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 of their 'in-group' and, in
addition, they want to adjust their opinions to match the 'inverse' of those of
the agents of their 'out-group'. Our paradigm can account for persistent
disagreement in connected societies as well as bi- and multi-polarization.
Outcomes depend upon network structure and the choice of deviation function
modeling the mode of opposition between agents. For a particular choice of
deviation function, which we call soft opposition, we derive necessary and
sufficient conditions for long-run polarization. We also consider social
influence (who are the opinion leaders in the network?) as well as the question
of wisdom in our naive learning paradigm, finding that wisdom is difficult to
attain when there exist sufficiently strong negative relations between agents.Comment: Further slight/minor ameliorations throughout. Also, fixed a small
error in Example 3.