Multivariate Almost Stochastic Dominance: Transfer Characterizations and Sufficient Conditions Under Dependence Uncertainty

Most often, important decisions involve several unknown attributes. This produces a double challenge in the sense that both assessing the individual multiattribute preferences and assessing the joint distribution of the attributes can be extremely hard. To handle the first challenge, we suggest multivariate almost stochastic dominance, a relation based on bounding marginal utilities. We provide necessary and sufficient characterizations in terms of simple transfers, which are easily communicated to decision makers and, thus, can be used for preference elicitation. To handle the second challenge, we develop sufficient conditions that do not consider the dependence structure and are based on either marginal distributions of the attributes or just their means and variances. We apply the theoretical results to a case study of comparing the efficiency of photovoltaic plants.

Funding: M. Scarsini is a member of Gruppo Nazionale per l’Analisi Matematica, la Probabilità, e le loro Applicazioni-Istituto Nazionale di Alta Matematica Francesco Severi (GNAMPA-INdAM). His work was partially supported by GNAMPA-INdAM (Project CUP_E53C22001930001 “Limiting behavior of stochastic dynamics in the Schelling segregation model”) and the Italian Ministry of Education, Universities, and Research (Research Projects of National Interest 2017 Project ALGADIMAR “Algorithms, Games, and Digital Markets”).

Supplemental Material: The online companion is available at https://doi.org/10.1287/opre.2022.0596.