Heterophilious dynamics enhances consensus (1301.4123v3)

Abstract: We review a general class of models for self-organized dynamics based on alignment. The dynamics of such systems is governed solely by interactions among individuals or "agents," with the tendency to adjust to their `environmental averages'. This, in turn, leads to the formation of clusters, e.g., colonies of ants, flocks of birds, parties of people, etc. A natural question which arises in this context is to understand when and how clusters emerge through the self-alignment of agents, and what type of "rules of engagement" influence the formation of such clusters. Of particular interest to us are cases in which the self-organized behavior tends to concentrate into one cluster, reflecting a consensus of opinions, flocking or concentration of other positions intrinsic to the dynamics. Many standard models for self-organized dynamics in social, biological and physical science assume that the intensity of alignment increases as agents get closer, reflecting a common tendency to align with those who think or act alike. Moreover, "Similarity breeds connection," reflects our intuition that increasing the intensity of alignment as the difference of positions decreases, is more likely to lead to a consensus. We argue here that the converse is true: when the dynamics is driven by local interactions, it is more likely to approach a consensus when the interactions among agents \emph{increase} as a function of their difference in position. \emph{Heterophily} --- the tendency to bond more with those who are different rather than with those who are similar, plays a decisive r^{o}le in the process of clustering. We point out that the number of clusters in heterophilious dynamics \emph{decreases} as the heterophily dependence among agents increases. In particular, sufficiently strong heterophilious interactions enhance consensus.