  Opinion dynamics is of paramount importance as it provides insights into the
complex dynamics of opinion propagation and social relationship adjustment. It
is assumed in most of the previous works that social relationships evolve much
faster than opinions. This is not always true in reality. We propose an
analytical approximation to study this issue for arbitrary time scales between
opinion adjustment and network evolution. To this end, the coefficient of
determination in statistics is introduced and a one-dimensional stable manifold
is analytically found, i.e., the most likely trajectory. With the aid of the
stable manifold, we further obtain the fate of opinions and the consensus time,
i.e., fixation probability and fixation time. We find that for in-group bias,
the more likely individuals are to adopt the popular opinion, the less likely
the majority opinion takes over the population, i.e., conformity inhibits the
domination of popular opinions. This counter-intuitive result can be
interpreted from a game perspective, in which in-group bias refers to a
coordination game and rewiring probability refers to a rescaling of the
selection intensity. Our work proposes an efficient approximation method to
foster the understanding of opinion dynamics in dynamical networks.
