Answering Layer 3 queries with DiscoSCMs

Addressing causal queries across the Pearl Causal Hierarchy (PCH) (i.e., associational, interventional and counterfactual), which is formalized as \Layer{} Valuations, is a central task in contemporary causal inference research. Counterfactual questions, in particular, pose a significant challenge as they often necessitate a complete knowledge of structural equations. This paper identifies \textbf{the degeneracy problem} caused by the consistency rule. To tackle this, the \textit{Distribution-consistency Structural Causal Models} (DiscoSCMs) is introduced, which extends both the structural causal models (SCM) and the potential outcome framework. The correlation pattern of potential outcomes in personalized incentive scenarios, described by $P(y_x, y'_{x'})$, is used as a case study for elucidation. Although counterfactuals are no longer degenerate, they remain indeterminable. As a result, the condition of independent potential noise is incorporated into DiscoSCM. It is found that by adeptly using homogeneity, counterfactuals can be identified. Furthermore, more refined results are achieved in the unit problem scenario. In simpler terms, when modeling counterfactuals, one should contemplate: "Consider a person with average ability who takes a test and, due to good luck, achieves an exceptionally high score. If this person were to retake the test under identical external conditions, what score will he obtain? An exceptionally high score or an average score?" If your choose is predicting an average score, then you are essentially choosing DiscoSCM over the traditional frameworks based on the consistency rule.