Abstract: In this paper, we study a discrete dynamical system modeling an iterative process of choice in a group of agents between two possible outcomes. The model under study is based on the bounded confidence principle introduced by Hegselmann and Krause. According to this principle, at each step of the process, an agent forms their opinion based on similar opinions of other agents. The resulting dynamical system is nonlinear and discontinuous. The principal novelty of the model studied in this paper is that we consider not a finite but an infinite (continual) group of agents. Such an approach requires the application of essentially new research methods. The structure of possible fixed points of the arising dynamical system is described and their stability is studied. It is shown that any trajectory tends to a fixed point.