No one can serve two epistemic masters

Consider two epistemic experts—for concreteness, let them be two weather forecasters. Suppose that you aren’t certain that they will issue identical forecasts, and you would like to proportion your degrees of belief to theirs in the following way: first, conditional on either’s forecast of rain being x, you’d like your own degree of belief in rain to be x. Secondly, conditional on them issuing different forecasts of rain, you’d like your own degree of belief in rain to be some weighted average of the forecast of each (perhaps with weights determined by their prior reliability). Finally, you’d like your degrees of belief to be given by an orthodox probability measure. Moderate ambitions, all. But you can’t always get what you want.