 As formulated above, RCCP assumes that there are only two possible states of the common cause: C and \(\overline{C}\). That is, C is a binary event that is either present or absent. A natural extension of RCCP would be to allow the common cause to be a random variable Z with many possible values \(z_1,\dots,z_n\). In this case we would expect that \(Z = z_i\) screens off A from B for \(i=1,\dots,n\). However, this does not imply that we can divide the values of Z into two sets \(\mathbf{S}\) and \(\mathbf{S^\prime}\) such that \(Z\in \mathbf{S}\) (corresponding to C) and \(Z \in \mathbf{S^\prime}\) (corresponding to \(\overline{C}\)) each screen off A and B. More generally, we would not expect coarsenings of Z to yield events that screen off A and B.