Sasha Glendinning | Searcharxiv

arXiv2026

Speaking of Opinions: Comparing Approaches to Modelling Opinion Manipulation

This review outlines the major approaches to modelling opinion formation and manipulation in mathematics and computer science. Key tools such as ordinary and partial differential equations, stochastic models, control theory, and interaction protocols are introduced and compared as methods for describing manipulation. The review is separated into those models using a continuous opinion space and those using discrete or binary opinions, with the advantages and disadvantages of each discussed. Finally, the authors provide an interdisciplinary perspective on the field of opinion dynamics and its social significance.

math.OC↗

arXiv2025

What is the optimal way to lie? From microscopic to kinetic descriptions of consensus control

We establish an approach for consensus control of opinion dynamics by introducing a liar to the classical system. The liar's aim is to steer the population towards consensus at their goal opinion by showing 'apparent opinions', or 'lies', to members of the population. We analyse this as an optimal control problem for how best to lie to a population in order to guarantee the consensus that the liar desires. We consider a range of regularisations, each motivated by some social convention, such as the liar wanting to present an opinion close to their true opinion. For each regularisation, we demonstrate the effect of instantaneous controls. Furthermore, we introduce a Boltzmann-type description for the corresponding kinetic system and present analysis and numerical results for the resulting Boltzmann and Fokker-Planck equations.

math.OC↗