The undecided have the key: Interaction-driven opinion dynamics in a three state model

TL;DR

This paper introduces a novel three-state opinion model where agents can be for one of two opinions or undecided, exploring how initial undecidedness and conviction sensitivity influence collective states like consensus or polarization.

Contribution

The study presents a new opinion dynamics model incorporating undecided agents and analyzes how initial conditions and interaction sensitivities affect social consensus and polarization.

Findings

Undecided agents are crucial for reaching consensus.

The model exhibits diverse outcomes: consensus, polarization, or indecision.

A minimum fraction of undecided agents influences the dominant opinion.

Abstract

The effects of interpersonal interactions on individual's agreements result in a social aggregation process which is reflected in the formation of collective states, as for instance, groups of individuals with a similar opinion about a given issue. This field, which has been a longstanding concern of sociologists and psychologists, has been extended into an area of experimental social psychology, and even has attracted the attention of physicists and mathematicians. In this article, we present a novel model of opinion formation in which agents may either have a strict preference for a choice, or be undecided. The opinion shift emerges during interpersonal communications, as a consequence of a cumulative process of conviction for one of the two extremes opinions through repeated interactions. There are two main ingredients which play key roles in determining the steady state: the initial fraction of undecided agents and the conviction's sensitivity in each interaction. As a function of these two parameters, the model presents a wide range of possible solutions, as for instance, consensus of each opinion, bi-polarisation or convergence of undecided individuals. We found that a minimum fraction of undecided agents is crucial not only for reaching consensus of a given opinion, but also to determine a dominant opinion in a polarised situation. In order to gain a deeper comprehension of the dynamics, we also present the theoretical master equations of the model.