Coherent combination of experts’ opinions: another impossibility result

Abstract How should rational agents revise their opinions given the opinions of multiple experts? One attractive answer is linear averaging: upon learning multiple experts’ opinions about a proposition A , one’s own probability of A should equal a linear average of the experts’ opinions about A . However, this answer has a well-known problem: it is compatible with Bayesian conditionalization only when the agent is certain that the experts assign the exact same probability to A (Dawid et al. in TEST, 4(2):263–313, 1995, Ranjan and Gneiting in J Royal Stat Soc Ser B Stat Methodol 72(1):71–91, 2010, Bradley in Theory Decis 85(1):5-20, 2018, Gallow in Philos Stud 175(10):2389–2398, 2018). This paper shows that, for priors of finite domains, a similar result holds for the much weaker norm of strict convexity . To this extent, the triviality phenomenon is more widespread than it has been previously appreciated.