Social learning with bounded confidence

Motivated by the homophily principle in social networks, this paper investigates a social learning model with bounded confidence, in which two individuals are neighbors only if the difference of their beliefs is not larger than a constant called bound of confidence. Each individual updates her belief through Bayesian inference based on her private signal plus consensus algorithm based on the beliefs of her neighbors. We find that the whole group can learning the true state only if the bound of confidence is larger than a positive threshold, which implies that people should try to communicate with others whose beliefs are quite different with themselves, in addition to those similar to themselves. Furthermore, we introduce a neighborhood-preserved strategy to guarantee that once two individuals are neighbors they will be neighbors forever. We show that social learning in the revised model can be realized with much smaller threshold, and therefore, provide an effective mechanism for social learning.