While deciding which political candidate to vote for, which cellphone to purchase, or whether to wear a face-mask in public, individuals tend to gather relevant information from internet-based information sources as well as from the social networks they belong to. To study the impact of such social networks and external sources of information on the evolution of individuals’ beliefs, several non-Bayesian models of social learning have been proposed during the last few years. However, most of these models make two unrealistic assumptions: (a) the network structure is deterministic (non-random), and (b) the network is strongly connected over periodically occurring time intervals (i.e., it is uniformly strongly connected).
To address these shortcomings, we show that under mild assumptions on the connectivity of the network, all the agents learn the true state of the world asymptotically almost surely provided the sequence of the associated weighted adjacency matrices belongs to Class P* (a broad class of stochastic chains that subsumes uniformly strongly connected chains). We then show how our main result applies to a few variants of the original model, namely, inertial non-Bayesian learning, learning via diffusion and adaptation, and learning in the presence of link failures. Besides, we show that our main result is an extension of a few known results that pertain to learning on time-varying graphs. We also show that if the network of influences is balanced in a certain sense, then asymptotic learning occurs almost surely even in the absence of uniform strong connectivity.