Impact of the Network Size and Frequency of Information Receipt on Polarization in Social Networks

TL;DR

The models of opinion formation in individuals are recast to create a proper dynamical system and inject the idea of clock time into evolving individuals’ opinions and the extent of polarisation is defined as the width of the region around neutral within which an individual is unable to have an opinion.

Abstract

Opinion Dynamics is an interdisciplinary area of research. Psychology and Sociology have proposed models of how individuals form opinions and how social interactions influence this process. Socio-Physicists have interpreted patterns in opinion formation as arising from non-linearity in the underlying process, shaping the models. Agent-based modeling has offered a platform to study the Opinion Dynamics of large groups. This paper recasts recent models in opinion formation into a proper dynamical system, injecting the idea of clock time into evolving opinions. The time interval between successive receipts of new information (frequency of information receipts) becomes a factor to study. Social media has shrunk time intervals between information receipts, increasing their frequency. The recast models show that shorter intervals and larger networks increase an individual's propensity for polarization, defined as an inability to hold a neutral opinion. A Polarization number based on sociological parameters is proposed, with critical values beyond which individuals are prone to polarization, depending on psychological parameters. Reduced time intervals and larger interacting groups can push the Polarization number to critical values, contributing to polarization. The Extent of Polarization is defined as the width of the region around neutral within which an individual cannot hold an opinion. Results are reported for model parameters found in the literature. The findings offer an opportunity to adjust model parameters to align with empirical evidence, aiding the study of Opinion Dynamics in large social networks using Agent-Based Modeling.

Figures (7)

• Figure 1: At time $t=0$, there exists a specific initial value of $A$ that will decay with time and when new information arrives after time $\tau$, spike back to the same initial value. For $\tau=6$ hours, we illustrate the time history both for an arbitrary initial value and the specific initial value.
• Figure 2: For a given polarization number (P), Attention ($A$) oscillates between $A_{UP}$ and $A_{LP}$. Both values increase with decreasing polarization number ($P$) and eventually converge to $A_{max}$, in this case, 2.
• Figure 3: For a given periodicity of information arrival ($\tau$), starting from any arbitrary value, attention ($A$) quickly converges to the corresponding periodic solution. For $\tau=6$ hours, two cases of $N$ are illustrated.
• Figure 4: Parameter values: $A_{\text{crit}}=0.5$, $A_{\text{max}}=2.0$, $k=0.2$. The Cusp Catastrophic surface for $O$ is scaled such that $-1 \leq O \leq 1$ for $0 \leq A \leq A_{\text{max}}$ and $-1 \leq I \leq 1$. No bias was required and the scaling factor used is inverse of max($A$) = 1.475687. (A) The Cusp Catastrophe Surface. The fold begins at $A=A_{\text{crit}}=0.5$, and the surface extends until $A=A_{\text{max}}=2.0$. (B) The cross-section at $A=0.3$ reveals that $O$ is stable over its full range of values across neutral. (C) The cross-section at $A=1.8$ reveals no stable opinions in the range $-O_{\text{sn}} \leq O \leq O_{\text{sn}}$. Individuals can either have opinions in the band $-1 \leq O \leq -O_{\text{sn}}$ or $O_{\text{sn}} \leq O \leq 1$. The extent of polarization at $A=1.8$ is $E_p=O_{\text{sn}}=0.46$. (D) The shaded region indicates the area where no stable opinions are possible. The extent of polarization, $E_p$, is the semi-height of the shaded region. $E_p = 0$ for $A \leq A_{\text{crit}}$ and increases thereafter with $A$.
• Figure 5: Critical values of polarization numbers, $P_1$ and $P_2$, bracket the transition region. On one side lies the region where the extent of polarization, $E_p$= $0$ and the other side where $E_p > 0$ respectively.