Commitment Versus Persuasion in the Three-Party Constrained Voter Model

In the framework of the three-party constrained voter model, where voters of two radical parties (A and B) interact with "centrists" (C and C), we study the competition between a persuasive majority and a committed minority. In this model, A's and B's are incompatible voters that can convince centrists or be swayed by them. Here, radical voters are more persuasive than centrists, whose sub-population comprises susceptible agents C and a fraction ζ of centrist zealots C. Whereas C's may adopt the opinions A and B with respective rates 1+δ and 1+δ (with δ≥δ&0), C's are committed individuals that always remain centrists. Furthermore, A and B voters can become (susceptible) centrists C with a rate 1. The resulting competition between commitment and persuasion is studied in the mean field limit and for a finite population on a complete graph. At mean field level, there is a continuous transition from a coexistence phase when ζ<Δ=δ/(1+δ) to a phase where centrism prevails when ζ≥Δ. In a finite population of size N, demographic fluctuations lead to centrism consensus and the dynamics is characterized by the mean consensus time τ. Because of the competition between commitment and persuasion, here consensus is reached much slower (ζ<Δ) or faster (ζ≥Δ) than in the absence of zealots (when τ~N). In fact, when ζ<Δ and there is an initial minority of centrists, the mean consensus time grows as τ~Ne, with N≫1 and γ = δ - ζ(1 + ln (δ/ζ)) + O(δ ). The dynamics is thus characterized by a metastable state where the most persuasive voters and centrists coexist when δ&δ, whereas all species coexist when δ=δ. When ζ≥Δ and the initial density of centrists is low, one finds τ~lnN (when N≫1). Our analytical findings are corroborated by stochastic simulations. © 2012 Springer Science+Business Media New York.