Causal Direction in Causal Bayes Nets

Abstract Some authors maintain that we can use causal Bayes nets to infer whether $X \to Y$ or $X \leftarrow Y$ 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 $X$ ( ${E_x}$ ) has no probabilistic influence on $Y$ no matter the direction of causation—namely, cases where ${E_x} \to X \to Y$ and ${E_x} \to X \leftarrow Y$ are probabilistically indistinguishable. We then assess the philosophical significance of this problem and discuss some potential solutions.