Collective decision analysis and social learning in Boolean networks

In this paper, the social learning in Boolean networks is investigated. Each agent makes its decision and takes an action from two possible actions in light of its private belief and the actions of neighbors. In the decision process based on the majority principle, if all agents do not receive private signal about the underlying state of the world, then all agents will make the same decision under mild assumptions but the collective decision is false with a positive probability. If at least one agent can receive private signal, then, with updating their private beliefs in a Bayesian way, all agents will make the same decision and the common decision is right with probability one, that is, the asymptotic learning is achieved almost surely.