Skip to main content
Springer Nature Link
Log in

Binary Opinion Models of Influence and Opinion Dynamics in Social Networks

  • Conference paper
  • First Online:
Cellular Automata and Discrete Complex Systems (AUTOMATA 2024)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14782))

  • 193 Accesses

Abstract

The process of influence and opinion dynamics is predominant in many kinds of real-life situations involving agents’ interactions. This phenomenon is extensively analyzed in different fields and with the help of various methods and tools. Network analysis is particularly suitable for the study of influence and opinion formation. The aim of this paper is to provide an overview of selected results on models of influence and opinion dynamics in social networks with non-strategic updating of binary opinions. We start with presenting some results on the relation between a static binary opinion model of influence with influence indices, follower and influence functions, and a framework of simple games called command games. Then, we focus on binary opinion dynamics with non-strategic agents embedded in a social network. In this overview, a special attention is paid to models based on aggregation functions which can be seen as a generalization of the threshold model. In particular, we present some of the main results of the convergence analysis concerning anonymous social influence, conformism and anti-conformism in social networks. Also the phenomenon of diffusion in large networks with the diffusion mechanism represented by an aggregation function is briefly presented. Finally, we conclude this overview paper by indicating some possible directions for future research on the discrete opinion dynamics in social networks.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Acemoglu, D., Ozdaglar, A.: Opinion dynamics and learning in social networks. Dyn. Games Appl. 1, 3–49 (2011)

    Article  MathSciNet  Google Scholar 

  2. Aracena, J., Demongeot, J., Goles, E.: On limit cycles of monotone functions with symmetric connection graph. Theoret. Comput. Sci. 322, 237–244 (2004)

    Article  MathSciNet  Google Scholar 

  3. Berge, C.: Graphs and Hypergraphs, 2nd edn. North-Holland, Amsterdam (1976)

    Google Scholar 

  4. Bramoullé, Y., Galeotti, A., Rogers, B.W.: The Oxford Handbook of the Economics of Networks. Oxford University Press, Oxford (2016)

    Google Scholar 

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

    Article  Google Scholar 

  6. Clifford, P., Sudbury, A.: A model for spatial conflict. Biometrika 60, 581–588 (1973)

    Article  MathSciNet  Google Scholar 

  7. Davey, B.A., Priestley, H.A.: Introduction to Lattices and Orders. Cambridge University Press, Cambridge (1990)

    Google Scholar 

  8. Förster, M., Grabisch, M., Rusinowska, A.: Anonymous social influence. Games Econ. Behav. 82(C), 621–635 (2013)

    Google Scholar 

  9. Galam, S.: Minority opinion spreading in random geometry. Eur. Phys. J. B 25, 403–406 (2002)

    Article  Google Scholar 

  10. Galam, S.: Contrarian deterministic effects on opinion dynamics: “the hung elections scenario.” Phys. A 333, 453–460 (2004)

    Google Scholar 

  11. Ginosar, Y., Holzman, R.: The majority action on infinite graphs: strings and puppets. Discret. Math. 215, 59–71 (2000)

    Article  MathSciNet  Google Scholar 

  12. Goles, E., Olivos, J.: Periodic behavior of generalized threshold functions. Discret. Math. 30, 187–189 (1980)

    Article  Google Scholar 

  13. Grabisch, M., Li, F.: Anti-conformism in the threshold model of collective behavior. Dyn. Games Appl. 10, 444–477 (2020)

    Article  MathSciNet  Google Scholar 

  14. Grabisch, M., Marichal, J.-L., Mesiar, R., Pap., E.: Aggregation functions. Number 127. In: Encyclopedia of Mathematics and its Applications. Cambridge University Press, Cambridge (2009)

    Google Scholar 

  15. Grabisch, M., Poindron, A., Rusinowska, A.: A model of anonymous influence with anti-conformist agents. J. Econ. Dyn. Control 109(C), 103773 (2019)

    Google Scholar 

  16. Grabisch, M., Rusinowska, A.: Measuring influence in command games. Soc. Choice Welfare 33(2), 177–209 (2009)

    Article  MathSciNet  Google Scholar 

  17. Grabisch, M., Rusinowska, A.: A model of influence in a social network. Theor. Decis. 69(1), 69–96 (2010)

    Article  MathSciNet  Google Scholar 

  18. Grabisch, M., Rusinowska, A.: A model of influence with an ordered set of possible actions. Theor. Decis. 69(4), 635–656 (2010)

    Article  MathSciNet  Google Scholar 

  19. Grabisch, M., Rusinowska, A.: Different approaches to influence based on social networks and simple games. In: Van Deemen, A., Rusinowska, A. (eds.) Collective Decision Making: Views from Social Choice and Game Theory. Theory and Decision Library C, vol. 43, pp. 185–209. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-02865-6_13

    Chapter  Google Scholar 

  20. Grabisch, M., Rusinowska, A.: Iterating influence between players in a social network. CES Working Papers, 2010.89 (2010). https://shs.hal.science/halshs-00543840

  21. Grabisch, M., Rusinowska, A.: Influence functions, followers and command games. Games Econom. Behav. 72(1), 123–138 (2011)

    Article  MathSciNet  Google Scholar 

  22. Grabisch, M., Rusinowska, A.: Lattices in social networks with influence. In: Proceedings of the ICFCA 2011 (9th International Conference on Formal Concept Analysis), Nicosia, Cyprus (2011)

    Google Scholar 

  23. Grabisch, M., Rusinowska, A.: A model of influence based on aggregation functions. Math. Soc. Sci. 66(3), 316–330 (2013)

    Article  MathSciNet  Google Scholar 

  24. Grabisch, M., Rusinowska, A.: Determining influential models. Oper. Res. Decis. 26(2), 69–85 (2016)

    MathSciNet  Google Scholar 

  25. Grabisch, M., Rusinowska, A.: A survey on nonstrategic models of opinion dynamics. Games 11(4), 65 (2020)

    Article  MathSciNet  Google Scholar 

  26. Grabisch, M., Rusinowska, A., Venel, X.: Diffusion in large networks. J. Econ. Dyn. Control 139(C), 104439 (2022)

    Google Scholar 

  27. Granovetter, M.: Threshold models of collective behavior. Am. J. Sociol. 83, 1420–1443 (1978)

    Article  Google Scholar 

  28. Gravner, J., Griffeath, D.: Cellular automaton growth on \(\mathbb{Z} ^2\): theorems, examples and problems. Adv. Appl. Math. 21, 241–304 (1998)

    Article  MathSciNet  Google Scholar 

  29. Holley, R.A., Liggett, T.M.: Ergodic theorems for weakly interacting infinite systems and the voter model. Ann. Probab. 3(4), 643–663 (1975)

    Article  MathSciNet  Google Scholar 

  30. Hoede, C., Bakker, R.: A theory of decisional power. J. Math. Sociol. 8, 309–322 (1982)

    Article  MathSciNet  Google Scholar 

  31. Hu, X., Shapley, L.S.: On authority distributions in organizations: controls. Games Econom. Behav. 45, 153–170 (2003)

    Article  MathSciNet  Google Scholar 

  32. Hu, X., Shapley, L.S.: On authority distributions in organizations: equilibrium. Games Econom. Behav. 45, 132–152 (2003)

    Article  MathSciNet  Google Scholar 

  33. Jackson, M.: Social and Economic Networks. Princeton University Press, Princeton (2008)

    Google Scholar 

  34. Jȩdrzejewski, A., Sznajd-Weron, K.: Statistical physics of opinion formation: is it a SPOOF? C R Phys. 20, 244–261 (2019)

    Article  Google Scholar 

  35. Kemeny, J.G., Snell, J.L.: Finite Markov Chains. Springer, New York (1976)

    Google Scholar 

  36. Morris, S.: Contagion. Rev. Econ. Stud. 67, 57–78 (2000)

    Article  MathSciNet  Google Scholar 

  37. Mossel, E., Tamuz, O.: Opinion exchange dynamics. Probab. Surv. 14, 155–204 (2017)

    Article  MathSciNet  Google Scholar 

  38. Nowak, N., Sznajd-Weron, K.: Homogeneous symmetrical threshold model with nonconformity: independence versus anticonformity. Complexity 2019, 5150825 (2019)

    Article  Google Scholar 

  39. Poindron, A.: A general model of binary opinions updating. Math. Soc. Sci. 109(C), 52–76 (2021)

    Google Scholar 

  40. Remy, E., Ruet, P., Thieffry, D.: Graphic requirements for multistability and attractive cycles in a Boolean dynamical framework. Adv. Appl. Math. 41, 335–350 (2008)

    Article  MathSciNet  Google Scholar 

  41. Rusinowska, A., Berghammer, R., De Swart, H., Grabisch, M.: Social networks: prestige, centrality, and influence. In: de Swart, H. (ed.) RAMICS 2011. LNCS, vol. 6663, pp. 22–39. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-21070-9_2

    Chapter  Google Scholar 

  42. Schelling, T.: Micromotives and Macrobehaviour. Norton, New York (1978)

    Google Scholar 

  43. Seneta, E.: Non-negative Matrices and Markov Chains. Springer Series in Statistics, Springer, New York (2006). https://doi.org/10.1007/0-387-32792-4

    Book  Google Scholar 

  44. Yager, R.: On ordered weighted averaging aggregation operators in multicriteria decision making. IEEE Trans. Syst. Man Cybern. 18(1), 183–190 (1988)

    Article  Google Scholar 

  45. Yager, R., Kacprzyk, J.: The Ordered Weighted Averaging Operators. Kluwer Academic Publishers (1997)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Centre d’Economie de la Sorbonne, 106-112 Bd de l’Hôpital, 75647, Paris, France

    Agnieszka Rusinowska & Michel Grabisch

  2. CNRS, Paris, France

    Agnieszka Rusinowska

  3. Paris School of Economics, Université Paris 1 Panthéon-Sorbonne, Paris, France

    Agnieszka Rusinowska & Michel Grabisch

Authors
  1. Agnieszka Rusinowska
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Michel Grabisch
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Agnieszka Rusinowska .

Editor information

Editors and Affiliations

  1. Durham University, Durham, UK

    Maximilien Gadouleau

  2. University of Guadalajara, Guadalajara, Mexico

    Alonso Castillo-Ramirez

Rights and permissions

Reprints and permissions

Copyright information

© 2024 IFIP International Federation for Information Processing

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Rusinowska, A., Grabisch, M. (2024). Binary Opinion Models of Influence and Opinion Dynamics in Social Networks. In: Gadouleau, M., Castillo-Ramirez, A. (eds) Cellular Automata and Discrete Complex Systems. AUTOMATA 2024. Lecture Notes in Computer Science, vol 14782. Springer, Cham. https://doi.org/10.1007/978-3-031-65887-7_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-65887-7_4

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-65886-0

  • Online ISBN: 978-3-031-65887-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Societies and partnerships