I am trying to explain in simple words the Causal Markov condition to establish probabilistic causation. The original definition (Hausman and Woodward 1999) is the following:
“Let G be a causal graph with vertex set V and P be a probability distribution over the vertices in V generated by the causal structure represented by G. G and P satisfy the Causal Markov Condition if and only if for every X in V, Y is independent of V\(Descendants(X) ∪ Parents(X)) given Parents(X)”
My explanation is that a Causal Markov condition is satisfied if the set of variables in a causal relationship with given probability distributions are independent of all the other variables unless they are their parents or their descendants. This is slightly different than other definitions around so, is my explanation first, correct?, second clear? Any advice will be appreciated.