  We investigate the dynamics of the voter model in which the population itself
changes endogenously via the birth-death process. There are two species of
voters, labeled A and B, and the population of each species can grow or shrink
by the birth-death process at equal rates $b$. Individuals of opposite species
also undergo voter model dynamics in which an AB pair can equiprobably become
AA or BB with rate $v$---neutral evolution. In the limit $b/v\to\infty$, the
distribution of consensus times varies as $t^{-3}$ and the probability that the
population size equals $n$ at the moment of consensus varies as $n^{-3}$. As
the birth/death rate $b$ is increased, fixation occurs more more quickly; that
is, population fluctuations promote consensus.
