Opinion dynamics and wisdom under in-group bias and out-group discrimination

We study a DeGroot-like opinion dynamics model in which agents may oppose other agents. As an underlying motivation, in our setup, agents want to adjust their opinions to match those of the agents they follow (their `in-group', friends, or those they trust) and, in addition, they want to adjust their opinions to match the `inverse' of those of the agents they oppose (their `out-group', enemies, or those they distrust). Our paradigm can account for both long-run consensus as well as bi- and multi-polarization and persistent disagreement in connected societies. Outcomes depend upon network (`multigraph') structure and the choice of deviation function modeling the mode of opposition between agents. We also consider social influence (who are the opinion leaders in the network?) as well as the question of wisdom in our na\"ive learning paradigm, finding that wisdom is difficult to attain when there exist sufficiently strong negative relations between agents. Psychologically and socio-economically, we interpret opposition as arising from group identity structure (out-group discrimination) or, more particularly, from rebels/anti-conformists; countercultures; rejection of the norms and values of disliked others, as `negative referents'; or, simply, distrust.