Balance and fragmentation in societies with homophily and social balance

Abstract

Recent attempts to understand the origin of social fragmentation on the basis of spin models include terms accounting for two social phenomena: homophily—the tendency for people with similar opinions to establish positive relations—and social balance—the tendency for people to establish balanced triadic relations. Spins represent attribute vectors that encode G different opinions of individuals whose social interactions can be positive or negative. Here we present a co-evolutionary Hamiltonian model of societies where people minimise their individual social stresses. We show that societies always reach stationary, balanced, and fragmented states, if—in addition to homophily—individuals take into account a significant fraction, q, of their triadic relations. Above a critical value, $$q_c$$ q c , balanced and fragmented states exist for any number of opinions.

Empirical social triad statistics can be explained with dyadic homophylic interactions

“…Following Heider’s intuition ( 18 – 41 ), current approaches toward social balance often account for the effect of triangles on social network formation in one way or another. For example, the models in refs.…”

“…The latter process sometimes leads to imbalance due to the existence of so-called jammed states ( 42 ). In order to reach social balance, individuals can also update their links according to their relations to common neighbors ( 18 – 21 ) or adjust link weights via opinion updates ( 24 , 25 ) or via a minimization of social stress based on triadic interactions ( 37 – 44 ). These works not only ignore the difficulty of individuals to know the social interactions beyond their direct neighbors in reality, so far, they also have not considered the detailed statistical properties of the over- or underrepresentation of the different types of triads, such as those reported in refs.…”

Structural complementarity and similarity: linking relational principles to network motifs

“…In other words, this suggests that too strong a pressure on structural similarity, assuming fixed average degree, must inevitably lead to a decomposition of a system into disconnected parts. We believe that this result may be useful for studies on polarization and social fragmentation [6,47].…”

A general framework to link theory and empirics in opinion formation models

“…Besides, we will assume that opinions are represented by scalar quantities describing individuals’ positions on a single issue. More complex situations could arise when several topics (logically connected or independent) are analyzed at once 18 , 19 . However, gathering data on individuals’ opinions on two or more topics simultaneously is a challenging and costly task.…”