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.

翻译：反事实效用不仅通过给定决策下的实际结果评估决策，还通过替代决策下可能产生的反事实结果进行评估。通过泛化标准效用框架，反事实效用使决策者能够编码非对称准则，例如避免伤害和预期后悔。然而，近期研究对反事实效用的一致性及传递性提出了根本性质疑。为应对这些质疑，我们将冯·诺伊曼-摩根斯坦（vNM）框架扩展至基于所有潜在结果（而非仅实际结果）的扩展空间上定义的偏好。我们证明，在此扩展域上，期望反事实效用满足vNM公理，从而允诺一致的偏好表征。我们进一步考察了反事实偏好如何通过菜单依赖与情境依赖的投影映射到实际结果空间。这一公理化框架调和了统计学文献中“俄罗斯轮盘赌”示例所突显的表观矛盾，并解决了行为经济学中著名的阿莱悖论。我们还推导了将反事实效用约简为同一潜在结果空间上的标准效用所需的额外公理，并为加性反事实效用建立了公理化基础——加性反事实效用满足点识别的充分必要条件。最后，我们证明无论个体潜在结果是确定性的还是随机性的，这些结论均成立。