  We use Monte Carlo simulations and finite-size scaling theory to investigate
the phase transition and critical behavior of the $S$-state block voter model
on square lattices. It is shown that the system exhibits an order-disorder
phase transition at a given value of the noise parameter, which changes from a
continuous transition for $S\le4$ to a discontinuous transition for $S\ge5$.
Moreover, for the cases of continuous transition, the calculated critical
exponents indicate that the present studied nonequilibrium model system is in
the same universality class of its counterpart equilibrium two-dimensional
S-state Potts model. We also provide a first estimation of the long-range
exponents governing the dependence on the range of interaction of the
magnetization, the susceptibility, and the derivative of Binder's cumulant.
