BOUNDED CONFIDENCE WITH REJECTION: THE INFINITE POPULATION LIMIT WITH PERFECT UNIFORM INITIAL DENSITY

Abstract – Huet and Deffuant (2007) propose a new opinion dynamics model based on the bounded confidence principles, with a rejection mechanism. The simulations of the agent-based model show that this new model leads generally to fewer clusters than the classical bounded confidence model. We build an aggregated model of this agent-based model (ABM), considering the limit case of an infinite population, in order to better understand the clustering process in the ABM. The dynamics of the aggregated model, starting from a perfectly uniform distribution of opinions, and the dynamics of the ABM are significantly different. However, the aggregated model provides relevant information about how the rejection mechanism and bounding the attitude space influence the clustering process. It firstly outlines that, with a perfectly symmetric density, the clustering process is almost impossible and that the only final stable state is one centred cluster. Secondly we notice that one centred cluster can be lead with the only rejection mechanism or with an unbounded attitude space