Social Influencing and Associated Random Walk Models: Asymptotic Consensus Times on the Complete Graph
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.
Keywords
Cite
@article{arxiv.1103.4659,
title = {Social Influencing and Associated Random Walk Models: Asymptotic Consensus Times on the Complete Graph},
author = {W. Zhang and C. Lim and S. Sreenivasan and J. Xie and B. K. Szymanski and G. Korniss},
journal= {arXiv preprint arXiv:1103.4659},
year = {2011}
}