A data-driven kinetic model for opinion dynamics with social network contacts

TL;DR

The paper advances a data-driven kinetic framework for opinion dynamics on social networks by coupling a social-contact distribution, learned from Twitter data, with opinion updates governed by binary interactions. Through grazing (quasi-invariant) limits, it derives a Fokker-Planck description and analyzes steady states, obtaining lognormal contact distributions and explicit stationary opinion profiles under simplifying assumptions. The authors validate the model qualitatively with simulations of bounded-confidence and Sznajd-type dynamics, and quantitatively by calibrating kernels to Twitter sentiment data on topics such as politics and climate, using Wasserstein and L1 discrepancies. The work demonstrates how data-driven kernel reconstruction can reveal mechanisms of consensus and polarization driven by influencers, offering a tractable framework for predicting and potentially guiding online opinion dynamics. Its data-driven calibration and tractable FP limit hold practical value for understanding social-media-driven phenomena and informing interventions aimed at reducing polarization.

Abstract

Opinion dynamics is an important and very active area of research that delves into the complex processes through which individuals form and modify their opinions within a social context. The ability to comprehend and unravel the mechanisms that drive opinion formation is of great significance for predicting a wide range of social phenomena such as political polarization, the diffusion of misinformation, the formation of public consensus, and the emergence of collective behaviors. In this paper, we aim to contribute to that field by introducing a novel mathematical model that specifically accounts for the influence of social media networks on opinion dynamics. With the rise of platforms such as Twitter, Facebook, and Instagram and many others, social networks have become significant arenas where opinions are shared, discussed, and potentially altered. To this aim after an analytical construction of our new model and through incorporation of real-life data from Twitter, we calibrate the model parameters to accurately reflect the dynamics that unfold in social media, showing in particular the role played by the so-called influencers in driving individual opinions towards predetermined directions.

Figures (11)

• Figure 2.1: Profiles of the value function \ref{['eq:vf']} for different choices of $\delta$ and $\mu=0.15$. The red dashed lines represent the bounds \ref{['eq:psibounds']}
• Figure 2.2: Representation of the social network using a sample of $N_{\texttt{s}}=400$ accounts from the $N=10^6$ data-set extracted from Twitter. Sizes of the bubbles are proportional to the logarithm of agents' contacts,where edges are reconstructed based on the statistical distribution of the connections
• Figure 2.3: Comparison between the tails of the data distribution and the different possible equilibrium distributions of the Fokker-Planck models of Section \ref{['kinetic_model']}
• Figure 3.4: Profiles of the steady state solution $g_\infty(v)$ and its numerical approximation in the case of $\sigma^2/\alpha = 1$ (left) and $\sigma^2/\alpha = 0.2$ (right), both with scaling parameter $\epsilon = 0.01$
• Figure 4.5: Test $1$, $\sigma^2/\alpha = 0.005$. The pictures show the time evolution of the distribution function $f(v,c,t)$ for $t=0,4,8,12,16,20$ for a homogeneous distribution of the number of connections with respect to opinions. After the emergence of two clusters the agents reach consensus at the final time

Theorems & Definitions (1)

• proof