The role of voting intention in public opinion polarization

TL;DR

This paper models voting intention dynamics, showing how agents' biases and interactions lead to polarization or consensus, with the system's behavior depending on the weight assigned to self versus others' opinions.

Contribution

It introduces a simple agent-based model for voting dynamics, analyzing how different weighting of self versus others' opinions affects polarization and consensus formation.

Findings

Agents quickly reach extremist consensus when they prioritize others' opinions.

A quasi-stationary polarized state emerges for certain parameters before consensus.

The lifetime of polarization diverges as the weight on self increases, following a specific scaling law.

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 $p \in [0,1]$. When an agent $i$ interacts with another agent $j$ with propensity $p_j$, then $i$ either increases its propensity $p_i$ by $h$ with probability $P_{ij}=\omega p_i+(1-\omega)p_j$, or decreases $p_i$ by $h$ with probability $1-P_{ij}$, where $h$ is a fixed step. We analyze the system by a rate equation approach and contrast the results with Monte Carlo simulations. We found that the dynamics of propensities depends on the weight $\omega$ that an agent assigns to its own propensity. When all the weight is assigned to the interacting partner ($\omega=0$), 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 $\omega>0$ the system first reaches a quasi-stationary 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 $\tau$, diverges as $\tau \sim (1-\omega)^{-2} \ln N$ when $\omega$ approaches $1$, where $N$ is the system size. Finally, a continuous approximation allows to derive a transport equation whose convection term is compatible with a drift of particles from the center towards the extremes.