Asymmetrical triadic relationship based on the structural difficulty

A Bayesian approach for balance theory
Original Paper

Abstract

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.

Keywords

Balance theory Bayesian modeling Hermitian form model 

Notes

Acknowledgements

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.).

References

  1. Abelson R, Rosenberg M (1958) Symbolic psycho-logic: a model of attitudinal cognition. Behav Sci 3:1–13CrossRefGoogle Scholar
  2. Cartwright D, Harary F (1956) Structural balance: a generalization of Heider’s theory. Psychol Rev 63:277–293CrossRefGoogle Scholar
  3. Chino N (1997) Asymmetric multi-dimensional scaling. Genda Sugaku Sha, KyotoGoogle Scholar
  4. Chino N (2011) Asymmetric multidimensional scaling. J Inst Psychol Phys Sci 3(1):101–107Google Scholar
  5. Davis J (1967) Clustering and structural balance in graphs. Hum Relat 20:181–187CrossRefGoogle Scholar
  6. Davis JA, Leinhardt S (1967) The structure of positive interpersonal relations in small groups. In: Berger J, Zelditch M Jr (eds) Sociological theories in progress, vol 2. Mifflin Company, Boston, pp 218–251Google Scholar
  7. Doreian P, Krackhardt D (2001) Pre-transitive balance mechanisms for signed networks. J Math Sociol 25(1):43–67CrossRefMATHGoogle Scholar
  8. Festinger L (1962) A theory of cognitive dissonance, vol 2. Stanford University Press, Palo AltoGoogle Scholar
  9. Gelman A et al (2006) Prior distributions for variance parameters in hierarchical models (comment on article by browne and draper). Bayesian Anal 1(3):515–534MathSciNetCrossRefMATHGoogle Scholar
  10. Heider F (1958) The psychology of interpersonal relations. Wiley, New YorkCrossRefGoogle Scholar
  11. Hunter J (1978) Dynamic sociomtery. J Math Sociol 6:87–138MathSciNetCrossRefGoogle Scholar
  12. Jordan N (1953) Behavioral forces that are a function of attitudes and of cognitive organization. Hum Relat 6:273–287CrossRefGoogle Scholar
  13. Kass RE, Raftery AE (1995) Bayes factors. J Am Stat Assoc 90(430):773–795MathSciNetCrossRefMATHGoogle Scholar
  14. Katz L (1947) On the matric analysis of sociometric data. Sociometry 10:233–241CrossRefGoogle Scholar
  15. Klugkist I, Laudy O, Hoijtink H (2005) Inequality constrained analysis of variance: a Bayesian approach. Psychol Methods 10(4):477CrossRefGoogle Scholar
  16. Kosugi K, Fujisawa T, Fujihara T (2004) Isomorphism of balance theory and Eigen-decomposition. Sociol Theory Methods 19(1):87–100Google Scholar
  17. Kruschke J (2014) Doing Bayesian data analysis: a tutorial with R, JAGS, and Stan. Academic Press, CambridgeMATHGoogle Scholar
  18. Lee MD, Wagenmakers EJ (2014) Bayesian cognitive modeling: a practical course. Cambridge University Press, CambridgeGoogle Scholar
  19. MacRae D Jr (1960) Direct factor analysis of sociometric data. Sociometry 23:360–371CrossRefGoogle Scholar
  20. Morrissette J (1958) An experimental study of the theory of structural balance. Hum Relat 11:239–254CrossRefGoogle Scholar
  21. Newcomb T (1953) An approach to the study of communicative acts. Psychol Rev 60(6):393–404CrossRefGoogle Scholar
  22. Nishisato S (1994) Elements of dual scaling: an introduction to practical data analysis. Lawrence Erlbaum, HillsdaleGoogle Scholar
  23. Noma E, Smith D (1985a) Benchmark for the blocking of sociometric data. Psychol Bull 97(3):583–591CrossRefGoogle Scholar
  24. Noma E, Smith D (1985b) Scaling sociometrics by optimizing an explicit function: correspondence analysis of binary single response soiciomatrices. Multivar Behav Res 20:179–197CrossRefGoogle Scholar
  25. Okada A, Imaizumi T (1997) Asymmetric multidimensional scaling of two-mode three-way proximities. J Classif 14(2):195–224CrossRefMATHGoogle Scholar
  26. Okada K (2014) Does Bayesian evaluation of informative hypothesis outperform analysis of variance? Jpn J Psychon Sci 32(2):223–231Google Scholar
  27. Osgood C, Tannenbaum P (1955) The principle of congruity in the prediction of attitude change. Psychol Rev 62(1):42–55CrossRefGoogle Scholar
  28. Phillips J (1967) A model for cognitive balance. Psychol Rev 74:481–495CrossRefGoogle Scholar
  29. Plummer M, Best N, Cowles K, Vines K (2006) CODA: convergence diagnosis and output analysis for MCMC. R News 6(1):7–11. https://journal.r-project.org/archive/
  30. R Core Team (2016) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. https://www.R-project.org/
  31. Rubin Z, Zajonc B (1969) Structural bias and generalization in the learning of social structures. J Personal 37:310–324CrossRefGoogle Scholar
  32. Stan Development Team (2016) RStan: the R interface to Stan. http://mc-stan.org/ (R package version 2.14.1)
  33. Taylor H (1970) Balance in small groups. Litton Educational Publishing, New YorkGoogle Scholar
  34. Wasserman S, Faust K, Galaskiewicz J (1990) Correspondence and canonical analysis of relational data. J Math Sociol 15(1):11–64MathSciNetCrossRefMATHGoogle Scholar
  35. Watts DJ (1999) Small worlds: the dynamics of networks between order and randomness. Princeton University Press, PrincetonMATHGoogle Scholar
  36. Zajonc R, Burnstein E (1965a) The learning of balance and unbalanced social structures. J Personal 33:153–163CrossRefGoogle Scholar
  37. Zajonc R, Burnstein E (1965b) Structural balance, reciprocity, and positivity as sources of cognitive bias. J Personal 33:570–583CrossRefGoogle Scholar
  38. Zajonc R, Sherman S (1967) Structural balance and the induction of relations. J Personal 35:635–650CrossRefGoogle Scholar

Copyright information

© The Behaviormetric Society 2017

Authors and Affiliations

  1. 1.Faculty of EducationYamaguchi UniversityYamaguchiJapan

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