Majority Rule in Nonlinear Opinion Dynamics
Using a nonlinear model of opinion dynamics on networks, we show the existence of asymmetric majority rule solutions for symmetric initial opinion distributions and symmetric network structure. We show that this occurs in triads as the result of a pitchfork bifurcation and arises in both chain and complete topologies with symmetric as well as asymmetric coupling. Analytical approximations for bifurcation boundaries are derived which closely match numerically-obtained boundaries. Bifurcation-induced symmetry breaking represents a novel mechanism for generating majority rule outcomes without built-in structural or dynamical asymmetries; however, the policy outcome is fundamentally unpredictable.
KeywordsCoupling Strength Majority Rule Center Node Chain Network Coupling Function
We acknowledge the support of the Defense Threat Reduction Agency and the Office of Naval Research under grant HDTRA1-10-1-0075.
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