This paper introduces a model of boundedly rational observational learning, which is rationally founded and applicable to general environments. Under Quasi-Bayesian updating each action is treated as if it were based only on the private information of its respective observed agent. We analyze the theoretical long run implications of Quasi-Bayesian updating in a model of repeated interaction in social networks with binary actions. We characterize the environments in which consensus and information aggregation is achieved and establish that for any environment information aggregation fails in large networks. Evidence from a laboratory experiment supports Quasi-Bayesian updating and our theoretical predictions.