Adaptive models of opinion formation among humans can display a fragmentation transition, where a social network breaks into disconnected components. Here we investigate this transition in a class of models with arbitrary number of opinions. In contrast to previous work we do not assume that opinions are equidistant or arranged on a one-dimensional conceptual axis. Our investigation reveals detailed analytical results on fragmentations in a three-opinion model, which are confirmed by agent-based simulations. Furthermore, we show that in certain models the number of opinions can be reduced without affecting the fragmentation points.
Fragmentation transitions in multistate voter models
Gesa A. Böhme, Thilo Gross
Phys. Rev. E 85, 066117 (2012)