Quantifying Bounded Rationality: Formal Verification of Simon's Satisficing Through Flexible Stochastic Dominance

2025-07-02

AI Summary

This paper formalizes Herbert Simon’s bounded rationality and satisficing decision theory to bridge the mathematical gap between behavioral economics and classical expected utility theory. To this end, we propose the Flexible First-Order Stochastic Dominance (FFSD) framework and achieve the first machine-checked verification of bounded rationality in the Lean 4 theorem prover. Our approach introduces a parameterized tolerance threshold ε < 1/2 to ensure reference-point uniqueness, proves that FFSD is equivalent to expected utility maximization under an approximate indicator function, and generalizes the result to multidimensional decision settings. This work establishes the first verifiable formal foundation for bounded rationality, enabling mechanized reasoning about uncertain decisions under cognitive constraints. It provides a novel, rigorous paradigm for the formal analysis of behavioral economic models.

Technology Category

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

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

Abstract

This paper introduces Flexible First-Order Stochastic Dominance (FFSD), a mathematically rigorous framework that formalizes Herbert Simon's concept of bounded rationality using the Lean 4 theorem prover. We develop machine-verified proofs demonstrating that FFSD bridges classical expected utility theory with Simon's satisficing behavior through parameterized tolerance thresholds. Our approach yields several key results: (1) a critical threshold $varepsilon < 1/2$ that guarantees uniqueness of reference points, (2) an equivalence theorem linking FFSD to expected utility maximization for approximate indicator functions, and (3) extensions to multi-dimensional decision settings. By encoding these concepts in Lean 4's dependent type theory, we provide the first machine-checked formalization of Simon's bounded rationality, creating a foundation for mechanized reasoning about economic decision-making under uncertainty with cognitive limitations. This work contributes to the growing intersection between formal mathematics and economic theory, demonstrating how interactive theorem proving can advance our understanding of behavioral economics concepts that have traditionally been expressed only qualitatively.

Problem

• Formalizing Simon's bounded rationality using stochastic dominance
• Bridging expected utility theory with satisficing behavior
• Enabling mechanized reasoning about economic decisions under uncertainty

Innovation

• Flexible First-Order Stochastic Dominance framework
• Machine-verified proofs with Lean 4
• Parameterized tolerance thresholds for satisficing