Stochastic Binary Opinion Model

We 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 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" when one opinion is dominant.