  We propose a generalized framework for the study of voter models in complex
networks at the the heterogeneous mean-field (HMF) level that (i) yields a
unified picture for existing copy/invasion processes and (ii) allows for the
introduction of further heterogeneity through degree-selectivity rules. In the
context of the HMF approximation, our model is capable of providing
straightforward estimates for central quantities such as the exit probability
and the consensus/fixation time, based on the statistical properties of the
complex network alone. The HMF approach has the advantage of being readily
applicable also in those cases in which exact solutions are difficult to work
out. Finally, the unified formalism allows one to understand previously
proposed voter-like processes as simple limits of the generalized model.
