 One justification for assuming the Causal Markov Condition is a theorem due to Pearl and Verma (1991). Suppose that we have a variable set \(\mathbf{V}\), and DAG \(\mathcal{G}\) representing the causal relations among the variables in \(\mathbf{V}\). Suppose, in addition, that the value of each variable X in \(\mathbf{V}\) is a deterministic function of its parents in \(\mathbf{V}\), together with an error variable \(U_{X}\), which represents the influence of any variables that are not included in \(\mathbf{V}\). In other words, \(X = f_{X}(\PA(X), U_{X})\). Then the values of all of the error variables will uniquely determine the value of all of the variables in \(\mathbf{V}\), and a probability distribution \(p^{*}\) over the error variables will induce a probability distribution p over the variables in \(\mathbf{V}\). If the error variables are independent in \(p^{*}\), then the induced probability distribution p will satisfy the Causal Markov Condition with respect to \(\mathcal{G}\). The idea is that if we include enough variables in \(\mathbf{V}\) so that any remaining causal influences are probabilistically independent of one another, then the probability distribution over \(\mathbf{V}\) will satisfy the Causal Markov Condition.