplet) consistency. Our approach introduces a novel axiomatization for rule selection and implements a sampling-based algorithm that operates without assuming an underlying data-generating model. Contribution: This work bridges the long-standing gap between social choice theory and statistical ranking aggregation. The proposed mechanism provides formal axiomatic guarantees while remaining computationally tractable. Empirical evaluation demonstrates that it accurately recovers the maximum-likelihood estimator under diverse statistical models—including Mallows, Plackett–Luce, and Thurstone—while significantly improving ranking consistency across synthetic benchmarks and real-world applications.

This paper investigates structural stability in von Neumann–Morgenstern utility aggregation under bounded violations of the Pareto condition. Specifically, it addresses social preference functions that only approximately satisfy Pareto efficiency. Using tools from utility theory, social choice theory, and real analysis, the authors establish a precise quantitative relationship between the magnitude ε of Pareto violation and the distance of the aggregation rule from a utilitarian weighted-sum form. They rigorously prove that every ε-Pareto aggregation function lies within the ε/2-neighborhood (in the sup-norm) of some weighted sum of individual utilities. This result provides the first robustness characterization of Harsanyi’s theorem, demonstrating that utilitarian aggregation remains structurally stable even under weak (ε-approximate) Pareto conditions. The analysis yields a novel theoretical benchmark for the robustness of welfare aggregation mechanisms, advancing foundational understanding of stability in normative economic frameworks.

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)

This paper studies collective aggregation of individual budget distributions in multi-dimensional budget allocation, focusing on mechanism design within the star-shaped preference domain. Method: We introduce a novel star-shaped utility function based on share ratios and analyze mechanisms—including the Nash product maximization mechanism and the uniform phantom mechanism—under various distance metrics (e.g., ℓ₁, ℓ₂). Contribution/Results: We establish the first mechanism achieving simultaneous Pareto efficiency, group strategyproofness, and core fairness in multi-option settings. We characterize the Nash product maximization mechanism as both group strategyproof and core fair. For two alternatives, we prove the uniform phantom mechanism is the unique rule satisfying all three properties; however, under ℓ₁ or ℓ₂ distances, no mechanism can satisfy all three in settings with three or more alternatives. Finally, we construct a computationally tractable mechanism that ensures both fairness and efficiency, offering a new paradigm for budget aggregation that balances theoretical rigor with practical implementability.

This study investigates whether dictatorship remains unavoidable in collective multi-class classification when surjectivity—requiring every class to be nonempty—is satisfied only with high probability and the aggregation function is far from constant. By extending impossibility theorems from social choice theory to a general setting featuring probabilistic surjectivity and non-degenerate aggregation functions, and leveraging the combinatorial framework of Alekseev and Filmus together with probabilistic methods under symmetric i.i.d. assumptions, the authors demonstrate that even if surjectivity holds merely with probability $1-\varepsilon$, dictatorship is still inevitable provided the aggregation function is not approximately constant. This result is further generalized to the setting of equivalence relation aggregation.

This study addresses the aggregation of individual preferences that incorporate altruistic or other-regarding concerns while respecting individual sovereignty. By introducing an individual sovereignty axiom and imposing two key requirements—sequential aggregation consistency and consensus stability—the authors demonstrate that social utility must be a linear combination of individuals’ self-interested utilities, with other-regarding concerns influencing only the weighting scheme. Moreover, the framework uniquely identifies the geometric mean as the rule for inter-individual weight allocation. Employing an axiomatic approach grounded in social choice theory, the analysis extends to settings with feasibility constraints and subjective uncertainty, thereby establishing both the structural role of other-regarding preferences and the uniqueness of the admissible weighting mechanism.

This study addresses the challenge of achieving individual proportionality (IP)—ensuring that the preferences of distinct groups are reflected in aggregate rankings in proportion to their population sizes—under repeatedly applied linear scoring rules. Focusing on batch ranking aggregation with a fixed linear scoring vector, the work proposes using the angular mean from spherical geometry as the aggregation rule. Theoretical analysis establishes, for the first time, that the angular mean satisfies long-term individual proportionality, while also revealing that exact proportionality per batch is unattainable under any fixed linear rule; however, fairness rapidly converges to the ideal as batch size increases. Empirical evaluation on real-world preference data with high inter-group disagreement demonstrates that the angular mean substantially outperforms conventional approaches such as the arithmetic mean, significantly enhancing proportional fairness without compromising ranking utility.

This work addresses the tendency of standard rank aggregation methods to exacerbate underrepresentation of disadvantaged groups in applications such as hiring and recommendation. Focusing on fairness-aware rank aggregation under the Spearman footrule (i.e., L1 distance), the paper presents the first optimal algorithm for fair Top-$k$ ranking and improves the approximation ratio for fair full-ranking aggregation from 3 to 2. Through careful design of combinatorial optimization and approximation algorithms, the authors theoretically establish the optimality of their Top-$k$ solution and an improved approximation guarantee for the full-ranking setting. Extensive experiments on multiple real-world datasets demonstrate that the proposed methods significantly outperform existing baselines, effectively narrowing the performance gap between fair constrained rankings and their unconstrained counterparts.

This work addresses the challenge of aggregating individual distributions over multiple options into a collective distribution while simultaneously satisfying fairness and efficiency desiderata. Existing budget aggregation methods struggle to reconcile individual fairness with Pareto efficiency. We introduce two individual fairness guarantees grounded in ℓₜ (t ≥ 1) utility models and develop polynomial-time algorithms that achieve compatibility between fairness and Pareto efficiency under ℓ₁ and ℓ₂ norms. For small-scale settings, we construct an aggregation rule that satisfies strategyproofness, Pareto efficiency, and a weak fairness notion. However, we prove that these three properties are incompatible in large-scale settings, thereby uncovering a fundamental trade-off inherent in the design of such mechanisms.