  We consider the discrete-time voter model on complete bipartite graphs and
study the quasi-stationary distribution (QSD) for the model as the size of one
of the partitions tends to infinity while the other partition remains fixed. We
show that the QSDs converge weakly to a nontrivial limit which features a
consensus with the exception of a random number of dissenting vertices in the
"large" partition. Moreover, we explicitly calculate the law of the number of
dissenters and show that it follows the heavy-tailed Sibuya distribution with
parameter depending on the size of the "small" partition. Our results rely on a
discrete-time analogue of the well-known duality between the continuous-time
voter model and coalescing random walks which we develop in the paper.
