  We construct and analyze a random graph model for discrete choice with social
interaction and several groups of equal size. We concentrate on the case of two
groups of equal sizes and we allow the interaction strength within a group to
differ from the interaction strength between the two groups. Given that the
resulting graph is sufficiently dense we show that, with probability one, the
average decision in each of the two groups is the same as in the fully
connected model. In particular, we show that there is a phase transition: If
the interaction among a group and between the groups is strong enough the
average decision per group will either be positive or negative and the decision
of the two groups will be correlated. We also compute the free energy per
particle in our model.
