  We propose and study a stochastic binary opinion model where agents in a
group are considered to hold an opinion of 0 or 1 at each moment. An agent in
the group updates his/her opinion based on the group's opinion configuration
and his/her \emph{personality}. Considering the number of agents with opinion 1
as a continuous time Markov process, we analyze the long-term probabilities for
large population size in relation to the personalities of the group. In
particular, we focus on the question of ``balance'' where both opinions are
present in nearly equal numbers as opposed to ``dominance'' where one opinion
is present in a greater number.
