A lifting approach to models of opinion dynamics with antagonisms

Different recent works have studied polarized versions of models of opinion dynamics, in which an agent opinion can be attracted by the opinions of some agents and by the opinions opposite to those of some others, representing a form of antagonism. We show that these systems correspond to the projection of specific trajectories of classical opinion dynamics systems involving twice as many agents, to which a large number of existing results apply. We take advantage of this to prove several convergence results for models with antagonisms, extending those previously available. Our approach can be applied in both discrete and continuous time.