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In recent years, opinion dynamics has received an increasing attention, andvarious models have been introduced and evaluated mainly by simulation. In thisstudy, we introduce and study a dynamical model inspired by the so-called`bounded confidence' approach where voters engaged in an electoral decisionwith two options are influenced by individuals sharing an opinion similar totheir own. This model allows one to capture salient features of the evolutionof opinions and results in final clusters of voters. The model is nonlinear anddiscontinuous. We provide a detailed study of the model, including a completeclassification of fixed points of the appearing dynamical system and analysisof their stability. It is shown that any trajectory tends to a fixed point. Themodel highlights that the final electoral outcome depends on the level ofinteraction in the society, besides the initial opinion of each individual, sothat a strongly interconnected society can reverse the electoral outcome ascompared to a society with looser exchange.

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