We investigate the opinion dynamics by extending the majority rule model to a
preferential selection model, in which agents choose opinions with some
probability rather than absolutely follow the majority. In the model, agent $i$
agrees with one of binary opinions with the probability that is a power
function of the number of agents holding this opinion among agent $i$ and its
nearest neighbors, where an adjustable parameter $\alpha$ controls the degree
of preferential selection. We find that global consensus is unable to be
reached if $\alpha<1$. Moreover, there exists an optimal value of $\alpha$,
leading to fastest consensus on square lattices, random graphs, small-world
networks and scale-free networks. We explore the evolution of opinion clusters
to understand the emergence of the optimal value of $\alpha$.