No One Can Serve Two Epistemic Masters

Abstract

There are two local weather forecasters, Al and Bert. 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, you'd like to have your degrees of belief be an orthodox probability function. Second, conditional on Al's forecast of rain being a, you'd like your own degree of belief in rain to be a. Third, conditional on Bert's forecast of rain being b, you'd like your own degree of belief in rain to be b. And, fourth, conditional on Al's forecast of rain being a and Bert's forecast of rain being b, you'd like your own degree of belief in rain to be some linear average of a and b. Moderate ambitions, all. But you can't always get what you want.