Bi-layer voter model: Modeling intolerant/tolerant positions and bots in opinion dynamics

TL;DR

This paper introduces a bi-layer voter model incorporating tolerance levels and social bots to study opinion dynamics, revealing how intolerance and bots influence consensus formation and slow down or dominate opinion evolution.

Contribution

It presents a novel multiplex network model that integrates tolerance dynamics and social bots, analyzing their effects on opinion consensus and polarization.

Findings

Intolerance causes a two-stage consensus process with a slowdown for highly intolerant agents.

Social bots can dominate opinion formation, leading to a consensus aligned with their opinion.

The model quantifies how tolerance and bots affect the timescales of opinion dynamics.

Abstract

The diffusion of opinions in Social Networks is a relevant process for adopting positions and attracting potential voters in political campaigns. Opinion polarization, bias, targeted diffusion, and the radicalization of postures are key elements for understanding voting dynamics. In particular, social bots are a new element that can have a pronounced effect on the formation of opinions during elections by, for instance, creating fake accounts in social networks to manipulate elections. Here we propose a voter model incorporating bots and radical or intolerant individuals in the decision-making process. The dynamics of the system occur in a multiplex network of interacting agents composed of two layers, one for the dynamics of opinions where agents choose between two possible alternatives, and the other for the tolerance dynamics, in which agents adopt one of two tolerance levels. The tolerance accounts for the likelihood to change opinion in an interaction, with tolerant (intolerant) agents switching opinion with probability $1.0$ ($\gamma \le 1$). We find that intolerance leads to a consensus of tolerant agents during an initial stage that scales as $\tau^+ \sim \gamma^{-1} \ln N$, who then reach an opinion consensus during the second stage in a time that scales as $\tau \sim N$, where $N$ is the number of agents. Therefore, very intolerant agents ($\gamma \ll 1$) could considerably slow down dynamics towards the final consensus state. We also find that the inclusion of a fraction $\sigma_{\mathbb{B}}^-$ of bots breaks the symmetry between both opinions, driving the system to a consensus of intolerant agents with the bots' opinion. Thus, bots eventually impose their opinion to the entire population, in a time that scales as $\tau_B^- \sim \gamma^{-1}$ for $\gamma \ll \sigma_{\mathbb{B}}^-$ and $\tau_B^- \sim 1/\sigma_{\mathbb{B}}^-$ for $\sigma_{\mathbb{B}}^- \ll \gamma$.