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 do-interventions 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：因果建模领域的大多数科学文献认为Pearl的结构框架与Rubin的潜在结果框架在形式上是等价的，因此通常交替使用干预操作符号与潜在结果下标符号来表示反事实结果。本文以不可知论的视角将这两种因果模型叠加，以阐明在何种数学条件下结构反事实结果与潜在结果必须相等、不必相等、可能相等或不可能相等（几乎必然或依分布）。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因果模型并不必然重合，并着重指出了二者甚至无法对应的现实问题。在此基础上，我们依据这些结果检视了因果推断文献中常见的论断与实践。通过这一分析，我们旨在澄清两种因果框架之间的关系，以及各自反事实结果的解释方式。