Treating health as a continuous rather than binary variable does complicate this problem and, I think, breaks my solution. If the doctors agree on an ordinal ranking of all patients from “most ill” to “most hale”, they can coordinate their diagnoses much easier, as they can search over a smaller space of ensemble diagnoses. If there are lots of “degenerate cases” (i.e. people with the same degree of illness) this might be harder. Requiring a certain minimum Hamming distance (based on some prior) from the all-ill Schelling point doesn’t help at all in the case of nondegenerate ordinal ranking.
Treating health as a continuous rather than binary variable does complicate this problem and, I think, breaks my solution. If the doctors agree on an ordinal ranking of all patients from “most ill” to “most hale”, they can coordinate their diagnoses much easier, as they can search over a smaller space of ensemble diagnoses. If there are lots of “degenerate cases” (i.e. people with the same degree of illness) this might be harder. Requiring a certain minimum Hamming distance (based on some prior) from the all-ill Schelling point doesn’t help at all in the case of nondegenerate ordinal ranking.