Nonlinear Opinion Dynamics on Networks

A model which treats group decision making as nonlinear opinion dynamics occurring over a network is presented. The model makes predictions regarding the interaction of network structure and initial disagreement level upon decision outcomes and consensus formation. The model displays bifurcations at high disagreement levels which lead to behaviors that are qualitatively distinct from those at low disagreement. For example, at high disagreement, the model exhibits asymmetric, majority rule outcomes that arise even when the system is symmetric with respect to the distribution of initial opinions and network structure. Analytical approximations for the bifurcation boundaries agree well with numerically-determined boundaries. An ongoing experimental effort involving the use of online discussion groups to test the model predictions is briefly described.