 Local connectivity, as we have seen, ensures that the agent has an opinion as to the relative plausibility of informationally equivalent worlds. Converse well-foundedness guarantees that the agent can always stratify informationally equivalent worlds in such a way that some worlds are the most plausible overall. As a result, we cannot have a situation where agent a has some sequence \[ w_1\gt_a w_2\gt_a w_3 \gt_a \cdots \] of worlds of strictly increasing plausibility, a circumstance in which it would be impossible to find “the most plausible worlds”. By forbidding such a circumstance, converse well-foundedness guarantees that the notion of “the most plausible worlds” is always well-defined.  