Decision-Making under Combinatorial Risk

2026-06-08

AI Summary

This study presents the first systematic investigation into human decision-making under composite risk—situations where outcomes are determined by multiple uncertain components and the full probability distribution is difficult to evaluate directly. Through an investment allocation experiment integrating behavioral testing, symbolic regression, and prospect theory modeling, the authors find that individuals primarily rely on key risk features such as the post-investment probability of success when making judgments. The results reveal that when participants are presented with the induced probability mass function (PMF), their choices align more closely with theoretical predictions, exhibit reduced variance, and yield significantly improved model fit. Leveraging these insights, the study develops a concise and interpretable descriptive model of decision-making under composite risk.

Abstract

Decision-making under risk is typically studied through single-shot lottery choices. Yet many real decisions involve combinatorial risk, where risk arises from multiple risky components, so the lottery over outcomes is induced rather than given outright and can be costly to evaluate exactly. We introduce an investment-allocation task to study decision under combinatorial risk, where investing in a component raises its success probability and thereby reshapes the outcome distribution. Participants favor the option with the larger probability increment, and, when increments are equal, the option with the higher initial success probability. Revealing the induced probability mass function (PMF) substantially changes behavior, making participants less responsive to combinatorial-risk features and reducing choice variance. To explain these patterns, we move beyond standard benchmarks and hand-crafted hypotheses with symbolic regression to discover compact descriptive models. The discovered models rely mainly on combinatorial-risk features, such as the after-investment success probability, rather than exact evaluation of the full induced distribution. Behavior under the displayed PMF is then well explained by augmenting this model with a prospect-theoretic residual model. The results show that people navigate combinatorial risk primarily through its core features, shifting toward lottery valuation only when the induced PMF is displayed.

Problem

• combinatorial risk
• decision-making under risk
• probability mass function
• investment allocation
• risk perception

Innovation

• combinatorial risk
• symbolic regression
• investment-allocation task
• probability mass function
• descriptive modeling