  In this paper we are concerned with bias voter models on trees and lattices,
where the vertex in state 0 reconsiders its opinion at a larger rate than that
of the vertex in state 1. For the process on tree with product measure as
initial distribution, we obtain a mean field limit at each moment of the
probability that a given vertex is in state 1 as the degree of the tree grows
to infinity. Furthermore, for our model on trees and lattices, we show that the
process converges weakly to the configuration where all the vertices are in
state 1 when the rate at which a vertex in state 0 reconsiders its opinion is
sufficiently large. The approach of graphical representation and the complete
convergence theorem of contact process are main tools for the proofs of our
results.
