  We generalize Galam's model of opinion spreading by introducing three
competing choices. At each update, the population is randomly divided in groups
of three agents, whose members adopt the opinion of the local majority. In the
case of a tie, the local group adopts opinion A, B or C with probabilities
alpha, beta and (1-alpha-beta) respectively. We derive the associated phase
diagrams and dynamics by both analytical means and simulations. Polarization is
always reached within very short time scales. We point out situations in which
an initially very small minority opinion can invade the whole system.
