 First we  specify an acceptance rule. Lin and Kelly propose the  odds threshold rule. The  degree of belief function \(\Pr\) is used to determine a plausibility order by setting \[H_i \prec_p H_j \text{ if and only if } \frac{\Pr(H_i)}{\Pr(H_j)} &gt; t,\] where \(t\) is a constant greater than \(1\) and \(\Pr(H_i),\Pr(H_j)&gt;0\). This determines an acceptance rule by setting \(\alpha(\Pr)= \Bel_{\prec_p}.\) Since the odds threshold rule determines a plausibility order \(\prec_p\) and any plausibility order \(\prec\)  gives rise to a deductively cogent belief state \(\Bel_\prec,\) the Lottery paradox is avoided. In other words: the bridge principle that any rational \(\langle \Bel,p \rangle\)  are related by \(\Bel=\alpha(\Pr)\) enures that \(\Bel\) is deductively cogent. Furthermore, the odds threshold rule allows non-trivial qualitative beliefs in situations where the stability theory precludes them. Recall the case of the doctor. Consider the odds threshold \(2^{10} -1\). Given this threshold, the hypothesis that Job will survive exactly 1 month is strictly more plausible than the proposition that he will survive at least \(n\) months for any \(n\geq 10\). This threshold yields the full belief that Job will survive at most 10 months. However, in the case of the Lottery, the odds threshold rule precludes any non-trivial beliefs. (The content-dependent threshold rule proposed by Kelly and Lin (forthcoming) may allow non-trivial beliefs in the Lottery situation.) See Rott (2017) and  Douven and Rott (2018) for an extensive comparison of the relative likelihood of forming non-trivial qualitative beliefs on the odds-threshold and stability proposals. 