 It is usually assumed that if a variable set is causally sufficient, then the error variables will be probabilistically independent, and the probability distribution over \(\mathbf{V}\) will satisfy the Causal Markov Condition with respect to the true causal graph. Note that this assumption is very similar to the Common Cause Principle itself. If X and Y are variables included in a causally sufficient DAG, and \(U_X\) and \(U_Y\) are their corresponding error variables, then neither \(U_X\) nor \(U_Y\) is a cause of the other, and they do not have a common cause. If they had a common cause, this would be a common cause of X and Y; if \(U_X\) is a cause of \(U_Y\), then \(U_X\) is a common cause of X and Y. So the causal sufficiency of the variable set implies that \(U_X\) and \(U_Y\) are causally unrelated. The Common Cause Principle would then imply that they are probabilistically independent. Thus it would be inaccurate to say that the Causal Markov Condition can be used to justify the Common Cause Principle: both involve comparable assumptions about the relationship between causation and probability.