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）是两大主流框架。然而，这些框架在实际建模反事实（形式化为潜在结果联合分布的参数）时面临显著挑战。反事实推理在当代决策过程中至关重要，尤其是在基于$(Y(0), Y(1))$的联合值需要个性化激励的场景中。本文首先考察了用于建模反事实的PO和SCM框架。通过分析，我们识别出一个固有的模型容量限制，称为"退化反事实问题"，该问题源于作为两个框架基石的"一致性规则"。为克服这一限制，我们提出了一种新的"分布一致性"假设，并据此提出分布一致性结构因果模型（DiscoSCMs），以增强建模反事实的能力。为具体揭示模型容量的提升，我们引入了一个新的可识别因果参数——"一致性概率"，该参数仅在DiscoSCM框架中具有实际意义，并通过个性化激励示例加以展示。此外，我们给出了关于DiscoSCM框架内"因果之梯"的全面理论结果。我们希望这能为未来反事实建模研究开辟新路径，最终深化对因果关系及其实际应用的理解。