Opinion dynamics with noisy information

This paper considers a social opinion model with noisy information when one agent obtains the opinion of another. Stochastic approximation with bounded confidence is introduced to update the opinions. The asymptotic behavior of the stochastic algorithm is intimately related to a deterministic vector field. We show that the presence of noise can cause a defragmentation of the state space. This in turn can generate more orderly collective behavior, which is very different from noiseless models which have the well known fragmentation property during the evolution of the individual opinions.