On the boundary between qualitative and quantitative methods for causal inference

We consider how to quantify the causal effect from a random variable to a response variable. We show that with multiple Markov boundaries, conditional mutual information (CMI) will produce 0, while causal strength (CS) and part mutual information (PMI), which claim to behave better, are not well-defined, and have other problems. The reason is that the quantitative causal inference with multiple Markov boundaries is an ill-posed problem. We will give a criterion and some applicable algorithms to determine whether a distribution has non-unique Markov boundaries.