 When this condition holds, the evidence will support \(h_i\) over \(h_j\) according to \(P_{\alpha}\) just in case it does so for \(P_{\beta}\) as well, although the strength of support may differ. Furthermore, although the rate at which the likelihood ratios increase or decrease on a stream of evidence may differ for the two support functions, the impact of the cumulative evidence should ultimately affect their refutation or support in much the same way. 