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, balanced and fragmented states exist for any number of opinions.
Highlights
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
Structural balance has been investigated by social scientists for a long time[5,6,7] and, more recently, by physicists and network s cientists[8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24]
A general survey of statistical physics methods applied to opinion dynamics is found in45,46
Summary
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. In this paper, motivated by the lack of a consistent theory of balance and fragmentation in societies of agents with multidimensional opinions and homophilic interactions, we propose an individual-stress-based model that takes into account the homophily effect between adjacent individuals and structural balance within a time-varying local neighborhood.
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