D-MODD: A Diffusion Model of Opinion Dynamics Derived from Online Data

TL;DR

The results provide the first direct evidence that online opinion dynamics on a polarized topic admit a Markovian description at the operator level, with empirically reconstructed transition kernels accurately reproduced by a data-driven Langevin model, bridging sociophysics, behavioral data, and complex-systems modeling.

Abstract

We present the first empirical derivation of a continuous-time stochastic model for real-world opinion dynamics. Using longitudinal social-media data to infer users opinion on a binary climate-change topic, we reconstruct the underlying drift and diffusion functions governing individual opinion updates. We show that the observed dynamics are well described by a Langevin-type stochastic differential equation, with persistent attractor basins and spatially sensitive drift and diffusion terms. The empirically inferred one-step transition probabilities closely reproduce the transition kernel generated from the D-MODD model we introduce. Our results provide the first direct evidence that online opinion dynamics on a polarized topic admit a Markovian description at the operator level, with empirically reconstructed transition kernels accurately reproduced by a data-driven Langevin model, bridging sociophysics, behavioral data, and complex-systems modeling.

Figures (4)

• Figure 1: Opinion flow density at three representative times in the two-dimensional latent space. Green and red stars mark the barycenters of the pro-climate and denialist anchors, respectively. Colored dots indicate the locations of maximum user density.
• Figure 2: Trajectories of the maximum of the density in each quadrant.
• Figure 3: Drift $A(x)$, Eq.\ref{['eqFx']} (left) and diffusion $D(x)$ (right) estimated from longitudinal opinion trajectories $x$ of users.
• Figure 4: Empirical and modeled one-step opinion transition kernels. Left: Empirical conditional transition probability $P(x_{t+\Delta t}\mid x_t)$ reconstructed from longitudinal user trajectories in the latent opinion space. Middle: Transition density generated by the fitted D-MODD Langevin model using the empirically inferred drift $A(x)$ and diffusion $D(x)$. Right: Distribution of the real parts of the eigenvalues of the empirical and model transition operators; the Wasserstein spectral distance is $<0.01$.