Reaching Consensus in Social Networks

This paper considers network based non-Bayesian opinion formation on a linearly ordered set of opinions. The general class of constricting and continuous Markov revision functions, that contains the standard weighted average revision functions, is analyzed. A revision function is constricting if the revised opinion is strictly higher (lower) ranked than the lowest (highest) ranked observed opinion. The main advantages of the general approach are that (i) it captures a wide range of applications, and (ii) the constricting property is easily testable. It is shown that asymptotic consensus occurs in strongly connected networks whenever the revision functions of all agents are constricting and continuous. The revision function does not need to be the same across agents, or across time for a given agent. Additionally, asymptotic consensus is shown to hold almost surely if agents are subject to a natural class of probabilistic mistakes when forming their opinions.