Dissensus algorithms for opinion dynamics

Abstract

Opinion dynamics is a disciplinary field that studies how opinions of individuals or groups are formed, changed, and spread. The process of establishing models serves a crucial purpose. These models are designed to describe and offer explanations for the dynamic evolution process of opinions. This evolution occurs either among individuals or within groups. The ultimate objective of using these models is to understand how opinions develop towards a particular end-state. This end-state could be the achievement of a consensus, where individuals or groups come to share similar viewpoints. Alternatively, it could lead to dissensus, with opinions moving further apart from one another in the final stage of the evolution. Up to now, extensive research has been carried out regarding opinion dynamics. With the aim of offer a lucid view of the evolution process in opinion dynamics, this dissertation briefly shows the core concepts and recently developed theories on modeling opinion dynamics. This dissertation offers an overview of the structure and formulation of opinion dynamics, along with certain fundamental models, such as the averaged consensus algorithm, the voter model, the DeGroot model, and the bounded confidence model.

This dissertation also focus on the research of algorithms for dissensus that are grounded in the Oja principal component analysis (PCA) flow. We formulate a model related to the opinion dynamics of a nonlinear multi-agent system on the unit sphere, conduct stability analysis on achieving dissensus equilibrium and unstable consensus equilibrium under different conditions of invariable covariance and temporally varying covariance. Moreover, we conduct simulation trials to demonstrate the performance of the algorithm. These simulation trials will be carried out on a multi-agent system. The multi-agent system in question is situated within a two-dimensional space.