Document Open Access Logo

Fairness and Consensus in an Asynchronous Opinion Model for Social Networks

Authors Jesús Aranda , Sebastián Betancourt , Juan Fco. Díaz , Frank Valencia

PDF
Thumbnail PDF

File

LIPIcs.CONCUR.2024.7.pdf
  • Filesize: 1.49 MB
  • 17 pages

Document Identifiers

Author Details

Jesús Aranda
  • Universidad del Valle, Colombia
Sebastián Betancourt
  • Universidad del Valle, Colombia
Juan Fco. Díaz
  • Universidad del Valle, Colombia
Frank Valencia
  • CNRS LIX, École Polytechnique de Paris, France
  • Pontificia Universidad Javeriana Cali, Colombia

Funding

This work is partly supported by the Colombian Minciencias project PROMUEVA, BPIN 2021000100160.

Cite AsGet BibTex

Jesús Aranda, Sebastián Betancourt, Juan Fco. Díaz, and Frank Valencia. Fairness and Consensus in an Asynchronous Opinion Model for Social Networks. In 35th International Conference on Concurrency Theory (CONCUR 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 311, pp. 7:1-7:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.CONCUR.2024.7

Abstract

We introduce a DeGroot-based model for opinion dynamics in social networks. A community of agents is represented as a weighted directed graph whose edges indicate how much agents influence one another. The model is formalized using labeled transition systems, henceforth called opinion transition systems (OTS), whose states represent the agents' opinions and whose actions are the edges of the influence graph. If a transition labeled (i,j) is performed, agent j updates their opinion taking into account the opinion of agent i and the influence i has over j. We study (convergence to) opinion consensus among the agents of strongly-connected graphs with influence values in the interval (0,1). We show that consensus cannot be guaranteed under the standard strong fairness assumption on transition systems. We derive that consensus is guaranteed under a stronger notion from the literature of concurrent systems; bounded fairness. We argue that bounded-fairness is too strong of a notion for consensus as it almost surely rules out random runs and it is not a constructive liveness property. We introduce a weaker fairness notion, called m-bounded fairness, and show that it guarantees consensus. The new notion includes almost surely all random runs and it is a constructive liveness property. Finally, we consider OTS with dynamic influence and show convergence to consensus holds under m-bounded fairness if the influence changes within a fixed interval [L,U] with 0 < L < U < 1. We illustrate OTS with examples and simulations, offering insights into opinion formation under fairness and dynamic influence.

Subject Classification

ACM Subject Classification
  • Theory of computation → Social networks
Keywords
  • Social networks
  • fairness
  • DeGroot
  • consensus
  • asynchrony

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

Related Versions

Supplementary Materials

References

  1. Martín Abadi and Leslie Lamport. An old-fashioned recipe for real time. In Real-Time: Theory in Practice. Springer Berlin Heidelberg, 1992. Google Scholar
  2. Emerico Aguilar and Yasumasa Fujisaki. Opinion dynamics via a gossip algorithm with asynchronous group interactions. Proceedings of the ISCIE International Symposium on Stochastic Systems Theory and its Applications, 2019:99-102, 2019. URL: https://doi.org/10.5687/sss.2019.99.
  3. Shaull Almagor, Yoram Hirshfeld, and Orna Kupferman. Promptness in ω-regular automata. In Automated Technology for Verification and Analysis. Springer Berlin Heidelberg, 2010. Google Scholar
  4. Mário S. Alvim, Bernardo Amorim, Sophia Knight, Santiago Quintero, and Frank Valencia. A Multi-agent Model for Polarization Under Confirmation Bias in Social Networks. In 41th International Conference on Formal Techniques for Distributed Objects, Components, and Systems (FORTE), 2021. URL: https://inria.hal.science/hal-03740263.
  5. Krzysztof R. Apt, Nissim Francez, and Shmuel Katz. Appraising fairness in languages for distributed programming. In 14th ACM SIGACT-SIGPLAN Symposium on Principles of Programming Languages, POPL 1987, 1987. URL: https://doi.org/10.1145/41625.41642.
  6. Jesús Aranda, Frank D. Valencia, and Cristian Versari. On the expressive power of restriction and priorities in CCS with replication. In Foundations of Software Science and Computational Structures, FoSSaCS 2009, volume 5504 of Lecture Notes in Computer Science, 2009. URL: https://doi.org/10.1007/978-3-642-00596-1_18.
  7. Jesús Aranda, Sebastián Betancourt, Juan Fco. Díaz, and Frank Valencia. Fairness and consensus in opinion models (technical report), 2024. URL: https://arxiv.org/abs/2312.12251.
  8. Elliot Aronson, Timothy Wilson, and Robin Akert. Social Psychology. Upper Saddle River, NJ : Prentice Hall, 7 edition, 2010. Google Scholar
  9. Eike Best. Fairness and conspiracies. Information Processing Letters, 18(4):215-220, 1984. URL: https://doi.org/10.1016/0020-0190(84)90114-5.
  10. Arun G Chandrasekhar, Horacio Larreguy, and Juan Pablo Xandri. Testing models of social learning on networks: Evidence from a lab experiment in the field. Working Paper 21468, National Bureau of Economic Research, August 2015. URL: https://doi.org/10.3386/w21468.
  11. S. Chatterjee and E. Seneta. Towards consensus: Some convergence theorems on repeated averaging. Journal of Applied Probability, 14(1):89-97, 1977. URL: https://doi.org/10.2307/3213262.
  12. Zihan Chen, Jiahu Qin, Bo Li, Hongsheng Qi, Peter Buchhorn, and Guodong Shi. Dynamics of opinions with social biases. Automatica, 106:374-383, 2019. URL: https://doi.org/10.1016/j.automatica.2019.04.035.
  13. Pranav Dandekar, Ashish Goel, and David Lee. Biased assimilation, homophily and the dynamics of polarization. Proceedings of the National Academy of Sciences of the United States of America, 110, March 2013. URL: https://doi.org/10.1073/pnas.1217220110.
  14. Morris H. DeGroot. Reaching a consensus. Journal of the American Statistical Association, 1974. URL: http://www.jstor.org/stable/2285509.
  15. Peter M. DeMarzo et al. Persuasion bias, social influence, and unidimensional opinions. The Quarterly Journal of Economics, 118(3):909-968, 2003. URL: http://www.jstor.org/stable/25053927.
  16. Nachum Dershowitz, D. N. Jayasimha, and Seungjoon Park. Bounded Fairness, pages 304-317. Springer Berlin Heidelberg, Berlin, Heidelberg, 2003. URL: https://doi.org/10.1007/978-3-540-39910-0_14.
  17. F. Fagnani and S. Zampieri. Asymmetric randomized gossip algorithms for consensus. IFAC Proceedings Volumes, 2008. URL: https://doi.org/10.3182/20080706-5-KR-1001.01528.
  18. Moreno Falaschi, Carlos Olarte, Catuscia Palamidessi, and Frank D. Valencia. Declarative diagnosis of temporal concurrent constraint programs. In Logic Programming. ICLP 2007, 2007. URL: https://doi.org/10.1007/978-3-540-74610-2_19.
  19. Rob Van Glabbeek and Peter Höfner. Progress, justness, and fairness. ACM Computing Surveys, 52(4):1-38, August 2019. URL: https://doi.org/10.1145/3329125.
  20. Elizabeth B. Goldsmith. Introduction to Social Influence: Why It Matters, pages 3-22. Springer International Publishing, Cham, 2015. URL: https://doi.org/10.1007/978-3-319-20738-4_1.
  21. Benjamin Golub and Evan Sadler. Learning in social networks. Available at SSRN 2919146, 2017. Google Scholar
  22. Orna Grumberg, Nissim Francez, Johann A. Makowsky, and Willem P. de Roever. A proof rule for fair termination of guarded commands. Information and Control, 66(1):83-102, 1985. URL: https://doi.org/10.1016/S0019-9958(85)80014-0.
  23. Michell Guzmán, Stefan Haar, Salim Perchy, Camilo Rueda, and Frank Valencia. Belief, Knowledge, Lies and Other Utterances in an Algebra for Space and Extrusion. Journal of Logical and Algebraic Methods in Programming, September 2016. URL: https://doi.org/10.1016/j.jlamp.2016.09.001.
  24. Stefan Haar, Salim Perchy, Camilo Rueda, and Frank Valencia. An Algebraic View of Space/Belief and Extrusion/Utterance for Concurrency/Epistemic Logic. In 17th International Symposium on Principles and Practice of Declarative Programming (PPDP 2015), 2015. URL: https://doi.org/10.1145/2790449.2790520.
  25. M.Z. Kwiatkowska. Survey of fairness notions. Information and Software Technology, 31(7):371-386, 1989. URL: https://doi.org/10.1016/0950-5849(89)90159-6.
  26. Leslie Lamport. Fairness and hyperfairness. Distributed Computing, 13(4):239-245, November 2000. URL: https://doi.org/10.1007/PL00008921.
  27. D. Lehmann, A. Pnueli, and J. Stavi. Impartiality, justice and fairness: The ethics of concurrent termination. In Shimon Even and Oded Kariv, editors, Automata, Languages and Programming, pages 264-277, Berlin, Heidelberg, 1981. Springer Berlin Heidelberg. Google Scholar
  28. R.D. Mauldin. The Scottish Book: Mathematics from the Scottish Café. Birkhäuser, 1981. URL: https://books.google.com.co/books?id=gaqEAAAAIAAJ.
  29. Hossein Noorazar. Recent advances in opinion propagation dynamics: a 2020 survey. The European Physical Journal Plus, 135(6):521, June 2020. URL: https://doi.org/10.1140/epjp/s13360-020-00541-2.
  30. Guodong Shi, Bo Li, Mikael Johansson, and Karl Henrik Johansson. Finite-time convergent gossiping. IEEE/ACM Transactions on Networking, 24(5):2782-2794, 2016. URL: https://doi.org/10.1109/TNET.2015.2484345.
  31. Albert N. Shiryaev. Probability-1: Volume 1. Springer New York, 2016. URL: https://doi.org/10.1007/978-0-387-72206-1.
  32. Houshang H. Sohrab. Basic Real Analysis. Birkhauser Basel, 2nd edition, 2014. URL: https://doi.org/10.1007/0-8176-4441-5.
  33. Hagen Völzer and Daniele Varacca. Defining fairness in reactive and concurrent systems. J. ACM, 59(3), June 2012. URL: https://doi.org/10.1145/2220357.2220360.
  34. Hagen Völzer, Daniele Varacca, and Ekkart Kindler. Defining fairness. In Martín Abadi and Luca de Alfaro, editors, CONCUR 2005 - Concurrency Theory, Berlin, Heidelberg, 2005. Springer Berlin Heidelberg. Google Scholar
  35. Xing Wang, Bingjue Jiang, and Bo Li. Opinion dynamics on social networks. Acta Mathematica Scientia, 42(6):2459-2477, November 2022. URL: https://doi.org/10.1007/s10473-022-0616-8.
  36. Stanley Wasserman and Katherine Faust. Social network analysis in the social and behavioral sciences. In Social Network Analysis: Methods and Applications, pages 1-27. Cambridge University Press, 1994. Google Scholar
  37. Chen X, Tsaparas P, Lijffijt J, and De Bie T. Opinion dynamics with backfire effect and biased assimilation. PLoS ONE, 16(9), 2021. URL: https://doi.org/10.1371/journal.pone.0256922.
  38. Weiguo Xia, Mengbin Ye, Ji Liu, Ming Cao, and Xi-Ming Sun. Analysis of a nonlinear opinion dynamics model with biased assimilation. Automatica, 120:109113, 2020. URL: https://doi.org/10.1016/j.automatica.2020.109113.
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH Imprint Privacy Contact