7 de enero de 2003

Constrained opinion dynamics: Freezing and slow evolution

F. Vazquez, P. L. Krapivsky, S. Redner, J. Phys. A: Math. Gen. 36, L61 (2003) 

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 ρ0. For any spatial dimension the system reaches a centrist consensus with probability ρ0, while with probability 1 − ρ0 the final state is either an extremist consensus, or a frozen population of leftists and rightists. In one dimension,we determine the opinion evolution bymapping the system onto a spin-1 Ising model with zero-temperature Glauber kinetics. The approach to the final state is governed by a t−ψ long-time tail, with ψ → 2ρ0/π as ρ0 → 0. In the one-dimensional frozen state, the length distribution of single-opinion domains has an algebraic small-size tail x−2(1−ψ) and the average domain length is L, where L is the length of the system.