Naive learning in social networks with random communication

We study social learning in a social network setting where agents receive independent noisy signals about the truth. Agents naively update beliefs by repeatedly taking weighted averages of neighbors' opinions. The weights are fixed in the sense of representing average frequency and intensity of social interaction. However, the way people communicate is random such that agents do not update their belief in exactly the same way at every point in time. Our findings, based on Theorem 1, Corollary 1 and simulated examples, suggest the following. Even if the social network does not privilege any agent in terms of influence, a large society almost always fails to converge to the truth. We conclude that wisdom of crowds seems an illusive concept and bares the danger of mistaking consensus for truth.