 The first two sequences may be called G-chains and the other two H-chains. Moreover, Mellor assumes that all tokens of \(A, B\) and \(C\) are distributed among the four chains so that the number of chains is exactly the same, namely one fourth of the sequences. Mellor then defines a causal relation between two singular events \(a\) and \(b\) in terms of a situation \(k\) which makes \(b\) more likely to occur given \(a\) than without \(a\), i.e., \(\rP(b\mid a) \gt \rP(b\mid {\sim}a)\). But we can see that the number of chains in which \(b\) is combined with \(a\) is equal to the number of chains in which \(b\) is not combined with \(a\). In fact we have that \(\rP(b\mid a) =\) \(\rP({\sim}b\mid {\sim}a) =\) \(\rP(b\mid {\sim}a) =\) \(\rP({\sim}b\mid a)\). From this it follows that a particular \(b\)’s chance in \(k\) cannot increase with respect to \(a\) compared to its chance without \(a\). Hence \(a\) cannot affect \(b\), and therefore causal loops are impossible.