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（SCMs）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具有首要重要性，尤其在需要基于$(Y(0), Y(1))$的联合值进行个性化激励的场景中。本文首先探究了用于建模反事实的PO和SCM框架。通过分析，我们发现一种内在的模型容量限制，称为"退化反事实问题"，该问题源于作为两大框架基石的"一致性规则"。为克服这一局限，我们提出了一种新颖的"分布一致性"假设，并据此设计了分布一致性结构因果模型（DiscoSCMs），以增强建模反事实的能力。为具体揭示增强的模型容量，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，我们还围绕DiscoSCM框架下的"因果之梯"提供了一套全面的理论结果。我们期望本研究能为反事实建模的未来研究开辟新路径，最终加深对因果关系及其实际应用的理解。