Opinion Dynamics and Influencing on Random Geometric Graphs

Abstract

We investigate the two-word Naming Game on two-dimensional random geometric graphs. Studying this model advances our understanding of the spatial distribution and propagation of opinions in social dynamics. A main feature of this model is the spontaneous emergence of spatial structures called opinion domains which are geographic regions with clear boundaries within which all individuals share the same opinion. We provide the mean-field equation for the underlying dynamics and discuss several properties of the equation such as the stationary solutions and two-time-scale separation. For the evolution of the opinion domains we find that the opinion domain boundary propagates at a speed proportional to its curvature. Finally we investigate the impact of committed agents on opinion domains and find the scaling of consensus time.

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• Curvature-driven growth and interfacial noise in the voter model with self-induced zealots
• A Graphical Representation of Membrane Filtration
• Navigability of Random Geometric Graphs in the Universe and Other Spacetimes
• The Impact of Social Attractiveness on Casual Group Formation: Power-Law Group Sizes and Suppressed Percolation
• Resource-Mediated Consensus Formation