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

TL;DR

This paper formalizes Herbert Simon's bounded rationality concept using a new framework called Flexible First-Order Stochastic Dominance, verified through the Lean 4 theorem prover, bridging classical utility theory with satisficing behavior.

Contribution

It introduces FFSD, a rigorous formalization of bounded rationality, and provides the first machine-verified proofs connecting it to expected utility theory and decision-making under cognitive limitations.

Findings

Critical threshold $ < 1/2$ ensures reference point uniqueness

FFSD is equivalent to expected utility maximization for approximate indicator functions

Extensions to multi-dimensional decision settings

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.