Stochastic versus deterministic consensus dynamics on graphs

Abstract

We study two agent based models of opinion formation - one stochastic in nature and one deterministic. Both models are defined in terms of an underlying graph; we study how the structure of the graph affects the long time behavior of the models in all possible cases of graph topology. We are especially interested in the emergence of a consensus among the agents and provide a condition on the graph that is necessary and sufficient for convergence to a consensus in both models. This investigation reveals several contrasts between the models - notably the convergence rates - which are explored through analytical arguments and several numerical experiments.

References in corpus (7)

• Statistical physics of social dynamics
• Critical Coarsening without Surface Tension: the Voter Universality Class
• Incomplete ordering of the voter model on small-world networks
• Kinetic limits for pair-interaction driven master equations and biological swarm models
• Kinetic hierarchy and propagation of chaos in biological swarm models
• Stochastic dynamics on hypergraphs and the spatial majority rule model
• Communicability Angles Reveal Critical Edges for Network Consensus Dynamics