Causal Inference (C-inf) -- asymmetric scenario of typical phase transitions

Causal inference (C-inf) deals with the design of estimation strategies that allow researchers to draw causal conclusions based on data. The overarching goal is to draw a conclusion regarding the effect of a causal variable, which is typically referred to as the "treatment" or the "intervention" on some outcome of interest. For example, suppose we want to estimate the causal effect of a drug on deadly cancer progression (vs no exposure to the drug). Then we want to compare metastasis in the patient's body one month after the drug regime has begun versus metastasis in the absence of exposure to the drug. The main challenge for causal inference is that we are not generally able to observe both of these states: at the point in time when we are measuring the outcomes, each individual either has had drug exposure or has not. The problem of estimating the counterfactual, i.e., what would have been the outcome in the absence of a treatement, is central in many disciplines, including economics, health, and social sciences (see, e.g.