Community Learning from External Information Sources

We model the persuasive effect of external information sources such as media on social networks using a new endogenous social learning framework. The agents are thought to hold uninformative probabilistic prior beliefs about an issue that concerns them and learn about this state of the world through a non-Bayesian myopic DeGroot-style update process applied on the priors using social influence 'mixtures'. We model external information sources in this framework as entities that can bring to the attention of agents 'global' beliefs that are potentially from beyond the confines of a community, and may well be in conflict among themselves. In our model agents score these information sources on the basis of how closely the beliefs propounded by the sources match their own beliefs, but determine how to assimilate such beliefs on the basis of the views of their community of connected neighbors. This form of social learning of external information allows local social influences to carry shared views resulting in the potential emergence of modified homophyllic structures, for example to capture the notion that those who view external information sources in a similar manner might be inclined to demonstrate higher affinities among themselves. We show that this form of social learning of externally expounded beliefs has a learnable dynamic which achieves convergence, and can mirror scenarios where external sources can bring about consensus among opposed cliques, or break emerging consensus. We illustrate the working of the learning model on a simple example.