We investigate majority rule dynamics in a population with two classes of people, each with two opinion states $pm 1$, and with tunable interactions between people in different classes. In an update, a randomly selected group adopts the majority opinion if all group members belong to the same class; if not, majority rule is applied with probability $epsilon$. Consensus is achieved in a time that scales logarithmically with population size if $epsilongeq epsilon_c=frac{1}{9}$. For $epsilon <epsilon_c$, the population can get trapped in a polarized state, with one class preferring the $+1$ state and the other preferring $-1$. The time to escape this polarized state and reach consensus scales exponentially with population size.
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