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 divided into models that use a continuous opinion space and those that use discrete opinions, with the advantages and disadvantages of each discussed. Particular emphasis is placed on bounded-confidence models in continuous opinion dynamics and on binary opinion models in the discrete setting. Finally, the authors provide an interdisciplinary perspective on opinion dynamics and its social significance.