# From Axioms to Algorithms: Mechanized Proofs of the vNM Utility Theorem

arXiv: https://arxiv.org/abs/2506.07066 · HTML: https://mlsanity.com/paper/2506.07066/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 34 references that are in the map.
- First posted on arXiv 8 Jun 2025.

## Builds on (most cited first, 1 of 1)

- [The Lean mathematical library](https://mlsanity.com/paper/1910.09336/) (2019)

## Abstract (arXiv)

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.