Risk and Monotone Comparative Statics without Independence

2026-01-15

AI Summary

This study addresses the lack of systematic conditions for comparative statics within non-expected utility frameworks, particularly when the independence axiom fails. By introducing novel conditions based on local utility functions, the paper develops a general monotone comparative statics approach applicable to a broad class of non-expected utility preferences, thereby overcoming the traditional reliance on independence assumptions. This method unifies and extends existing theories, successfully establishing monotonicity across diverse preference structures. The framework is further demonstrated to be effective in analyzing key economic decisions, including portfolio choice and precautionary saving, offering a robust analytical tool for settings where standard expected utility theory does not apply.

Technology Category

• Reasoning under Uncertainty: Decision/Utility Theory
• Knowledge Representation and Reasoning: Nonmonotonic Reasoning
• Game Theory and Economic Paradigms: Social Choice / Voting

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

We extend well-known comparative results under expected utility to models of non-expected utility by providing novel conditions on local utility functions. We illustrate how our results parallel, and are distinct from, existing results for monotone comparative statics under expected utility, as well as risk preferences for non-expected utility. Our conditions generalize existing results for specific preferences (including expected utility) and allow us to verify monotone comparative statics for novel environments and preferences. We apply our results to portfolio choice problems where preferences or wealth might change, as well as precautionary savings.

Problem

• Risk
• Monotone Comparative Statics
• Non-Expected Utility
• Local Utility Functions
• Independence

Innovation

• non-expected utility
• monotone comparative statics
• local utility functions
• risk preferences
• portfolio choice