D-MODD: A diffusion model of opinion dynamics derived from online data

We present an empirical derivation of a continuous-time stochastic model for real-world opinion dynamics. To the best of our knowledge, this is the first study to reconstruct the one-step conditional opinion transition kernel directly from longitudinal social-media observations and to infer the corresponding continuous-time stochastic dynamics. Using 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.