  We define a stochastic reaction-diffusion process that describes a consensus
formation in a non-sedentary 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 hop to neighbor nodes with different
probabilities for the respective spin orientation, 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. The
threshold vanishes for unequal diffusion probabilities, which means that the
system has a consensus state for all values of population densities. The
stationary collective opinion is dominated by the individuals that diffuse
more.
