Diffusive Majority Vote Model

TL;DR

This paper introduces a diffusive majority vote model where individuals move and update opinions, revealing phase transitions between consensus and paramagnetic states depending on diffusion probabilities and population density.

Contribution

It presents a novel stochastic reaction-diffusion framework for consensus formation, incorporating asymmetric diffusion and analyzing phase behavior in opinion dynamics.

Findings

Consensus phase exists above a population density threshold

Equal diffusion probabilities lead to a paramagnetic phase

Unequal diffusion probabilities result in consensus for all densities

Abstract

We define a stochastic reaction-diffusion process that describes a consensus formation in a non-sedentary population. The process is a diffusive version of the Majority Vote model, where the state update follows two stages: in the first stage, spins are allowed to hop to neighbor nodes with different probabilities for the respective spin orientation, and in the second stage, the spins in the same node can change its values according to the majority vote update rule. The model presents a consensus formation phase when concentration is greater than a threshold value, and a paramagnetic phase on the converse for equal diffusion probabilities, i.e., maintaining the inversion symmetry. The threshold vanishes for unequal diffusion probabilities, which means that the system has a consensus state for all values of population densities. The stationary collective opinion is dominated by the individuals that diffuse more.