Why do populations often self-organize into antagonistic groups even in the absence of competition over scarce resources? We look for answers by exploring the dynamics of influence and attraction between computational agents. Our model is an extension of Hopfield’s attractor network. Agents are attracted to others with similar states (the principle of homophily) and are also influenced by others, as conditioned by the strength and valence of the social tie. Negative valence implies xenophobia (instead of homophily) and differentiation (instead of imitation). Consistent with earlier work on structural balance, we find that networks can self-organize into two antagonistic factions, without the knowledge or intent of the agents. We model this tendency as a function of network size, the number of potentially contentious issues, and agents’ openness and flexibility toward alternative positions. Although we find that polarization into two antagonistic groups is a unique global attractor, we investigate the conditions under which global uniformity or pluralistic alignments may also be equilibria.

Macy, Michael W., Kitts, James A., Flache, Andreas, and Steve Benard. “Polarization in Dynamic Networks: A Hopfield Model of Emergent Structure. Dynamic Social Network Modeling and Analysis, National Academies Press, 162-173, 2003.