On the boundary between qualitative and quantitative measures of causal effects.

Causal relationships among variables are commonly represented via directed acyclic graphs. There are many methods in the literature to quantify the strength of arrows in a causal acyclic graph. These methods, however, have undesirable properties when the causal system represented by a directed acyclic graph is degenerate. In this paper, we characterize a degenerate causal system using multiplicity of Markov boundaries, and show that in this case, it is impossible to quantify causal effects in a reasonable fashion. We then propose algorithms to identify such degenerate scenarios from observed data. Performance of our algorithms is investigated through synthetic data analysis.