  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.
