 This broadening of vagueness and diversity sets to accommodate vague and diverse likelihood values makes no trouble for the convergence to truth results for hypotheses. For, provided that the Directional Agreement Condition is satisfied by all support functions in an extended vagueness or diversity set under consideration, the Likelihood Ratio Convergence Theorem applies to each individual support function in that set. For, the the proof of that convergence theorem doesn’t depend on the supposition that likelihoods are objective or have intersubjectively agreed values. Rather, it applies to each individual support function \(P_{\alpha}\). The only possible problem with applying this result across a range of support functions is that when their values for likelihoods differ, function \(P_{\alpha}\) may disagree with \(P_{\beta}\) on which of the hypotheses is favored by a given sequence of evidence. That can happen because different support functions may represent the evidential import of hypotheses differently, by specifying different likelihood values for the very same evidence claims. So, an evidence stream that favors \(h_i\) according to \(P_{\alpha}\) may instead favor \(h_j\) according to \(P_{\beta}\). However, when the Directional Agreement Condition holds for a given collection of support functions, this problem cannot arise. Directional Agreement means that the evidential import of hypotheses is similar enough for \(P_{\alpha}\) and \(P_{\beta}\) that a sequence of outcomes may favor a hypothesis according to \(P_{\alpha}\) only if it does so for \(P_{\beta}\) as well.