Role of voting intention in public opinion polarization

VAZQUEZ, FEDERICO; SAINTIER, NICOLAS; PINASCO, JUAN PABLO

Physical Review E

AMER PHYSICAL SOC

Año: 2020 vol. 101

2470-0045

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 jwithpropensitypj,thenieitherincreasesitspropensitypi byhwithprobabilityPij =ωpi +(1−ω)pj, or decreases pi by h with probability 1 − Pi j , 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)−2 ln N 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.