We study the merging and the testing of opinions in the context of a prediction model. In the absence of incentive problems, opinions can be tested and rejected, regardless of whether or not data produces consensus among Bayesian agents. In contrast, in the presence of incentive problems, opinions can only be tested and rejected when data produces consensus among Bayesian agents. These results show a strong connection between the testing and the merging of opinions. They also relate the literature on Bayesian learning and the literature on testing strategic experts.
"Merging and testing opinions." Ann. Statist. 42 (3) 1003 - 1028, June 2014. https://doi.org/10.1214/14-AOS1212