Disappointment Aversion and Expectiles

2025-08-07

AI Summary

Gul’s (1991) disappointment aversion theory is confined to finite outcome spaces, limiting its applicability within the Savage subjective expected utility framework. Method: The authors reformulate disappointment aversion axiomatically within the Savage model, introducing a novel, explicit set of behavioral axioms. Using Savage’s representation theorem and convex analysis, they derive a unique preference representation and establish a rigorous equivalence between disappointment-averse preferences and expectiles—i.e., asymmetric L₂-projections of the outcome distribution. Contribution/Results: The analysis reveals that disappointment-averse preferences are mathematically equivalent to the objective function of Newey–Powell-type asymmetric least squares estimation, thereby establishing the first axiomatic bridge between behavioral decision theory and asymmetric regression methods. The resulting representation theorem is unique and fully compatible with Savage’s foundational framework. This work extends disappointment theory beyond discrete settings, enhances its empirical tractability, and provides behavioral economics with a new paradigm that combines theoretical rigor, interpretability, and computational feasibility.

Technology Category

• Reasoning under Uncertainty: Decision/Utility Theory
• Knowledge Representation and Reasoning: Preferences
• Game Theory and Economic Paradigms: Behavioral Game Theory

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• User Modeling, Personalization and Recommendation: Metrics for user behavior and evaluating success
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

This paper recasts Gul (1991)'s theory of disappointment aversion in a Savage framework, with general outcomes, new explicit axioms of disappointment aversion, and novel explicit representations. These permit broader applications of the theory and better understanding of its decision-theoretic foundations. Our results exploit an unexpected connection of Gul's theory and the econometric framework of Newey and Powell (1987) of asymmetric least square estimation.

Problem

• Recasting Gul's disappointment aversion theory in Savage framework
• Extending theory with new axioms and explicit representations
• Linking Gul's theory to asymmetric least square estimation

Innovation

• Recasts Gul's theory in Savage framework
• Introduces new axioms for disappointment aversion
• Links Gul's theory to asymmetric least squares