Journal of Statistical Physics

, Volume 151, Issue 1–2, pp 174–202 | Cite as

Anticonformity or Independence?—Insights from Statistical Physics

  • Piotr Nyczka
  • Katarzyna Sznajd-Weron


The aim of this paper is to examine how different types of social influence, introduced on the microscopic (individual) level, manifest on the macroscopic level, i.e. in the society. The inspiration for this task came mainly from two sources—social psychology that recognize two different types of nonconformity (anticonformity and independence) and the observation related to the agent-based modeling that was verbalized in 2002 by Macy and Willer that there was a little effort to provide analysis of how results differ depending on the model designs. To achieve the goal, we propose a generalized model of opinion dynamics, that as a special cases reduces to the linear voter model, Sznajd model, q-voter model and the majority rule. We use the model to examine the differences, that appear at the macroscopic level, under the influence of two types of nonconformity, introduced on the microscopic level. We answer the question if the observed differences are universal or model dependent.


Agent-based modeling Opinion dynamics Phase transitions 


  1. 1.
    Macy, M.W., Willer, R.: From factors to actors: computational sociology and agent-based modeling. Annu. Rev. Sociol. 28, 143–166 (2002) CrossRefGoogle Scholar
  2. 2.
    Squazzoni, F.: The impact of agent-based models in the social sciences after 15 years of incursions. Hist. Econ. Ideas XVIII, 197–233 (2010) Google Scholar
  3. 3.
    Chen, S.: Varieties of agents in agent-based computational economics: a historical and an interdisciplinary perspective. J. Econ. Dyn. Control 36, 1–25 (2012) CrossRefGoogle Scholar
  4. 4.
    Rand, W., Rust, R.T.: Agent-based modeling in marketing: guidelines for rigor. Int. J. Res. Mark. 28, 181–193 (2011) CrossRefGoogle Scholar
  5. 5.
    Kiesling, E., Günther, M., Stummer, Ch., Wakolbinger, L.M.: Agent-based simulation of innovation diffusion: a review. Cent. Eur. J. Oper. Res. 20, 183–230 (2012) CrossRefGoogle Scholar
  6. 6.
    Galam, S., Gefen, Y., Shapir, Y.: Sociophysics: a new approach of sociological collective behavior. I. Mean-behavior description of a strike. J. Math. Sociol. 9, 1–13 (1982) zbMATHCrossRefGoogle Scholar
  7. 7.
    Galam, S.: Sociophysics: a personal testimony. Physica A 336, 49–55 (2004) MathSciNetADSCrossRefGoogle Scholar
  8. 8.
    Galam, S.: Sociophysics: A Physicist’s Modeling of Psycho-Political Phenomena. Springer, New York (2012) Google Scholar
  9. 9.
    Castellano, C., Fortunato, S., Loreto, V.: Statistical physics of social dynamics. Rev. Mod. Phys. 81, 591–646 (2009) ADSCrossRefGoogle Scholar
  10. 10.
    Nyczka, P., Sznajd-Weron, K., Cislo, J.: Phase transitions in the q-voter model with two types of stochastic driving. Phys. Rev. E 86, 011105 (2012) ADSCrossRefGoogle Scholar
  11. 11.
    Martins, A.C.R.: Discrete opinion models as a limit case of the CODA model. arXiv:1201.4565v1
  12. 12.
    Lewenstein, M., Nowak, A., Latane, B.: Statistical mechanics of social impact. Phys. Rev. A 45, 763–776 (1992) MathSciNetADSCrossRefGoogle Scholar
  13. 13.
    Hołyst, J.A., Kacperski, K., Schweitzer, F.: Social impact models of opinion dynamics. Ann. Rev. Comput. Phys. 9, 253–273 (2001) Google Scholar
  14. 14.
    Martins, A.C.R.: Continuous opinions and discrete actions in opinion dynamics problems. Int. J. Mod. Phys. C 19, 617–624 (2008) ADSzbMATHCrossRefGoogle Scholar
  15. 15.
    Axelrod, R.: The dissemination of culture: a model with local convergence and global polarization. J. Confl. Resolut. 41, 203–226 (1997) CrossRefGoogle Scholar
  16. 16.
    Deffuant, G., Neau, D., Amblard, F., Weisbuch, G.: Mixing beliefs among interacting agents. Adv. Complex Syst. 3, 87–98 (2001) Google Scholar
  17. 17.
    Hegselmann, R., Krause, U.: Opinion dynamics and bounded confidence: models, analysis and simulation. J. Artif. Soc. Soc. Simul. 5(3) (2002).
  18. 18.
    Liggett, T.M.: Interacting Particle Systems. Springer, Heidelberg (1985) zbMATHCrossRefGoogle Scholar
  19. 19.
    Krapivsky, P.L., Redner, S., Ben-Naim, E.: A Kinetic View of Statistical Physics. Cambridge University Press, Cambridge (2010) zbMATHCrossRefGoogle Scholar
  20. 20.
    Galam, S.: Majority rule, hierarchical structures and democratic totalitarianism: a statistical approach. J. Math. Psychol. 30, 426–434 (1986) zbMATHCrossRefGoogle Scholar
  21. 21.
    Galam, S.: Social paradoxes of majority rule voting and renormalization group. J. Stat. Phys. 61, 943–951 (1990) MathSciNetADSCrossRefGoogle Scholar
  22. 22.
    Krapivsky, P.L., Redner, S.: Dynamics of majority rule in two-state interacting spin systems. Phys. Rev. Lett. 90, 238701 (2003) ADSCrossRefGoogle Scholar
  23. 23.
    Sznajd-Weron, K., Sznajd, J.: Opinion evolution in closed community. Int. J. Mod. Phys. C 11, 1157–1165 (2000) ADSCrossRefGoogle Scholar
  24. 24.
    Galam, S.: Local dynamics vs. social mechanisms: a unifying frame. Europhys. Lett. 70, 705–711 (2005) ADSCrossRefGoogle Scholar
  25. 25.
    Lambiotte, R., Redner, S.: Dynamics of non-conservative voters. Europhys. Lett. 82, 18007 (2008) ADSCrossRefGoogle Scholar
  26. 26.
    Castellano, C., Muñoz, M.A., Pastor-Satorras, R.: Nonlinear q-voter model. Phys. Rev. E 80, 041129 (2009) ADSCrossRefGoogle Scholar
  27. 27.
    Cialdini, R.B., Goldstein, N.J.: Social influence: conformity and compliance. Annu. Rev. Psychol. 55, 591–621 (2004) CrossRefGoogle Scholar
  28. 28.
    Griskevicius, V., Goldstein, N.J., Mortensen, C.R., Cialdini, R.B., Kenrick, D.T.: Going along versus going alone: when fundamental motives facilitate strategic (non)conformity. J. Pers. Soc. Psychol. 91, 281–294 (2006) CrossRefGoogle Scholar
  29. 29.
    Latane, B.: The psychology of social impact. Am. Psychol. 36, 343–356 (1981) CrossRefGoogle Scholar
  30. 30.
    Asch, S.E.: Opinions and social pressure. Sci. Am. 193, 31–35 (1955) ADSCrossRefGoogle Scholar
  31. 31.
    Pronin, E., Berger, J., Molouki, S.: Alone in a crowd of sheep: asymmetric perceptions of conformity and their roots in an introspection illusion. J. Pers. Soc. Psychol. 92, 585–595 (2007) CrossRefGoogle Scholar
  32. 32.
    Murray, D.R., Trudeau, R., Schaller, M.: On the origins of cultural differences in conformity: four tests of the pathogen prevalence hypothesis. Pers. Soc. Psychol. Bull. 37, 318329 (2011) CrossRefGoogle Scholar
  33. 33.
    Willis, R.H.: Two dimensions of conformity-nonconformity. Sociometry 26, 499–513 (1963) CrossRefGoogle Scholar
  34. 34.
    Willis, R.H.: Conformity, independence, and anticonformity. Hum. Relat. 18, 373–388 (1965) MathSciNetCrossRefGoogle Scholar
  35. 35.
    Nail, P., MacDonald, G., Levy, D.: Proposal of a four-dimensional model of social response. Psychol. Bull. 126, 454–470 (2000) CrossRefGoogle Scholar
  36. 36.
    MacDonald, G., Nail, P.R., Levy, D.A.: Expanding the scope of the social response context model. Basic Appl. Soc. Psychol. 26, 77–92 (2004) CrossRefGoogle Scholar
  37. 37.
    MacDonald, G., Nail, P.R.: Attitude change and the public-private attitude distinction. Br. J. Soc. Psychol. 44, 15–28 (2005) CrossRefGoogle Scholar
  38. 38.
    Nail, P.R., MacDonald, G.: On the development of the social response context model. In: Pratkanis, A. (ed.) The Science of Social Influence: Advances and Future Progress, pp. 193–221. Psychology Press, New York (2007) Google Scholar
  39. 39.
    Solomon, M.R., Bamossy, G., Askegaard, S., Hogg, M.K.: Consumer Behavior, 3rd edn. Prentice Hall, New York (2006) Google Scholar
  40. 40.
    Brush, S.G.: History of the Lenz-Ising model. Rev. Mod. Phys. 39, 883–893 (1967) ADSCrossRefGoogle Scholar
  41. 41.
    Niss, M.: History of the Lenz-Ising model 1920–1950: from ferromagnetic to cooperative phenomena. Arch. Hist. Exact Sci. 59, 267–318 (2005) MathSciNetzbMATHCrossRefGoogle Scholar
  42. 42.
    Niss, M.: History of the Lenz-Ising model 1950–1965: from irrelevance to relevance. Arch. Hist. Exact Sci. 63, 243–287 (2009) MathSciNetzbMATHCrossRefGoogle Scholar
  43. 43.
    Niss, M.: History of the Lenz-Ising model 1965–1971: the role of a simple model in understanding critical phenomena. Arch. Hist. Exact Sci. 65, 625–658 (2011) MathSciNetzbMATHCrossRefGoogle Scholar
  44. 44.
    Galam, S.: Fragmentation versus stability in bimodal coalitions. Physica A 230, 174–188 (1996) ADSCrossRefGoogle Scholar
  45. 45.
    Galam, S., Moscovici, S.: Towards a theory of collective phenomena: consensus and attitude changes in groups. Eur. J. Soc. Psychol. 21, 49–74 (1991) CrossRefGoogle Scholar
  46. 46.
    Galam, S.: Rational group decision making: a random field Ising model at T=0. Physica A 238, 66–80 (1997) ADSCrossRefGoogle Scholar
  47. 47.
    Callen, H.B.: Thermodynamics and an Introduction to Thermostatics, 2nd edn. Wiley, New York (1985) Google Scholar
  48. 48.
    Schelling, T.C.: Dynamic models of segregation. J. Math. Sociol. 1, 143–186 (1971) CrossRefGoogle Scholar
  49. 49.
    Kawasaki, K.: Kinetics of Ising models. In: Domb, C., Green, M.S. (eds.) Phase Transitions and Critical Phenomena, vol. 2, pp. 443–501. Academic Press, San Diego (1972) Google Scholar
  50. 50.
    Goldenberg, J., Efroni, S.: Using cellular automata modeling of the emergence of innovations. Technol. Forecast. Soc. Change 68, 293–308 (2001) CrossRefGoogle Scholar
  51. 51.
    Goldenberg, J., Libai, B., Muller, E.: Using complex systems analysis to advance marketing theory development: modeling heterogeneity effects on new product growth. Acad. Market. Sci. Rev. 9, 1–18 (2001) Google Scholar
  52. 52.
    Garber, T., Goldenberg, J., Libai, B., Muller, E.: From density to destiny: using spatial dimension of sales data for early prediction of new product success. Mark. Sci. 23, 419–428 (2004) CrossRefGoogle Scholar
  53. 53.
    Moldovan, S., Goldenberg, J.: Cellular automata modeling of resistance to innovations: effects and solutions. Technol. Forecast. Soc. Change 71, 425–442 (2004) CrossRefGoogle Scholar
  54. 54.
    Wu, F.Y.: The Potts model. Rev. Mod. Phys. 54, 235–268 (1982) ADSCrossRefGoogle Scholar
  55. 55.
    Deffuant, G., Huet, S., Amblard, F.: An individual-based model of innovation diffusion mixing social value and individual benefit. Am. J. Sociol. 110, 1041–1069 (2005) CrossRefGoogle Scholar
  56. 56.
    Thiriot, S., Kant, J.D.: Using associative networks to represent adopters’ beliefs in a multiagent model of innovation diffusion. Adv. Complex Syst. 11, 261–272 (2008) zbMATHCrossRefGoogle Scholar
  57. 57.
    Kosterlitz, J.M., Thouless, D.J.: Ordering, metastability and phase transitions in two-dimensional systems. J. Phys. C, Solid State Phys. 6, 1181–1203 (1973) ADSCrossRefGoogle Scholar
  58. 58.
    Kosterlitz, J.M.: The critical properties of the two-dimensional xy model. J. Phys. C, Solid State Phys. 7, 1046–1060 (1974) ADSCrossRefGoogle Scholar
  59. 59.
    Flache, A., Macy, M.W.: Small worlds and cultural polarization. J. Math. Sociol. 35, 146–176 (2011) MathSciNetCrossRefGoogle Scholar
  60. 60.
    Deffuant, G., Neau, D., Amblard, F., Weisbuch, G.: Adv. Complex Syst. 3, 87 (2000) CrossRefGoogle Scholar
  61. 61.
    Ashkin, J., Teller, E.: Statistics of two-dimensional lattices with four components. Phys. Rev. 64, 178 (1943) ADSCrossRefGoogle Scholar
  62. 62.
    Sznajd-Weron, K., Sznajd, J.: Who is left, who is right? Physica A 351, 593 (2005) ADSCrossRefGoogle Scholar
  63. 63.
    Mobilia, M.: Does a single zealot affect an infinite group of voters? Phys. Rev. Lett. 91, 028701 (2003) ADSCrossRefGoogle Scholar
  64. 64.
    Galam, S.: Contrarian deterministic effects on opinion dynamics: the hung elections scenario. Physica A 333, 453–460 (2004) MathSciNetADSCrossRefGoogle Scholar
  65. 65.
    Schneider, J.: The influence of contrarians and opportunists on the stability of a democracy in the Sznajd model. Int. J. Mod. Phys. C 15, 659–674 (2004) ADSzbMATHCrossRefGoogle Scholar
  66. 66.
    de la Lama, M.S., Lopez, J.M., Wio, H.S.: Spontaneous emergence of contrarian-like behavior in an opinion spreading model. Europhys. Lett. 72, 851–857 (2005) ADSCrossRefGoogle Scholar
  67. 67.
    Galam, S., Jacobs, F.: The role of inflexible minorities in the breaking of democratic opinion dynamics. Physica A 381, 366–376 (2007) ADSCrossRefGoogle Scholar
  68. 68.
    Sznajd-Weron, K., Tabiszewski, M., Timpanaro, A.M.: Phase transition in the Sznajd model with independence. Europhys. Lett. 96, 48002 (2011) ADSCrossRefGoogle Scholar
  69. 69.
    Albert, R., Barabasi, A.L.: Statistical mechanics of complex networks. Rev. Mod. Phys. 74, 47–97 (2002) MathSciNetADSzbMATHCrossRefGoogle Scholar
  70. 70.
    Watts, D.J.: The “new” science of networks. Annu. Rev. Sociol. 30, 243–270 (2004) CrossRefGoogle Scholar
  71. 71.
    Dorogovtsev, S.N., Goltsev, A.V., Mendes, J.F.F.: Critical phenomena in complex networks. Rev. Mod. Phys. 80, 1275–1335 (2008) ADSCrossRefGoogle Scholar
  72. 72.
    Merton, R.K.: Social Theory and Social Structure. Free Press, New York (1968) Google Scholar
  73. 73.
    Conley, D.: You May Ask Yourself: An Introduction to Thinking Like a Sociologist, 2nd edn. Norton, New York (2011) Google Scholar
  74. 74.
    Sznajd-Weron, K., Weron, R.: A simple model of price formation. Int. J. Mod. Phys. C 13, 115–123 (2002) ADSCrossRefGoogle Scholar
  75. 75.
    Slanina, F., Lavicka, H.: Analytical results for the Sznajd model of opinion formation. Eur. Phys. J. B 35, 279 (2003) ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Institute of Theoretical PhysicsUniversity of WroclawWrocławPoland

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