 Theorem 1 provides a simple axiomatic characterization of the class of confirmation functions that are strictly increasing with the final probability of the hypothesis given the evidence (and \(k\)) (proven in Schippers 2017). All the functions in this class are ordinally equivalent, meaning that they imply the same rank order of \(C_{P}(h, e\mid k)\) and \(C_{P^*}(h^*,e^*\mid k^*)\) for any \(h, h^*,e, e^*,k, k^* \in \bL\) and any \(P, P^* \in \bP.\)