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Anticonformity or Independence?—Insights from Statistical Physics

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Abstract

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.

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References

  1. Macy, M.W., Willer, R.: From factors to actors: computational sociology and agent-based modeling. Annu. Rev. Sociol. 28, 143–166 (2002)

    Article  Google Scholar 

  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. Chen, S.: Varieties of agents in agent-based computational economics: a historical and an interdisciplinary perspective. J. Econ. Dyn. Control 36, 1–25 (2012)

    Article  Google Scholar 

  4. Rand, W., Rust, R.T.: Agent-based modeling in marketing: guidelines for rigor. Int. J. Res. Mark. 28, 181–193 (2011)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  7. Galam, S.: Sociophysics: a personal testimony. Physica A 336, 49–55 (2004)

    Article  MathSciNet  ADS  Google Scholar 

  8. Galam, S.: Sociophysics: A Physicist’s Modeling of Psycho-Political Phenomena. Springer, New York (2012)

    Google Scholar 

  9. Castellano, C., Fortunato, S., Loreto, V.: Statistical physics of social dynamics. Rev. Mod. Phys. 81, 591–646 (2009)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  11. Martins, A.C.R.: Discrete opinion models as a limit case of the CODA model. arXiv:1201.4565v1

  12. Lewenstein, M., Nowak, A., Latane, B.: Statistical mechanics of social impact. Phys. Rev. A 45, 763–776 (1992)

    Article  MathSciNet  ADS  Google Scholar 

  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. Martins, A.C.R.: Continuous opinions and discrete actions in opinion dynamics problems. Int. J. Mod. Phys. C 19, 617–624 (2008)

    Article  ADS  MATH  Google Scholar 

  15. Axelrod, R.: The dissemination of culture: a model with local convergence and global polarization. J. Confl. Resolut. 41, 203–226 (1997)

    Article  Google Scholar 

  16. Deffuant, G., Neau, D., Amblard, F., Weisbuch, G.: Mixing beliefs among interacting agents. Adv. Complex Syst. 3, 87–98 (2001)

    Google Scholar 

  17. Hegselmann, R., Krause, U.: Opinion dynamics and bounded confidence: models, analysis and simulation. J. Artif. Soc. Soc. Simul. 5(3) (2002). http://jasss.soc.surrey.ac.uk/5/3/2.html

  18. Liggett, T.M.: Interacting Particle Systems. Springer, Heidelberg (1985)

    Book  MATH  Google Scholar 

  19. Krapivsky, P.L., Redner, S., Ben-Naim, E.: A Kinetic View of Statistical Physics. Cambridge University Press, Cambridge (2010)

    Book  MATH  Google Scholar 

  20. Galam, S.: Majority rule, hierarchical structures and democratic totalitarianism: a statistical approach. J. Math. Psychol. 30, 426–434 (1986)

    Article  MATH  Google Scholar 

  21. Galam, S.: Social paradoxes of majority rule voting and renormalization group. J. Stat. Phys. 61, 943–951 (1990)

    Article  MathSciNet  ADS  Google Scholar 

  22. Krapivsky, P.L., Redner, S.: Dynamics of majority rule in two-state interacting spin systems. Phys. Rev. Lett. 90, 238701 (2003)

    Article  ADS  Google Scholar 

  23. Sznajd-Weron, K., Sznajd, J.: Opinion evolution in closed community. Int. J. Mod. Phys. C 11, 1157–1165 (2000)

    Article  ADS  Google Scholar 

  24. Galam, S.: Local dynamics vs. social mechanisms: a unifying frame. Europhys. Lett. 70, 705–711 (2005)

    Article  ADS  Google Scholar 

  25. Lambiotte, R., Redner, S.: Dynamics of non-conservative voters. Europhys. Lett. 82, 18007 (2008)

    Article  ADS  Google Scholar 

  26. Castellano, C., Muñoz, M.A., Pastor-Satorras, R.: Nonlinear q-voter model. Phys. Rev. E 80, 041129 (2009)

    Article  ADS  Google Scholar 

  27. Cialdini, R.B., Goldstein, N.J.: Social influence: conformity and compliance. Annu. Rev. Psychol. 55, 591–621 (2004)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  29. Latane, B.: The psychology of social impact. Am. Psychol. 36, 343–356 (1981)

    Article  Google Scholar 

  30. Asch, S.E.: Opinions and social pressure. Sci. Am. 193, 31–35 (1955)

    Article  ADS  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  33. Willis, R.H.: Two dimensions of conformity-nonconformity. Sociometry 26, 499–513 (1963)

    Article  Google Scholar 

  34. Willis, R.H.: Conformity, independence, and anticonformity. Hum. Relat. 18, 373–388 (1965)

    Article  MathSciNet  Google Scholar 

  35. Nail, P., MacDonald, G., Levy, D.: Proposal of a four-dimensional model of social response. Psychol. Bull. 126, 454–470 (2000)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  37. MacDonald, G., Nail, P.R.: Attitude change and the public-private attitude distinction. Br. J. Soc. Psychol. 44, 15–28 (2005)

    Article  Google Scholar 

  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. Solomon, M.R., Bamossy, G., Askegaard, S., Hogg, M.K.: Consumer Behavior, 3rd edn. Prentice Hall, New York (2006)

    Google Scholar 

  40. Brush, S.G.: History of the Lenz-Ising model. Rev. Mod. Phys. 39, 883–893 (1967)

    Article  ADS  Google Scholar 

  41. Niss, M.: History of the Lenz-Ising model 1920–1950: from ferromagnetic to cooperative phenomena. Arch. Hist. Exact Sci. 59, 267–318 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  42. Niss, M.: History of the Lenz-Ising model 1950–1965: from irrelevance to relevance. Arch. Hist. Exact Sci. 63, 243–287 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  44. Galam, S.: Fragmentation versus stability in bimodal coalitions. Physica A 230, 174–188 (1996)

    Article  ADS  Google Scholar 

  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)

    Article  Google Scholar 

  46. Galam, S.: Rational group decision making: a random field Ising model at T=0. Physica A 238, 66–80 (1997)

    Article  ADS  Google Scholar 

  47. Callen, H.B.: Thermodynamics and an Introduction to Thermostatics, 2nd edn. Wiley, New York (1985)

    Google Scholar 

  48. Schelling, T.C.: Dynamic models of segregation. J. Math. Sociol. 1, 143–186 (1971)

    Article  Google Scholar 

  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. Goldenberg, J., Efroni, S.: Using cellular automata modeling of the emergence of innovations. Technol. Forecast. Soc. Change 68, 293–308 (2001)

    Article  Google Scholar 

  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. 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)

    Article  Google Scholar 

  53. Moldovan, S., Goldenberg, J.: Cellular automata modeling of resistance to innovations: effects and solutions. Technol. Forecast. Soc. Change 71, 425–442 (2004)

    Article  Google Scholar 

  54. Wu, F.Y.: The Potts model. Rev. Mod. Phys. 54, 235–268 (1982)

    Article  ADS  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  58. Kosterlitz, J.M.: The critical properties of the two-dimensional xy model. J. Phys. C, Solid State Phys. 7, 1046–1060 (1974)

    Article  ADS  Google Scholar 

  59. Flache, A., Macy, M.W.: Small worlds and cultural polarization. J. Math. Sociol. 35, 146–176 (2011)

    Article  MathSciNet  Google Scholar 

  60. Deffuant, G., Neau, D., Amblard, F., Weisbuch, G.: Adv. Complex Syst. 3, 87 (2000)

    Article  Google Scholar 

  61. Ashkin, J., Teller, E.: Statistics of two-dimensional lattices with four components. Phys. Rev. 64, 178 (1943)

    Article  ADS  Google Scholar 

  62. Sznajd-Weron, K., Sznajd, J.: Who is left, who is right? Physica A 351, 593 (2005)

    Article  ADS  Google Scholar 

  63. Mobilia, M.: Does a single zealot affect an infinite group of voters? Phys. Rev. Lett. 91, 028701 (2003)

    Article  ADS  Google Scholar 

  64. Galam, S.: Contrarian deterministic effects on opinion dynamics: the hung elections scenario. Physica A 333, 453–460 (2004)

    Article  MathSciNet  ADS  Google Scholar 

  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)

    Article  ADS  MATH  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  67. Galam, S., Jacobs, F.: The role of inflexible minorities in the breaking of democratic opinion dynamics. Physica A 381, 366–376 (2007)

    Article  ADS  Google Scholar 

  68. Sznajd-Weron, K., Tabiszewski, M., Timpanaro, A.M.: Phase transition in the Sznajd model with independence. Europhys. Lett. 96, 48002 (2011)

    Article  ADS  Google Scholar 

  69. Albert, R., Barabasi, A.L.: Statistical mechanics of complex networks. Rev. Mod. Phys. 74, 47–97 (2002)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  70. Watts, D.J.: The “new” science of networks. Annu. Rev. Sociol. 30, 243–270 (2004)

    Article  Google Scholar 

  71. Dorogovtsev, S.N., Goltsev, A.V., Mendes, J.F.F.: Critical phenomena in complex networks. Rev. Mod. Phys. 80, 1275–1335 (2008)

    Article  ADS  Google Scholar 

  72. Merton, R.K.: Social Theory and Social Structure. Free Press, New York (1968)

    Google Scholar 

  73. Conley, D.: You May Ask Yourself: An Introduction to Thinking Like a Sociologist, 2nd edn. Norton, New York (2011)

    Google Scholar 

  74. Sznajd-Weron, K., Weron, R.: A simple model of price formation. Int. J. Mod. Phys. C 13, 115–123 (2002)

    Article  ADS  Google Scholar 

  75. Slanina, F., Lavicka, H.: Analytical results for the Sznajd model of opinion formation. Eur. Phys. J. B 35, 279 (2003)

    Article  ADS  Google Scholar 

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Correspondence to Katarzyna Sznajd-Weron.

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The work was supported by funds from the National Science Centre (NCN) through grant no. 2011/01/B/ST3/00727.

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Nyczka, P., Sznajd-Weron, K. Anticonformity or Independence?—Insights from Statistical Physics. J Stat Phys 151, 174–202 (2013). https://doi.org/10.1007/s10955-013-0701-4

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