Constrained opinion dynamics: freezing and slow evolution

FEDERICO VAZQUEZ; PAUL L. KRAPIVSKY; SIDNEY REDNER

JOURNAL OF PHYSICS. A - MATHEMATICAL AND GENERAL

INSTITUTE OF PHYSICS SCIENCE

Año: 2003 vol. 36 p. 61 - 68

0305-4470

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 iseither 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^−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^2ψ , where L is the length of the system.