Polarization in Dynamic Networks: A Hopfield Model of Emergent Structure

Why do populations often self-organize into antagonistic groups even in the absence of competition over scarce resources? Is there a tendency to demarcate groups of “us” and “them” that is inscribed in our cognitive architecture? 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 selforganize 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 uniform and pluralistic alignments may also be equilibria. From a random start, agents can self-organize into pluralistic arrangements if the population size is large relative to the size of the state space.