🤖 AI Summary
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.
📝 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.