  We study the collective motion of a large set of self-propelled particles
subject to voter-like interactions. Each particle moves on a two-dimensional
space at a constant speed in a direction that is randomly assigned initially.
Then, at every step of the dynamics, each particle adopts the direction of
motion of a randomly chosen neighboring particle. We investigate the time
evolution of the global alignment of particles measured by the order parameter
$\varphi$, until complete order $\varphi=1.0$ is reached (polar consensus). We
find that $\varphi$ increases as $t^{1/2}$ for short times and approaches
exponentially fast to $1.0$ for long times. Also, the mean time to consensus
$\tau$ varies non-monotonically with the density of particles $\rho$, reaching
a minimum at some intermediate density $\rho_{\tiny \mbox{min}}$. At
$\rho_{\tiny \mbox{min}}$, the mean consensus time scales with the system size
$N$ as $\tau_{\tiny \mbox{min}} \sim N^{0.765}$, and thus the consensus is
faster than in the case of all-to-all interactions (large $\rho$) where
$\tau=2N$. We show that the fast consensus, also observed at intermediate and
high densities, is a consequence of the segregation of the system into clusters
of equally-oriented particles which breaks the balance of transitions between
directional states in well mixed systems.
