In the field of causal modeling, potential outcomes (PO) and structural causal models (SCMs) stand as the predominant frameworks. However, these frameworks face notable challenges in practically modeling counterfactuals, formalized as parameters of the joint distribution of potential outcomes. Counterfactual reasoning holds paramount importance in contemporary decision-making processes, especially in scenarios that demand personalized incentives based on the joint values of $(Y(0), Y(1))$. This paper begins with an investigation of the PO and SCM frameworks for modeling counterfactuals. Through the analysis, we identify an inherent model capacity limitation, termed as the ``degenerative counterfactual problem'', emerging from the consistency rule that is the cornerstone of both frameworks. To address this limitation, we introduce a novel \textit{distribution-consistency} assumption, and in alignment with it, we propose the Distribution-consistency Structural Causal Models (DiscoSCMs) offering enhanced capabilities to model counterfactuals. To concretely reveal the enhanced model capacity, we introduce a new identifiable causal parameter, \textit{the probability of consistency}, which holds practical significance within DiscoSCM alone, showcased with a personalized incentive example. Furthermore, we provide a comprehensive set of theoretical results about the ``Ladder of Causation'' within the DiscoSCM framework. We hope it opens new avenues for future research of counterfactual modeling, ultimately enhancing our understanding of causality and its real-world applications.

翻译：在因果建模领域，潜在结果（PO）和结构因果模型（SCM）构成了两种主流框架。然而，这些框架在建模反事实时面临显著挑战——这类推理形式被形式化为潜在结果联合分布的参数。反事实推理在当代决策过程中至关重要，尤其当需要基于$(Y(0), Y(1))$的联合值制定个性化激励方案时。本文首先考察了PO与SCM框架对反事实的建模能力。通过分析，我们识别出这两种框架在模型容量上的固有局限，称为“退化反事实问题”，其根源在于作为二者基石的“一致性规则”。为解决这一局限，我们提出了一种新颖的“分布一致性”假设，并据此构建了分布一致性结构因果模型（DiscoSCM），从而增强了对反事实的建模能力。为具体揭示这种增强的模型容量，我们引入了一个可识别的新因果参数——“一致性概率”，该参数仅在DiscoSCM框架内具有实际意义，并通过个性化激励案例加以展示。此外，我们在DiscoSCM框架内系统论证了“因果之梯”的相关理论结果。我们期望该工作为反事实建模的未来研究开辟新路径，从而深化对因果机制及其现实应用的理解。