, Volume 34, Issue 4, pp 695–704 | Cite as

Two-dimensional opinion dynamics in social networks with conflicting beliefs

  • Shuwei ChenEmail author
  • David H. Glass
  • Mark McCartney
Original Article


Two models are developed for updating opinions in social networks under situations where certain beliefs might be considered to be competing. These two models represent different attitudes of people towards the perceived conflict between beliefs. In both models agents have a degree of tolerance, which represents the extent to which the agent takes into account the differing beliefs of other agents, and a degree of conflict, which represents the extent to which two beliefs are considered to be competing. Computer simulations are used to determine how the opinion dynamics are affected by the inclusion of conflict. Results show that conflict can enhance the formation of consensus within the network in certain circumstances according to one of the models.


Opinion dynamics Bounded confidence model Social network Conflicting opinions 



This publication was made possible by a grant from the John Templeton Foundation (Grant No. 40676). The opinions expressed in this publication are those of the authors and do not necessarily reflect the views of the John Templeton Foundation. The first author has been partially supported by the National Natural Science Foundation of China (Grant Nos. 61175055, 61305074 and 61673320).


  1. Acemoglu D, Ozdaglar A (2011) Opinion dynamics and learning in social networks. Dyn Games Appl 1:3–49MathSciNetCrossRefGoogle Scholar
  2. Chen S, Glass DH, McCartney M (2015) Dynamics of conflicting beliefs in social networks. In: Proceedings of the 6th workshop on complex networks (CompleNet 2015), Studies in computational intelligence, vol. 597, Springer, New York, 25–27 March 27, 2015, pp. 171–178Google Scholar
  3. Deffuant G, Neau D, Amblard F, Weisbuch G (2000) Mixing beliefs among interacting agents. Adv Complex Syst 3:87–98CrossRefGoogle Scholar
  4. Douven I, Riegler A (2010) Extending the Hegselmann–Krause model I. Logic J IGPL 18:323–335MathSciNetCrossRefGoogle Scholar
  5. Fortunato S, Latora V, Pluchino A, Rapisarda A (2005) Vector opinion dynamics in a bounded confidence consensus model. Int J Mod Phys C 16(10):1535–1551CrossRefGoogle Scholar
  6. French JRP (1956) A formal theory of social power. Psychol Rev 63:181–194CrossRefGoogle Scholar
  7. Fu G, Zhang W, Li Z (2015) Opinion dynamics of modified Hegselmann–Krause model in a group-based population with heterogeneous bounded confidence. Phys A 419:558–565CrossRefGoogle Scholar
  8. Harary F (1959) A criterion for unanimity in French’s theory of social power. In: Cartwright D (ed) Studies in social power. Oxford, England, pp 168–182Google Scholar
  9. Hegselmann R, Krause U (2002) Opinion dynamics and bounded confidence: models, analysis, and simulations. J Artif Soc Soc Simul 5(3):1–33Google Scholar
  10. Jacobmeier D (2005) Multidimensional consensus model on a Barabasi–Albert network. Int J Mod Phys C 16:633–646CrossRefGoogle Scholar
  11. Krause U (2000) A discrete nonlinear and non-autonomous model of consensus formation. In: Elaydi S, Ladas G, Popenda J, Rakowski J (eds) Communications in difference equations. Gordon and Breach Publishers, Amsterdam, pp 227–236CrossRefGoogle Scholar
  12. Liu Q, Wang X (2013) Opinion dynamics with similarity-based random neighbours. Sci Rep 3:2968CrossRefGoogle Scholar
  13. Lorenz J (2007) Continuous opinion dynamics under bounded confidence: a survey. Int J Mod Phys C 18(12):1819–1838CrossRefGoogle Scholar
  14. Lorenz J (2008) Fostering consensus in multidimensional continuous opinion dynamics under bounded confidence. In: Helbing D (ed) Managing complexity. Springer, Berlin, pp 321–334Google Scholar
  15. Pineda M, Buendía GM (2015) Mass media and heterogeneous bounds of confidence in continuous opinion dynamics. Phys A 420:73–84MathSciNetCrossRefGoogle Scholar
  16. Pluchino A, Latora V, Rapisarda A (2006) Compromise and synchronization in opinion dynamics. Eur Phys J B 50:169–176CrossRefGoogle Scholar
  17. Quattrociocchi W, Caldarelli G, Scala A (2014) Opinion dynamics on interacting networks: media competition and social influence. Sci Rep 4:4938CrossRefGoogle Scholar
  18. Riegler A, Douven I (2009) Extending the Hegselmann–Krause model III: from single beliefs to complex belief states. Episteme 6:145–163CrossRefGoogle Scholar
  19. Wang H, Shang L (2015) Opinion dynamics in networks with common-neighbours-based connections. Phys A 421:180–186MathSciNetCrossRefGoogle Scholar
  20. Weisbuch G, Deffuant G, Amblard F, Nadal JP (2002) Meet discuss and segregate! Complexity 7:55–63CrossRefGoogle Scholar
  21. Zollman KJ (2012) Social network structure and the achievement of consensus. Polit Philos Econ 11(1):26–44CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2017

Authors and Affiliations

  1. 1.School of MathematicsSouthwest Jiaotong UniversityChengduChina
  2. 2.School of Computing and MathematicsUniversity of UlsterAntrimUK

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