Spectral Aggregation of Quantile Preferences

Abstract: Many collective decisions under risk are made by people who care about different parts of the outcome distribution: downside losses, typical performance, or upside gains. This paper models this disagreement with quantile preferences and studies how the represented quantile levels can be aggregated. Our main result is a spectral support theorem: a spectral social aggregation satisfies the Pareto principle if and only if its social spectrum puts mass only on quantile levels represented in society. Hence, Pareto consistency makes representative-quantile aggregation a dictatorial case. In addition, we derive spectral aggregation from rank-based axioms, develop finite and threshold-Pareto consequences, and show when local benchmark-affine and elliptical common-shape domains admit a representative-quantile reduction.