Role of voting intention in public opinion polarization

Abstract

We introduce and study a simple model for the dynamics of voting intention in a population of agents that have to choose between two candidates. The level of indecision of a given agent is modeled by its propensity to vote for one of the two alternatives, represented by a variable p[0,1]. When an agent i interacts with another agent j with propensity pj, then i either increases its propensity pi by h with probability Pij=ωpi+(1-ω)pj, or decreases pi by h with probability 1-Pij, where h is a fixed step. We assume that the interactions form a complete graph, where each agent can interact with any other agent. We analyze the system by a rate equation approach and contrast the results with Monte Carlo simulations. We find that the dynamics of propensities depends on the weight ω that an agent assigns to its own propensity. When all the weight is assigned to the interacting partner (ω=0), agents' propensities are quickly driven to one of the extreme values p=0 or p=1, until an extremist absorbing consensus is achieved. However, for ω>0 the system first reaches a quasistationary state of symmetric polarization where the distribution of propensities has the shape of an inverted Gaussian with a minimum at the center p=1/2 and two maxima at the extreme values p=0,1, until the symmetry is broken and the system is driven to an extremist consensus. A linear stability analysis shows that the lifetime of the polarized state, estimated by the mean consensus time τ, diverges as τ∼(1-ω)-2lnN when ω approaches 1, where N is the system size. Finally, a continuous approximation allows us to derive a transport equation whose convection term is compatible with a drift of particles from the center toward the extremes.