We define a stochastic reaction-diffusion process that describes a consensus formation
in a nonsedentary population. The process is a diffusive version of the Majority Vote
model, where the state update follows two stages: in the first stage, spins are allowed
to jump to a random neighbor node with probabilities D_+ and D_− for the respective
spin orientations, and in the second stage, the spins in the same node can change its
values according to the majority vote update rule. The model presents a consensus
formation phase when concentration is greater than a threshold value and a
paramagnetic phase on the converse for equal diffusion probabilities, i.e., maintaining
the inversion symmetry. Setting unequal diffusion probabilities for the respective spin
orientations is the same as applying an external magnetic field. The system undergoes
a discontinuous phase transition for concentrations higher than the critical threshold on
the external field. The individuals that diffuse more dominate the stationary collective
opinion.