We consider a Bayesian game of pure informational externalities, in which a group of agents learn a binary state of the world from conditionally independent private signals by repeatedly observing the actions of their neighbors in a social network.

 We show that the question of whether or not the agents learn the state of the world depends on the topology of the social network. In particular, we identify a geometric "egalitarianism" condition on the social network graph that guarantees learning in infinite networks, or learning with high probability in large finite networks.