A dynamical model of opinion formation in voting processes under bounded confidence

Abstract: In recent years, opinion dynamics has received an increasing attention, and various models have been introduced and evaluated mainly by simulation. In this study, we introduce and study a dynamical model inspired by the so-called `bounded confidence' approach where voters engaged in an electoral decision with two options are influenced by individuals sharing an opinion similar to their own. This model allows one to capture salient features of the evolution of opinions and results in final clusters of voters. The model is nonlinear and discontinuous. We provide a detailed study of the model, including a complete classification of fixed points of the appearing dynamical system and analysis of their stability. It is shown that any trajectory tends to a fixed point. The model highlights that the final electoral outcome depends on the level of interaction in the society, besides the initial opinion of each individual, so that a strongly interconnected society can reverse the electoral outcome as compared to a society with looser exchange.