2025/06/08 by Jingyuan, Li
Computer Science · Decision Sciences · #Artificial Intelligence (cs.AI) #Computational Finance (q-fin.CP) #Constraint Satisfaction and Optimization #Decision-Making and Behavioral Economics #FOS: Computer and information sciences #FOS: Economics and business #Logic, Reasoning, and Knowledge #Theoretical Economics (econ.TH)
paper · pdf · doi:10.48550/arxiv.2506.07066
openalex publication_date 2025/06/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper presents a comprehensive formalization of the von Neumann-Morgenstern (vNM) expected utility theorem using the Lean 4 interactive theorem prover. We implement the classical axioms of preference-completeness, transitivity, continuity, and independence-enabling machine-verified proofs of both the existence and uniqueness of utility representations. Our formalization captures the mathematical structure of preference relations over lotteries, verifying that preferences satisfying the vNM axioms can be represented by expected utility maximization. Our contributions include a granular implementation of the independence axiom, formally verified proofs of fundamental claims about mixture lotteries, constructive demonstrations of utility existence, and computational experiments validating the results. We prove equivalence to classical presentations while offering greater precision at decision boundaries. This formalization provides a rigorous foundation for applications in economic modeling, AI alignment, and management decision systems, bridging the gap between theoretical decision theory and computational implementation.