  We determine the ultimate fate of individual opinions in a
socially-interacting population of leftists, centrists, and rightists. In an
elemental interaction between agents, a centrist and a leftist can become both
centrists or both become leftists with equal rates (and similarly for a
centrist and a rightist). However leftists and rightists do not interact. This
interaction step between pairs of agents is applied repeatedly until the system
can no longer evolve. In the mean-field limit, we determine the exact
probability that the system reaches consensus (either leftist, rightist, or
centrist) or a frozen mixture of leftists and rightists as a function of the
initial composition of the population. We also determine the mean time until
the final state is reached. Some implications of our results for the ultimate
fate in a limit of the Axelrod model are discussed.
