In the paper we study the evolution of social belief among rational agents. The agents receive private signals and use them to make decisions on the hypothesis (of two competing hypothesis) under which the signals are generated. Their individual information is imperfect and so are their decisions. We define the concept of social belief about the truthfulness of the two hypotheses and determine it in two cases. In one of them the agents make decisions simultaneously and independently and report the decisions whereas in the other, the agents make decisions sequentially and while making them they not only use their private signals but also the decisions of the previous agents. We discuss several analytical results and demonstrate some of them by computer simulations.