Research in sociology studies the effectiveness of social networks in achieving computational tasks. Typically the agents who are supposed to achieve a task are unaware of the underlying social network except their immediate friends. They have limited memory, communication, and coordination. These limitations result in computational obstacles in achieving otherwise trivial computational problems. One of the simplest problems studied in the social sciences involves reaching a consensus among players between two alternatives which are otherwise indistinguishable. In this paper we formalize the computational model of social networks. We then analyze the consensus problem as well as the problem of reaching a consensus which is identical to the majority of the original signals. In both models we seek to minimize the time it takes players to reach a consensus.