Opinion Dynamics: Models, Extensions and External Effects

  • Alina SîrbuEmail author
  • Vittorio Loreto
  • Vito D. P. Servedio
  • Francesca Tria
Part of the Understanding Complex Systems book series (UCS)


Recently, social phenomena have received a lot of attention not only from social scientists, but also from physicists, mathematicians and computer scientists, in the emerging interdisciplinary field of complex system science. Opinion dynamics is one of the processes studied, since opinions are the drivers of human behaviour, and play a crucial role in many global challenges that our complex world and societies are facing: global financial crises, global pandemics, growth of cities, urbanisation and migration patterns, and last but not least important, climate change and environmental sustainability and protection. Opinion formation is a complex process affected by the interplay of different elements, including the individual predisposition, the influence of positive and negative peer interaction (social networks playing a crucial role in this respect), the information each individual is exposed to, and many others. Several models inspired from those in use in physics have been developed to encompass many of these elements, and to allow for the identification of the mechanisms involved in the opinion formation process and the understanding of their role, with the practical aim of simulating opinion formation and spreading under various conditions. These modelling schemes range from binary simple models such as the voter model, to multi-dimensional continuous approaches. Here, we provide a review of recent methods, focusing on models employing both peer interaction and external information, and emphasising the role that less studied mechanisms, such as disagreement, has in driving the opinion dynamics. Due to the important role that external information (mainly in the form of mass media broadcast) can have in enhancing awareness of social issues, a special emphasis will be devoted to study different forms it can take, investigating their effectiveness in driving the opinion formation at the population level. The review shows that, although a large number of approaches exist, some mechanisms such as the effect of multiple external information sources could largely benefit from further studies. Additionally, model validation with real data, which are starting to become available, is still largely lacking and should in our opinion be the main ambition of future investigations.


External Information Norm Compliance Opinion Dynamic Collective Belief Regular Random Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. Acemoglu, D., Como, G.: Massachusetts Institute of Technology, Department of Economics Working Paper Series (2010)Google Scholar
  2. Axelrod, R.: J. Confl. Resolut. 41(2), 203 (1997)CrossRefGoogle Scholar
  3. Baker, G., Hague, J.: Int. J. Mod. Phys. C 19, 1459–1475 (2008)ADSCrossRefGoogle Scholar
  4. Ball, P.: Critical Mass: How One Thing Leads to Another. Farrar, Straus and Giroux, London (2004)Google Scholar
  5. Banisch, S., Araújo, T.: Phys. Lett. A 374(3197), 31–32 (2010)Google Scholar
  6. Barbosa, L., Fontanari, J.: Theory Biosci. 128(4), 205 (2009)CrossRefGoogle Scholar
  7. Baxter, R.J.: Exactly Solved Models in Statistical Mechanics. Courier Corporation, Mineola (2007)zbMATHGoogle Scholar
  8. Benczik, I.J., Benczik, S.Z., Schmittmann, B., Zia, R.: Phys. Rev. E 79(4), 29 (2009)CrossRefGoogle Scholar
  9. Bhattacharyya, A., Braverman, M., Chazelle, B., Nguyen, H.L.: ITCS’13 Proceedings of the 4th Conference on Innovation in Theoretical Computer Science, pp. 61–66 (2013)Google Scholar
  10. Biswas, S., Chandra, A.K., Chatterjee, A., Chakrabarti, B.K.: J. Phys.: Conf. Ser. 297(1), 012004 (2011)ADSGoogle Scholar
  11. Biswas, S., Chatterjee, A., Sen, P., Phys. A: Stat. Mech. Appl. 391(11), 3257 (2012)CrossRefGoogle Scholar
  12. Blondel, V.D., Hendrickx, J.M., Tsitsiklis, J.N.: IEEE Trans. Autom. Control 54(11), 2586 (2009)MathSciNetCrossRefGoogle Scholar
  13. Blondel, V.D., Hendrickx, J.M., Tsitsiklis, J.N.: SIAM J. Control Optim. 48(8), 5214 (2010)MathSciNetCrossRefGoogle Scholar
  14. Bray, A.: Adv. Phys. 43(3), 357 (1994). doi: 10.1080/00018739400101505 ADSMathSciNetCrossRefGoogle Scholar
  15. Buchanan, M.: The Social Atom. Bloomsbury, New York, NY (2007)Google Scholar
  16. Candia, J., Mazzitello, K.: J. Stat. Mech.: Theor. Exp. 2008, P07007 (2008)CrossRefGoogle Scholar
  17. Carletti, T., Fanelli, D., Grolli, S., Guarino, A.: Europhys. Lett. (EPL) 74(2), 222 (2006)Google Scholar
  18. Carletti, T., Righi, S., Fanelli, D.: Adv. Complex Syst. 14(01), 13 (2011)MathSciNetCrossRefGoogle Scholar
  19. Castellano, C., Fortunato, S., Loreto, V.: Rev. Mod. Phys. 81(2), 591 (2009)ADSCrossRefGoogle Scholar
  20. Castellano, C., Marsili, M., Vespignani, A.: Phys. Rev. Lett. 85(16), 3536 (2000). doi:10.1103/PhysRevLett.85.3536ADSCrossRefGoogle Scholar
  21. Castellano, C., Munoz, M.A., Pastor-Satorras, R.: Phys. Rev. E 80, 041129 (2009)ADSCrossRefGoogle Scholar
  22. Carro, A., Toral, R., San Miguel, M.: J. Stat. Phys. 151(1–2), 131 (2013)ADSMathSciNetCrossRefGoogle Scholar
  23. Centola, D.: J. Stat. Phys. 151(1–2), 238 (2013)ADSMathSciNetCrossRefGoogle Scholar
  24. Ciampaglia, G.L.: Adv. Comp. Syst. 16(04n05), 1350030 (2013)Google Scholar
  25. Clifford, P., Sudbury, A.: Biometrika 60(3), 581 (1973). doi:10.1093/biomet/60.3.581MathSciNetCrossRefGoogle Scholar
  26. Crokidakis, N.: Phys. A: Stat. Mech. Appl. 391(4), 1729–1734 (2012)Google Scholar
  27. Crokidakis, N.: J. Stat. Mech.: Theor. Exp. 2013, P07008 (2013)CrossRefGoogle Scholar
  28. Crokidakis, N., Anteneodo, C.: Phys. Rev. E 86, 061127 (2012)ADSCrossRefGoogle Scholar
  29. Crokidakis, N., Oliveira, C.D.: J. Stat. Mech.: Theor. Exp. 11, P11004 (2011)CrossRefGoogle Scholar
  30. Cox, J.: Ann. Probab. 17(4), 1333 (1989)MathSciNetCrossRefGoogle Scholar
  31. Cucchi, M.: Analisi di dinamiche di opinione con disaccordo e informazione esterna per diverse topologie di contatto (in Italian). Master’s thesis, Sapienza University of Rome (2015). Supervisors V.D.P. Servedio and L. PietroneroGoogle Scholar
  32. Dandekar, P., Goel, A., Lee, D.: Proc. Natl. Acad. Sci. U. S. A. 110(15), 5791–5796 (2013)ADSMathSciNetCrossRefGoogle Scholar
  33. De Sanctis, L., Galla, T.: Phys. Rev. E 79(4), 1 (2009)CrossRefGoogle Scholar
  34. Deffuant, G., Neau, D., Amblard, F., Weisbuch, G.: Adv. Complex Syst. 3(4), 87 (2000)CrossRefGoogle Scholar
  35. Deffuant, G., Carletti, T., Huet, S.: J. Artif. Soc. Soc. Simul. 16(1), 5 (2013)Google Scholar
  36. Deng, L., Liu, Y., Xiong, F.: Phys. A: Stat. Mech. Appl. 392(17), 3546 (2013)MathSciNetCrossRefGoogle Scholar
  37. Di Carlo, F.: Agent based modeling of the emergence of social norms. Master’s thesis, Sapienza University of Rome (2015). Supervisors V.D.P. Servedio and L. PietroneroGoogle Scholar
  38. Dornic, I., Chaté, H., Chave, J., Hinrichsen, H.: Phys. Rev. Lett. 87(4), 045701 (2001). doi:10.1103/PhysRevLett.87.045701ADSCrossRefGoogle Scholar
  39. Fent, T., Groeber, P., Schweitzer, F.: Adv. Complex Syst. 10(2), 271 (2007)MathSciNetCrossRefGoogle Scholar
  40. Fernández-Gracia, J., Eguíluz, V.M., Miguel, M.S.: Phys. Rev. E 84, 015103 (2011)ADSCrossRefGoogle Scholar
  41. Fernández-Gracia, J., Eguíluz, V.M., San Miguel, M.: Temporal Networks. Understanding Complex Systems, pp. 331–352 (2013)Google Scholar
  42. Fortunato, S., Latora, V., Pluchino, A., Rapisarda, A.: Int. J. Mod. Phys. C 16(10), 1535 (2005)ADSCrossRefGoogle Scholar
  43. Fotouhi, B., Rabbat, M.: Eur. Phys. J. B 87, eid 55 (2014)Google Scholar
  44. Friedman, R., Friedman, M.: The Tyranny of the Status Quo. Harcourt Brace Company, Orlando, FL (1984)Google Scholar
  45. Galam, S.: J. Math. Psychol. 30, 426 (1986)CrossRefGoogle Scholar
  46. Galam, S.: J. Stat. Phys. 61, 943 (1990)ADSMathSciNetCrossRefGoogle Scholar
  47. Galam, S.: Physica A 274, 132 (1999)ADSCrossRefGoogle Scholar
  48. Galam, S.: Physica A 285, 66 (2000)ADSCrossRefGoogle Scholar
  49. Galam, S.: Eur. Phys. J. B 25(4), 403 (2002)ADSGoogle Scholar
  50. Galam, S.: Int. J. Mod. Phys. C 19, 403 (2008)ADSCrossRefGoogle Scholar
  51. Galam, S.: arXiv:0803.2453 (2008, preprint)Google Scholar
  52. Galam, S.: Phys. A: Stat. Mech. Appl. 389(17), 3619 (2010)MathSciNetCrossRefGoogle Scholar
  53. Galam, S.: arXiv:1006.2332v1, pp. 1–12 (2010, preprint)Google Scholar
  54. Galam, S.: arXiv:1106.1577 1106.1577, 1 (2011, preprint)Google Scholar
  55. Galam, S.: J. Stat. Phys. 151(1–2), 46 (2013)ADSMathSciNetCrossRefGoogle Scholar
  56. Galam, S., Moscovici, S.: Eur. J. Soc. Psychol. 21, 49 (1991)CrossRefGoogle Scholar
  57. Galam, S., Gefen, Y., Shapir, Y.: J. Math. Sociol. 9, 1 (1982)CrossRefGoogle Scholar
  58. Gandica, Y., Charmell, A., Villegas-Febres, J., Bonalde, I.: Phys. Rev. E 84(4), 18 (2011)CrossRefGoogle Scholar
  59. Gandica, Y., del Castillo-Mussot, M., Vazquez, G., Rojas, S.: Phys. A: Stat. Mech. Appl. 389(24), 5864 (2010)CrossRefGoogle Scholar
  60. Gargiulo, F., Huet, S.: Proceedings of 5th International Workshop on Emergent Intelligence on Networked Agents, Toronto (2010)Google Scholar
  61. Gargiulo, F., Mazzoni, A.: J. Artif. Soc. Soc. Simul. 11(4), 1 (2008)Google Scholar
  62. Gargiulo, F., Ramasco, J.J.: PLoS ONE 7(11), e48916 (2012)ADSCrossRefGoogle Scholar
  63. Gargiulo, F., Lottini, S., Mazzoni, A.: ESSA, pp. 1–4 (2008). URL
  64. González-Avella, J.C., Cosenza, M.G., Eguíluz, V.M., San Miguel, M.: N. J. Phys. 12(1), 013010 (2010)CrossRefGoogle Scholar
  65. González-Avella, J.C., Cosenza, M.G., Klemm, K., Eguíluz, V.M., San Miguel, M.: J. Artif. Soc. Soc. Simul. 10(39), 1 (2007)Google Scholar
  66. González-Avella, J.C., Cosenza, M.G., San Miguel, M.: PLoS ONEGoogle Scholar
  67. González-Avella, J.C., Eguíluz, V.M., Cosenza, M.G., Klemm, K., Herrera, J., San Miguel, M.: Phys. Rev. E 73(4), 046119 (2006)ADSCrossRefGoogle Scholar
  68. González-Avella, J.C., Eguíluz, V.M., Marsili, M., Vega-Redondo, F., San Miguel, M.: PLoS ONE 6(5), e20207 (2011) 7(12), e51035 (2012)Google Scholar
  69. Gomez-Serrano, J., Graham, C., Le Boudec, J.: Math. Models Meth. Appl. Sci. 22(2), 1 (2012)CrossRefGoogle Scholar
  70. Griffin, E.: A First Look at Communication Theory McGraw-Hill, New York, NY (2012)Google Scholar
  71. Groeber, P., Rauhut, H.: Comput. Math. Organ. Theor. 16(1), 1 (2010)CrossRefGoogle Scholar
  72. Guerra, B., Poncela, J., Gómez-Gardeñes, J., Latora, V., Moreno, Y.: Phys. Rev. E 81(5), 1 (2010)CrossRefGoogle Scholar
  73. Halu, A., Zhao, K., Baronchelli, A., Bianconi, G.: EPL (Europhys. Lett.) 102, 16002 (2013)Google Scholar
  74. Hegselmann, R., Krause, U.: J. Artif. Soc. Soc. Simul. 9(3), 1 (2006)Google Scholar
  75. Hegselmann, R., Krause, U.: J. Artif. Soc. Soc. Simul. 5(3) (2002) 6(4), e1000758 (2010)Google Scholar
  76. Helbing, D., Szolnoki, A., Perc, M., Szabó, G.: PLoS Comput. Biol.Google Scholar
  77. Holley, R., Liggett, T.: Ann. Probab. 3(4), 643 (1975)MathSciNetCrossRefGoogle Scholar
  78. Hong, H., Strogatz, S.: Phys. Rev. E 84(4), 1 (2011)CrossRefGoogle Scholar
  79. Huckfeldt, R., Johnson, P., Sprague, J.: Political Disagreement: The Survival of Diverse Opinions Within Communication Networks. Cambridge University Press, Cambridge (2004)CrossRefGoogle Scholar
  80. Huet, S., Deffuant, G., Jager, W.: Adv. Complex Syst. 11(04), 529 (2008)MathSciNetCrossRefGoogle Scholar
  81. Jacobs, F., Galam, S.: arXiv:0803.3150, pp. 1–51 (2008, preprint)Google Scholar
  82. Jager, W., Amblard, F.: Comput. Math. Organ. Theor. 10(4), 295 (2005)CrossRefGoogle Scholar
  83. Kempe, D., Kleinberg, J., Oren, S., Slivkins, A.: arXiv:1304.7468 (2013, preprint)Google Scholar
  84. Klemm, K., Eguíluz, V.M., Toral, R., San Miguel, M.: Phys. Rev. E 67(4), 3 (2003)CrossRefGoogle Scholar
  85. Kondrat, G., Sznajd-Weron, K.: Int. J. Mod. Phys. C 21(4), 559 (2010)ADSCrossRefGoogle Scholar
  86. Krause, S.M., Bornholdt, S.: Phys. Rev. E 86, 056106 (2012)ADSCrossRefGoogle Scholar
  87. Kurmyshev, E., Juárez, H.A.: arXiv:1305.4677, pp. 1–18 (2013, preprint)Google Scholar
  88. Kurmyshev, E., Juárez, H.A., González-Silva, R.: Phys. A: Stat. Mech. Appl. 390(16), 2945–2955 (2011)CrossRefGoogle Scholar
  89. Kurz, S.: J. Differ. Equ. Appl. 13(6), 859–876 (2011)Google Scholar
  90. Laguna, M., Abramson, G., Iglesias, J.: Eur. Phys. J. B 86, 202 (2013)ADSCrossRefGoogle Scholar
  91. Lallouache, M., Chakraborti, A., Chakrabarti, B.K.: Sci. Cult. 76(9–10), 485 (2010a)Google Scholar
  92. Lallouache, M., Chakrabarti, A.S., Chakraborti, A., Chakrabarti, B.K.: Phys. Rev. E 82(5), 056112 (2010b)ADSCrossRefGoogle Scholar
  93. Lama, M., Lopez, J., Wio, H.: EPL (Europhys. Lett.) 72, 851 (2005)Google Scholar
  94. Lanchier, N.: Ann. Appl. Probab. 22(2), 860–880 (2012)Google Scholar
  95. Lanchier, N., Neufer, J.: J. Stat. Phys. 151(1–2), 21 (2013)ADSMathSciNetCrossRefGoogle Scholar
  96. Lanchier, N., Scarlatos, S.: Ann. Appl. Probab. 23(6), 2538–2559 (2013)MathSciNetGoogle Scholar
  97. Latane, B.: Am. Psychol. 36(4), 343 (1981)CrossRefGoogle Scholar
  98. Lewenstein, M., Nowak, A., Latané, B.,: Phys. Rev. A 45(2), 763 (1992)ADSMathSciNetCrossRefGoogle Scholar
  99. Li, Q., Braunstein, L.A., Wang, H., Shao, J., Stanley, H.E., Havlin, S.: J. Stat. Phys. 151(4), 92–112 (2013)ADSMathSciNetCrossRefGoogle Scholar
  100. Lima, F.W.S.: Theor. Econ. Lett. 2, 87 (2012a)CrossRefGoogle Scholar
  101. Lima, F.W.S.: Int. J. Mod. Phys. C 23, 1250047 (2012b)ADSCrossRefGoogle Scholar
  102. Lima, F.W.S.: Int. J. Mod. Phys. C 24, 1350083 (2013)ADSMathSciNetCrossRefGoogle Scholar
  103. Lorenz, J.: Proceedings of IASTED Conference “Modelling, Simulation and Optimization” (2005)Google Scholar
  104. Lorenz, J.: Eur. J. Econ. Soc. Syst. 19, 213 (2006)Google Scholar
  105. Lorenz, J.: Int. J. Mod. Phys. C 18(12), 1819 (2007a)ADSCrossRefGoogle Scholar
  106. Lorenz, J.: In: Ruffing, A., Suhrer, A., Suhrer, J. (eds.) Communications of the Laufen Colloquium on Science, pp. 1–18. Shaker Publishing, Maastricht (2007b)Google Scholar
  107. Lorenz, J.: In: Helbing, D. (ed.) Managing Complexity: Insights, Concepts, Applications. Understanding Complex Systems, vol. 32, pp. 321–334. Springer, Berlin/Heidelberg (2008)Google Scholar
  108. Lorenz, J.: Complexity 15(4), 43 (2010)MathSciNetGoogle Scholar
  109. Majorana, E.: Scientia 36, 58–66 (1942)Google Scholar
  110. Majorana, E.: J. Quantit. Fin. 5, 133 (2005)MathSciNetCrossRefGoogle Scholar
  111. Malarz, K., Kulakowski, K.: ACTA Phys. Pol. A 114(3), 1 (2008)CrossRefGoogle Scholar
  112. Malarz, K., Kulakowski, K.: Symposium “Physics in Economics and Social Sciences”, Rzeszów, vol. 17894 (2009)Google Scholar
  113. Malik, N.: Mucha, P.J.: Chaos 23, 043123 (2013)Google Scholar
  114. Martins, A.C.R.: Int. J. Mod. Phys. C 19, 617 (2008)ADSCrossRefGoogle Scholar
  115. Martins, A.C.R.: Phys. Rev. E 78(3), 036104 (2008)ADSCrossRefGoogle Scholar
  116. Martins, A.C.R.: Adv. Appl. Stat. Sci. 2(2), 333–346 (2010)Google Scholar
  117. Martins, A.C.R.: AIP Conf. Proc. 1490, 212 (2012)ADSCrossRefGoogle Scholar
  118. Martins, A.C.R.: Phys. Lett. A 377(37), 2333–2339 (2013)Google Scholar
  119. Martins, A.: In: Dabbaghian, V., Mago, V.K. (eds.) Theories and Simulations of Complex Social Systems. Intelligent Systems Reference Library, vol. 52, pp. 19–30. Springer, Berlin/Heidelberg (2014). doi: 10.1007/978-3-642-39149-1_3
  120. Martins, A.C.R., Kuba, C.D.: Adv. Complex Syst. 13(5), 621 (2010)MathSciNetCrossRefGoogle Scholar
  121. Mas, M., Flache, A., Helbing: PLoS Comput. Biol. 6(10), e1000959 (2010)ADSGoogle Scholar
  122. Mavrodiev, P., Tessone, C.J., Schweitzer, F.: Proceedings of Collective Intelligence (2012)Google Scholar
  123. Mazzitello, K., Candia, J., Dossetti, V.: Int. J. Mod. Phys. C 18(09), 1475 (2007)ADSCrossRefGoogle Scholar
  124. Mirtabatabaei, A., Bullo, F.: American Control Conference, pp. 2807–2812 (2011)Google Scholar
  125. Mirtabatabaei, A., Bullo, F.: SIAM J. Control Optim. 50(5), 2763 (2012)MathSciNetCrossRefGoogle Scholar
  126. Mirtabatabaei, A., Jia, P., Bullo, F.: Proceedings of the 3rd IFAC Workshop on Distributed Estimation and Control in Networked Systems, pp. 270–275 (2012)Google Scholar
  127. Mobilia, M.: EPL (Europhys. Lett.) 95, 50002 (2011)Google Scholar
  128. Mobilia, M.: J. Stat. Phys. 151(1–2), 69 (2013)ADSMathSciNetCrossRefGoogle Scholar
  129. Mobilia, M., Petersen, A., Redner, S.: J. Stat. Mech.: Theor. Exp. P08029 (2007)Google Scholar
  130. Moretti, P., Baronchelli, A., Starnini, M., Pastor-Satorras, R.: Dynamics On and Of Complex Networks, vol. 2, pp. 285–300. Springer, New York (2013a)Google Scholar
  131. Moretti, P., Liu, S., Castellano, C., Pastor-Satorras, R.: J. Stat. Phys. 151(1–2), 113 (2013b)ADSMathSciNetCrossRefGoogle Scholar
  132. Nowak, A., Lewenstein, M.: Modelling and Simulation in the Social Sciences from a Philosophy of Science Point of View, pp. 249–285. Kluwer Academic, Dordrecht (1996)Google Scholar
  133. Nyczka, P.: arXiv:1106.0008, pp. 1–21 (2011, preprint)Google Scholar
  134. Nyczka, P., Cislo, J., Sznajd-Weron, K.: Phys. A: Stat. Mech. Appl. 391(1–2), 317 (2012)CrossRefGoogle Scholar
  135. Nyczka, P., Sznajd-Weron, K., Cislo, J.: Phys. Rev. E 86(1) (2012)Google Scholar
  136. Pace, B., Prado, C.P.C.: Phys. Rev. E 89, 062804 (2014)ADSCrossRefGoogle Scholar
  137. Peres, L., Fontanari, J.: J. Phys. A: Math. Theor. 43(5) (2010)Google Scholar
  138. Peres, L., Fontanari, J.: EPL (Europhys. Lett.) 96, 38004 (2011)Google Scholar
  139. Perony, N., Pfitzner, R., Scholtes, I., Tessone, C.J., Schweitzer, F.: Proceedings of the 26th European Conference on Modelling and Simulation (ECMS), Koblenz (2012). arXiv: 1204.0015Google Scholar
  140. Pietrosantom, M.: Agent based study on cooperation and social norms. Master’s thesis, Sapienza University of Rome (2013). Supervisors V. Loreto, V.D.P. Servedio and F. TriaGoogle Scholar
  141. Pineda, M., Toral, R., Hernández-García, E.: J. Stat. Mech.: Theor. Exp. 2009, P08001 (2009)CrossRefGoogle Scholar
  142. Pineda, M., Toral, R., Hernández-García, E.: Eur. Phys. J. D 62(1), 109 (2011)ADSCrossRefGoogle Scholar
  143. Quattrociocchi, W., Caldarelli, G., Scala, A.: Sci. Rep. 4, 04938 (2014)ADSCrossRefGoogle Scholar
  144. Quattrociocchi, W., Conte, R., Lodi, E.: Adv. Complex Syst. 14, 567 (2011)MathSciNetCrossRefGoogle Scholar
  145. Radillo-Díaz, A., Pérez, L.A., del Castillo-Mussot, M.: Phys. Rev. E 80(6), 1 (2009)CrossRefGoogle Scholar
  146. Rodríguez, A., Moreno, Y.: Phys. Rev. E 82(1), 1 (2010)CrossRefGoogle Scholar
  147. Rodríguez, A., del Castillo-Mussot, M., Vázquez, G.: 7th International Conference on Practical Applications of Agents and Multi-Agent Systems (PAAMS 2009), vol. 2, pp. 310–318. Springer, New York (2009)Google Scholar
  148. Rybak, M., Kulakowski, K.: ACTA Phys. Polon. B 44, 1007–1012 (2013)ADSCrossRefGoogle Scholar
  149. Schweitzer, F., Behera, L.: Eur. Phys. J. B 67(3), 301 (2009)ADSMathSciNetCrossRefGoogle Scholar
  150. Schweitzer, F., Mavrodiev, P., Tessone, C.J.: Adv. Complex Syst. 16(04–05), 1350017 (2013)MathSciNetCrossRefGoogle Scholar
  151. Sen, P.: Phys. Rev. E 83, 016108 (2011)ADSCrossRefGoogle Scholar
  152. Sen, P.: Phys. Rev. E 86(1), 016115 (2012)ADSCrossRefGoogle Scholar
  153. Sherif, C.W., Sherif, M., Nebergall, R.E.: Attitude and Attitude Change. The Social Judgment-Involvement Approach. W.B. Saunders, Philadelphia (1965)Google Scholar
  154. Shin, J.K., Lorenz, J.: J. Stat. Mech.: Theor. Exp. 2010, P06005 (2010)CrossRefGoogle Scholar
  155. Singh, P., Sreenivasan, S., Szymanski, B.K., Korniss, G.: Phys. Rev. E 85, 046104 (2012)ADSCrossRefGoogle Scholar
  156. Sîrbu, A., Loreto, V., Servedio, V.D.P., Tria, F.: J. Stat. Phys. 151(1–2), 218 (2013)ADSMathSciNetCrossRefGoogle Scholar
  157. Sîrbu, A., Loreto, V., Servedio, V.D.P., Tria, F.: Adv. Complex Syst. 16, 1350035 (2013)MathSciNetCrossRefGoogle Scholar
  158. Slanina, F.: Eur. Phys. J. B 79(1), 99 (2010)ADSCrossRefGoogle Scholar
  159. Stauffer, D., Kulakowski, K.: J. Stat. Mech.: Theor. Exp. 2008, P04021 (2008)CrossRefGoogle Scholar
  160. Stauffer, D., Sousa, A., De Oliveira, S.: Int. J. Mod. Phys. 11, 1239 (2000)ADSCrossRefGoogle Scholar
  161. Sznajd-Weron, K., Tabiszewski, M., Timpanaro, A.: EPL (Europhys. Lett.) 96(4), 1 (2011)Google Scholar
  162. Sznajd-Weron, K., Sznajd, J.: Int. J. Mod. Phys. C 11, 1157 (2001)ADSCrossRefGoogle Scholar
  163. Sznajd-Weron, K., Weron, R., Wloszczowska, M.: J. Stat. Mech.: Theor. Exp. 2008(11), P11018 (2008)CrossRefGoogle Scholar
  164. Takaguchi, T., Masuda, N.: Phys. Rev. E 84(3), 1 (2011)CrossRefGoogle Scholar
  165. Tanabe, S., Masuda, N.: Chaos 23, 043136 (2013)ADSMathSciNetCrossRefGoogle Scholar
  166. Tessone, C., Toral, R., Amengual, P., Wio, H., San Miguel, M.: Eur. Phys. J. B 39, 535 (2004). doi:10.1140/epjb/e2004-00227-5ADSCrossRefGoogle Scholar
  167. Tessone, C.J., Sánchez, A., Schweitzer, F.: Phys. Rev. E 87, 022803 (2013)ADSCrossRefGoogle Scholar
  168. Timpanaro, A., Prado, C.P.: Phys. Rev. E 86, 046109 (2012)ADSCrossRefGoogle Scholar
  169. Vaz Martins, T., Pineda, M., Toral, R.: EPL (Europhys. Lett.) 91(4), 48003 (2010)Google Scholar
  170. Volovik, D., Redner, S.: J. Stat. Mech.: Theor. Exp. 2012, P04003 (2012)CrossRefGoogle Scholar
  171. Volovik, D., Mobilia, M., Redner, S.: EPL (Europhys. Lett.) 85, 48003 (2009)Google Scholar
  172. Weisbuch, G., Deffuant, G., Amblard, F., Nadal, J.P.: Complexity 7(3), 55 (2002)CrossRefGoogle Scholar
  173. Wu, Z.X., Chen, G.: arXiv:0807.4583, pp. 1–10 (2008, preprint)Google Scholar
  174. Yang, H., Wang, W., Lai, Y.: Phys. Lett. A, 1 (2011)Google Scholar
  175. Zaklan, G., Lima, F.W.S., Westerhoff, F.: Phys. A: Stat. Mech. Appl. 387(23), 5857 (2008)CrossRefGoogle Scholar
  176. Zschaler, G., Böhme, G., Seiß inger, M., Huepe, C., Gross, T.: Phys. Rev. E 85(4), 1046107 (2012)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2017

Authors and Affiliations

  • Alina Sîrbu
    • 1
    Email author
  • Vittorio Loreto
    • 2
    • 3
    • 4
  • Vito D. P. Servedio
    • 2
    • 5
  • Francesca Tria
    • 3
  1. 1.Department of Computer ScienceUniversity of PisaPisaItaly
  2. 2.Physics DepartmentSapienza University of RomeRomeItaly
  3. 3.ISI FoundationTurinItaly
  4. 4.SONY Computer Science LabParisFrance
  5. 5.CNR, Institute for Complex SystemsRomeItaly

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