Opposites repel: the effect of incorporating repulsion on opinion dynamics in the bounded confidence model

Various computer and analytical models have been studied that analyze population dynamics of opinions of agents in societies under various assumptions of interaction restrictions and influences. Of particular interest to us are societal models based on Self-categorization Theory which addresses how agent opinions are affected based on interactions with other agents. The Bounded~Confidence model, for example posits that two agents whose opinions are not too similar influence each other and are more likely to change their opinions towards each other after an interaction. Several extensions have also been proposed to such models that include interaction restrictions based on group memberships and the possibility of agents shifting their opinions away from each other after an interaction. We are motivated to study more realistic repulsion models where agents with extreme opinions will tend to further polarize after an interaction. We develop, simulate, and analyze several repulsion schemes within the Bounded Confidence Model of interaction and show interesting emergent phenomena that have been observed in real-life scenarios. We also present analytical models that are able to predict major features and timings of emergent opinion patterns in such interacting populations.