Mean Field Studies of a Society of Interacting Agents

Abstract

We model a society of agents that interact in pairs by exchanging for/against opinions about issues using an algorithm obtained with methods of Bayesian inference and maximum entropy. The agents gauge the incoming information with respect to the mistrust attributed to the other agents. There is no underlying lattice and all agents interact among themselves. The interaction pair can be described as a dynamics along the gradient of the logarithm of the evidence. By using a symmetric version of the two-body interactions we introduce a Hamiltonian for the whole society. Knowledge of the expected value of the Hamiltonian is relevant information for the state of the society. In the case of uniform mistrust, independent of the pair of agents, the phase diagram of the society in a mean field approximation shows a phase transition that separates an ordered phase where opinions are to a large extent shared by the agents and a disordered phase of dissension of opinions.