  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
$\epsilon\geq \epsilon_c=\frac{1}{9}$. 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.
