Causal Direction in Causal Bayes Nets

Some authors maintain that we can use causal Bayes nets to infer whether X → Y or X ← Y by consulting a probability distribution defined over some exogenous source of variation for X or Y . We raise a problem for this approach. Specifically, we point out that there are cases where an exogenous cause of X (Ex) has no probabilistic influence on Y no matter the direction of causation — namely, cases where Ex → X → Y and Ex → X ← Y are probabilistically indistinguishable. We then assess the philosophical significance of this problem and discuss some potential solutions