Title: On the boundary between qualitative and quantitative measures of causal effects,
Abstract: 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.