Constrained opinion dynamics: freezing and slow evolution

We study opinion formation in a population of leftists, centrists and rightist. In an interaction between neighbouring agents, a centrist and a leftist can become both centrists or leftists (and similarly for a centrist and a rightist), while leftists and rightists do not affect each other. The evolution is controlled by the initial density of centrists (o). For any spatial dimension the system reaches a centrist consensus with probability rho(o), while with probability 1 - rho(o) the final state is either an extremist consensus, or a frozen population of leftists and rightists. In one dimension, we determine the opinion evolution by mapping the system onto a spin-1 Ising model with zero- temperature Glauber kinetics. The approach to the final state is governed by a t(-->psi) long-time tail, with psi --> 2rho(o)/pi as rho(o) --> 0. In the one-dimensional frozen state, the length distribution of single-opinion domains has an algebraic small-size tail x(-2(l -psi)) and the average domain length is L-2psi, where L is the length of the system.