“An Axiomatic Foundation for Decisions with Counterfactual Utility”

Benedikt Koch, Kosuke Imai, and Tomasz Strzalecki write: 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.…