Social Influencing and Associated Random Walk Models: Asymptotic   Consensus Times on the Complete Graph
  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. 
W. Zhang, C. Lim, S. Sreenivasan, J. Xie, B.K. Szymanski, G. Korniss
physics.soc-ph cond-mat.stat-mech cs.SI