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We introduce a heterogeneous non-linear q-voter model with zealots and two types of susceptible voters, and study its non-equilibrium properties when the population is finite and well mixed. In this two-opinion model, each individual supports one of two parties and is either a zealot or a susceptible voter of type q1 or q2. While here zealots never change their opinion, a qi-susceptible voter consults a group of qi neighbors at each time step, and adopts their opinion only if all group members agree. We show that this model violates the detailed balance whenever q1≠q2 and has surprisingly rich properties. In particular we find that subpopulations which are more susceptible to opinion change (i.e. lower qi) are a driving force for the system, eventually forcing the system between stationary states. This analysis may go some way to explaining how there can be societal shifts in behaviour or voting stance, such as in recent global elections, despite a significant percentage of the population being robust in their conviction. The behaviour of the model can be studied through a characterization of the non-equilibrium stationary state (NESS) in terms of the probability distribution and currents which are examined through exact numerics and analytical calculation, the latter being obtained using a linear Gaussian approximation.
Authors
Andrew Mellor, University of Oxford, United Kingdom,mellor@maths.ox.ac.uk
Mauro Mobilia, University of Leeds, United Kingdom,m.mobilia@leeds.ac.uk
R.K.P. Zia, Virginia Tech and Iowa State University, U.S., rkpzia@vt.edu