Most of the scientific literature on causal modeling considers the structural framework of Pearl and the potential-outcome framework of Rubin to be formally equivalent, and therefore interchangeably uses the do-notation and the potential-outcome subscript notation to write counterfactual outcomes. In this paper, we agnostically superimpose the two causal models to specify under which mathematical conditions structural counterfactual outcomes and potential outcomes need to, do not need to, can, or cannot be equal (almost surely or law). Our comparison reminds that a structural causal model and a Rubin causal model compatible with the same observations do not have to coincide, and highlights real-world problems where they even cannot correspond. Then, we examine common claims and practices from the causal-inference literature in the light of these results. In doing so, we aim at clarifying the relationship between the two causal frameworks, and the interpretation of their respective counterfactuals.

翻译：大多数关于因果建模的科学文献认为Pearl的结构框架与Rubin的潜在结果框架在形式上等价，因此可互换地使用do算子符号和潜在结果下标符号来表述反事实结果。本文以无偏方式叠加两种因果模型，明确界定在何种数学条件下，结构性反事实结果与潜在结果需要、不需要、能够或不能（以几乎必然或依分布方式）相等。我们的比较表明，与相同观测数据兼容的结构因果模型和Rubin因果模型无需保持一致，并揭示了现实世界中甚至无法对应的实际问题。随后，我们根据这些结果审视因果推断文献中的常见论断与实践。通过这一研究，我们致力于阐明两种因果框架之间的关系，以及各自反事实结果的解释。