Does a single zealot affect an infinite group of voters?
A method for studying the exact properties of a class of inhomogeneous stochastic many-body systems is developed and presented in the framework of a voter model perturbed by the presence of a "zealot," an individual allowed to favor an "opinion." We compute exactly the magnetization of this model and find that in one (1D) and two dimensions (2D) it evolves, algebraically ( approximately t(-1/2)) in 1D and much slower ( approximately 1/ln(t) in 2D, towards the unanimity state chosen by the zealot. In higher dimensions the stationary magnetization is no longer uniform: the zealot cannot influence all the individuals. The implications to other physical problems are also pointed out.
Mobilia
Mauro
M
Laboratoire d'Optoélectronique des Matériaux Moléculaires (LOMM), Institut des Matériaux (IMX), Ecole Polytechnique Fédérale de Lausanne, CH-1015 Lausanne EPFL, Switzerland.
D001519:Behavior; D006801:Humans; D008962:Models, Theoretical; D013269:Stochastic Processes