Modified Axelrod Model Showing Opinion Convergence And Polarization In Realistic Scale-Free Networks

TL;DR

The study extends the Axelrod opinion‑dynamics framework by embedding agents in a Barabási–Albert scale-free network, representing opinions as continuous values in the interval $[-1,1]$, and introducing both convergence and divergence via an agreement threshold $a$. Simulations reveal persistent, population‑wide opinion polarization with a dominant cluster and characteristic cluster‑size scaling influenced by the network topology; increasing connectivity and decreasing $a$ amplify polarization. Mitigation via empathetic agents shows limited success unless a sizable fraction of highly connected agents adopt empathetic behavior, particularly when targeted at influential nodes or applied after polarization develops. Overall, the work highlights the critical roles of network structure and bounded-confidence dynamics in shaping polarization and offers targeted intervention insights for reducing polarization in real-world social systems.

Abstract

Axelrod model is an opinion dynamics model such that each agent on a square lattice has a finite number of possible nominal opinions on a finite number of issues that are usually called features in the field. Moreover, its dynamics between two agents is assimilative in the sense that the number of agreeing features between them never decreases upon interaction. Here we modify this model to study opinion convergence, polarization and more importantly to find ways to reduce opinion polarization in an already polarized population. We do so by changing or adding several elements from complex network and continuous opinion dynamics research. First, we put agents in a scale-free network. Second, we adopt the bounded confidence model by representing our agent's opinions by numbers in $[-1,1]$ those distances follow the standard Euclidean metric. Third, our rules allow both convergence and divergence of their resultant opinions after a pair of agents interacts. As a result, our modified model offers a more comprehensive exploration of opinion dynamics. Computer simulation results of our model show scaling behavior and a notable trend in opinion polarization on all features in the majority of reasonable simulation parameters. To mitigate this polarization, we introduce empathetic agents that work actively to reduce opinion differences. However, our findings indicate limited success in the approach for the most effective way is to change the behavior of a significant portion of highly connected agents. This research contributes to the understanding of opinion dynamics within society and highlights the nuanced complexities that arise when considering factors such as network structure and continuous opinion values. Our results prompt further exploration and open avenues for future investigations into effective methods of reducing opinion polarization.

Figures (11)

• Figure 1: Histograms showing the time evolution of opinion distribution with all but the parameter $t$ taken from Table \ref{['T:parameters']}. The $x$-axes of all subplots are the opinions in $[-1,1]$ and the $y$-axes are the occurrence frequencies of the opinion. Although the initial opinions concentrate around $0$, the system evolves to a state of extreme opinion polarization in the long time limit in which nearly all agents have extreme opinions on all features. Note that the $y$-axis ranges of all histogram subplots in this paper may be different.
• Figure 2: Opinion distributions after $N t/2$ time steps with $t = 200$ for different values of $N$. These subplots show no significant difference in opinion distribution for different $N$.
• Figure 3: Opinion cluster distributions of a typical run of our model on (a) a B-A network and (b) $20\times 20$ lattice using parameters in Table \ref{['T:parameters']} except that $N = 400$. Agents in the same opinion cluster are represented by dots of the same color; and no adjacent cluster is of the same color. Each adjacent agent pair in (a) is linked by a solid black line. In (b), a thick solid black (thin dashed black) line is drawn between a pair of adjacent similar (dissimilar) agents.
• Figure 4: The average number of opinion cluster divided by the number of agents $n/N$ as a function of cluster size $s$ and number of agents $N$ on a B-A network in (a) log-log and (b) semi-log plots as well as on a square lattice in (c) log-log and (d) semi-log plots using parameters in Table \ref{['T:parameters']} except that $N$ can vary. The red dots, green squares and blue triangles are for $N = 10^3$, $10^4$ and $10^5$, respectively for the B-A network and the responding closest square number for the square lattice. Each set of data is obtained by averaging over $1024$ independent runs. The uncertainty of $\log_{10}[n(s,N)/N]$ of each data point is of order of $(N S)^{-1/2}/n$ and the corresponding error bar is omitted in the subfigures for clarity. The dashed line in each subfigure is the best fit curve whose parameters are shown in Table \ref{['T:fit_parameters']}.
• Figure 5: Opinion distribution after $N t /2$ time steps with $N = 1000$ and $t = 200$ for different values of $m$. These subplots show no significant difference in opinion distribution for different $m$.