An Axiomatic Foundation for Decisions with Counterfactual Utility

TL;DR

This paper develops an axiomatic framework extending von Neumann-Morgenstern utility theory to counterfactual preferences, ensuring coherence and addressing paradoxes in decision-making involving hypothetical outcomes.

Contribution

It generalizes utility axioms to preferences over all potential outcomes, providing a coherent foundation for counterfactual utilities and resolving known decision paradoxes.

Findings

Expected counterfactual utility satisfies vNM axioms on extended domain

Framework reconciles inconsistencies like the Russian roulette example

Derives conditions for reducing counterfactual to standard utilities

Abstract

Counterfactual utilities evaluate decisions not only by the realized outcome under a given decision, but also by the counterfactual outcomes that would arise under alternative decisions. By generalizing standard utility frameworks, they allow decision-makers to encode asymmetric criteria, such as avoiding harm and anticipating regret. Recent work, however, has raised fundamental concerns about the coherence and transitivity of counterfactual utilities. We address these concerns by extending the von Neumann-Morgenstern (vNM) framework to preferences defined on the extended space of all potential outcomes rather than realized outcomes alone. We show that expected counterfactual utility satisfies the vNM axioms on this extended domain, thereby admitting a coherent preference representation. We further examine how counterfactual preferences map onto the realized outcome space through menu-dependent and context-dependent projections. This axiomatic framework reconciles apparent inconsistencies highlighted by the Russian roulette example in the statistics literature and resolves the well-known Allais paradox from behavioral economics. We also derive an additional axiom required to reduce counterfactual utilities to standard utilities on the same potential outcome space, and establish an axiomatic foundation for additive counterfactual utilities, which satisfy a necessary and sufficient condition for point identification. Finally, we show that our results hold regardless of whether individual potential outcomes are deterministic or stochastic.