  Building on recent work by Medvedev (2014) we establish new connections
between a basic consensus model, called the voting model, and the theory of
graph limits. We show that in the voting model if consensus is attained in the
continuum limit then solutions to the finite model will eventually be close to
a constant function, and a class of graph limits which guarantee consensus is
identified. It is also proven that the dynamics in the continuum limit can be
decomposed as a direct sum of dynamics on the connected components, using
Janson's definition of connectivity for graph limits. This implies that without
loss of generality it may be assumed that the continuum voting model occurs on
a connected graph limit.
