Asymmetrical triadic relationship based on the structural difficulty

A Bayesian approach for balance theory
Original Paper


Using Bayesian inference, this study aims to estimate the magnitude of the cognitive load when a person perceives asymmetric social relations. Some empirical evidence relating to balance theory has shown that a balanced state is comparatively easier to memorize than an unbalanced one. In this study, since a balanced state is defined by structural complexity, an experimental hypothesis was set whereby asymmetric social relationships have different difficulty levels depending on structural complexity. The balanced state of an asymmetric relation as structural difficulty is formally derived from the eigenvalue structure of a Hermitian matrix. Asymmetric triadic relations are modeled as featuring three kinds of structural difficulties according to the eigenvalue decomposition of the Hermitian matrix and pattern-specific difficulties. The differences among the structural difficulties were not sufficiently significant to exceed pattern-specific difficulties, but the Bayes factor of the informational hypothesis of this research yielded positive effects.


Balance theory Bayesian modeling Hermitian form model 



This work was supported by JSPS KAKENHI Grant number 16K13459 and special Thanks to Dr. Hiroshi Shimizu (Kwansei Gakuin Univ.) and Dr. Hirakawa Makoto (Hiroshima Univ.).


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Copyright information

© The Behaviormetric Society 2017

Authors and Affiliations

  1. 1.Faculty of EducationYamaguchi UniversityYamaguchiJapan

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