  An exact spectral analysis of the Markov Propagator for the Voter model is
presented for the complete graph, and extended to the complete bipartite graph
and uncorrelated random networks. Using a well-defined Martingale approximation
in diffusion-dominated regions of phase space, which is almost everywhere for
the Voter model, this method is applied to compute analytically several key
quantities such as exact expressions for the $m$ time step propagator of the
Voter model, all moments of consensus times, and the local times for each
macrostate. This spectral method is motivated by a related method for solving
the Ehrenfest Urn problem and by formulating the Voter model on the complete
graph as an Urn model. Comparisons of the analytical results from the spectral
method and numerical results from Monte-Carlo simulations are presented to
validate the spectral method.
