Answering Layer 3 queries with DiscoSCMs

In the realm of causal inference, the primary frameworks are the Potential Outcome (PO) and the Structural Causal Model (SCM), both predicated on the consistency rule. However, when facing Layer 3 valuations, i.e., counterfactual queries that inherently belong to individual-level semantics, they both seem inadequate due to the issue of degeneration caused by the consistency rule. For instance, in personalized incentive scenarios within the internet industry, the probability of one particular user being a complier, denoted as $P(y_x, y'_{x'})$, degenerates to a parameter that can only take values of 0 or 1. This paper leverages the DiscoSCM framework to theoretically tackle the aforementioned counterfactual degeneration problem, which is a novel framework for causal modeling that combines the strengths of both PO and SCM, and could be seen as an extension of them. The paper starts with a brief introduction to the background of causal modeling frameworks. It then illustrates, through an example, the difficulty in recovering counterfactual parameters from data without imposing strong assumptions. Following this, we propose the DiscoSCM with independent potential noise framework to address this problem. Subsequently, the superior performance of the DiscoSCM framework in answering counterfactual questions is demonstrated by several key results in the topic of unit select problems. We then elucidate that this superiority stems from the philosophy of individual causality. In conclusion, we suggest that DiscoSCM may serve as a significant milestone in the causal modeling field for addressing counterfactual queries.