Decision Making Under Multidimensional Risk

2026-08-05

AI Summary

This study addresses rational decision-making under multidimensional risk by proposing a structured expected utility framework based on rooted clustering trees, which unifies the joint, separate, and conditional evaluation of risks across dimensions. Through an axiomatic approach, the authors develop a theoretical system for modeling preferences over multidimensional risks, highlighting the pivotal role of bracketing effects in stochastic dominance and risk aversion. The framework is extended to practical contexts such as intergenerational equity, group inequality, and income from multiple sources. The model not only establishes uniqueness of its representation but also encompasses several useful special cases, offering novel theoretical tools and application pathways for measuring inequality and analyzing income risk.

Abstract

Choice alternatives are often multidimensional and risky. We introduce and axiomatize the \textit{structured multidimensional expected utility} representation, a unified framework that generalizes existing approaches to evaluating such alternatives. The representation uses a \textit{rooted clustered tree} to organize the joint, separate, and conditional evaluation of risk across dimensions within a common structure. We analyze the uniqueness of the representation and characterize useful special cases. We apply the representation to inequality across individuals, groups, and generations and to multisource income, characterizing the implications of bracketing for stochastic dominance and the avoidance of multidimensional risk.

Problem

• multidimensional risk
• decision making
• expected utility
• stochastic dominance
• risk evaluation

Innovation

• structured multidimensional expected utility
• rooted clustered tree
• multidimensional risk
• bracketing
• stochastic dominance