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

TL;DR

This paper explores how a strategic liar can influence opinion consensus in a population by formulating an optimal control problem, analyzing microscopic and kinetic models, and demonstrating the effects through numerical simulations.

Contribution

It introduces a novel framework for opinion manipulation via lying, combining microscopic, kinetic, and Fokker-Planck models with optimal control analysis.

Findings

Optimal lying strategies can effectively steer opinions towards a desired consensus.

Regularisations based on social conventions influence the liar’s control approach.

Numerical results validate the theoretical models and demonstrate the impact of lying strategies.

Abstract

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.