Most of the literature on causality considers the structural framework of Pearl and the potential-outcome framework of Neyman and 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 superimpose the two causal frameworks to prove that structural counterfactual outcomes and potential outcomes do not coincide in general -- not even in law. More precisely, we express the law of the potential outcomes in terms of the latent structural causal model under the fundamental assumptions of causal inference. This enables us to precisely identify when counterfactual inference is or is not equivalent between approaches, and to clarify the meaning of each kind of counterfactuals.

翻译：大多数因果推断文献认为Pearl的结构框架与Neyman和Rubin的潜在结果框架在形式上等价，因此可互换使用do算子和潜在结果下标符号来表示反事实结果。本文通过叠加两种因果框架证明，结构反事实结果与潜在结果在一般情况下并不一致——甚至不满足同分布。更具体地，我们在因果推断基本假设下，利用潜在结构因果模型表达潜在结果的分布，从而精确识别两种方法在反事实推断上等价与否的条件，并厘清各类反事实的含义。