Repeated Averaging and Bounded Confidence Modeling, Analysis and Simulation of Continuous Opinion Dynamics

Abstract

This thesis is about dynamical systems of agents which perform repeated averaging under bounded confidence. The main modeling issue is continuous opinion dynamics. This includes dynamics of agents in a political opinion space as well as dynamics of collective motion in swarms of mobile autonomous robots. Conditions for convergence to consensus are derived for systems where dynamics are driven by very generally defined averaging maps. Several conditions, examples and counter-examples for convergence of infinite products of row-stochastic matrices are given. Finally, the sets of fixed points are characterized. The density-based bounded confidence models are used to get an overview for the case when agents' initial opinions are uniformly distributed. Bifurcation diagrams for attractive states are computed as well as extended phase diagrams for the consensus transitions in populations with two different levels of confidence.