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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 thatof the vertex in state 1. For the process on tree with product measure asinitial distribution, we obtain a mean field limit at each moment of theprobability that a given vertex is in state 1 as the degree of the tree growsto infinity. Furthermore, for our model on trees and lattices, we show that theprocess converges weakly to the configuration where all the vertices are instate 1 when the rate at which a vertex in state 0 reconsiders its opinion issufficiently large. The approach of graphical representation and the completeconvergence theorem of contact process are main tools for the proofs of ourresults.

Mean field limit for bias voter model on regular trees