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Social influencing and associated random walk models: Asymptotic consensus times on the complete graph
W Zhang1, C Lim, S Sreenivasan
1Social and Cognitive Networks Academic Research Center, Rensselaer Polytechnic Institute, 110 8th Street, Troy, New York 12180-3590, USA.
Abstract:
We investigate consensus formation and the asymptotic consensus times in stylized individual- or agent-based models, in which global agreement is achieved through pairwise negotiations with or without a bias. Considering a class of individual-based models on finite complete graphs, we introduce a coarse-graining approach (lumping microscopic variables into macrostates) to analyze the ordering dynamics in an associated random-walk framework. Within this framework, yielding a linear system, we derive general equations for the expected consensus time and the expected time spent in each macro-state. Further, we present the asymptotic solutions of the 2-word naming game and separately discuss its behavior under the influence of an external field and with the introduction of committed agents.
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