Social Network DeGroot Model: Consensus and Convergence Speed

  • Chapter
  • First Online:
Social Network DeGroot Model

Abstract

This chapter presents the social network DeGroot (SNDG) model. Subsequently, we propose the consensus condition, weights and convergence speed in SNDG.

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

Access this chapter

Institutional subscriptions

References

  1. D. Acemoǧlu, G. Como, F. Fagnani, A. Ozdaglar, Opinion fluctuations and disagreement in social networks, Mathematics of Operations Research 38 (2013) 1–27.

    Article  Google Scholar 

  2. S. Alonso, E. Herrera-Viedma, F. Chiclana, F. Herrera, A web based consensus support system for group decision making problems and incomplete preferences original research article, Information Sciences 180 (2010) 4477–4495.

    Article  Google Scholar 

  3. S. Banisch, T. Araújo, R. Lima, Agent based models and opinion dynamics as markov chains, Social Networks 34 (2012) 549–561.

    Article  Google Scholar 

  4. Barabási A, Albert R, Emergence of scaling in random networks. Science 286 (1999) 509.

    Google Scholar 

  5. R. Berger, A necessary and sufficient condition for reaching a consensus using DeGroot’s method, Journal of the American Statistical Association 76 (1981) 415–418.

    Article  Google Scholar 

  6. C. Castellano, S. Fortunato, V. Loreto, Statistical physics of social dynamics, Reviews of Modern Physics 81 (2007) 591–646.

    Article  Google Scholar 

  7. Chen P, Redner S, Majority rule dynamics in finite dimensions. Physical Review E 71 (2005) 036101.

    Google Scholar 

  8. X. Chen, Z. Ding, Y. Dong, H. Liang, Managing consensus with minimum adjustments in group decision making with opinions evolution, IEEE Transactions on Systems Man & Cybernetics Systems 51 (2019) 2299–2311.

    Article  Google Scholar 

  9. X. Chen, H. Zhang, Y. Dong, The fusion process with heterogeneous preference structures in group decision making: A survey, Information Fusion 24 (2015) 72–83.

    Article  Google Scholar 

  10. F. Chiclana, J. García, M. Moral, E. Herrera-Viedma, A statistical comparative study of different similarity measures of consensus in group decision making original research article, Information Sciences 221 (2013) 110–123.

    Article  Google Scholar 

  11. L. Cvetković, V. Kostić, Between Geršgorin and minimal Geršgorin sets, Journal of Computational and Applied Mathematics 196 (2006) 452–458.

    Article  Google Scholar 

  12. G. Deffuant, D. Neau, F. Amblard, G. Weisbuch, Mixing beliefs among interacting agents, Advances in Complex Systems 3 (2000) 87–98.

    Article  Google Scholar 

  13. M. Degroot, Reaching a consensus, Journal of The American Statistical Association 69 (1974) 118–121.

    Article  Google Scholar 

  14. Z. Ding, X. Chen, Y. Dong, F. Herrera, Consensus reaching in social network DeGroot model: The roles of the self-confidence and node degree, Information Sciences 486 (2019) 62–72.

    Article  Google Scholar 

  15. Z. Ding, X. Chen, Y. Dong, S. Yu, F. Herrera, Consensus convergence speed in social network DeGroot model: The effects of the agents with high self-confidence levels, IEEE Transactions on Computational Social Systems 10 (2023) 2282–2292.

    Article  Google Scholar 

  16. Ding Z, Shi X, Wu Y, Notes on self-confidence in opinion dynamics. International Journal of Modern Physics C 31 (2020) 2050163.

    Google Scholar 

  17. Y. Dong, Z.Ding, L. Martínez, F. Herrera, Managing consensus based on leadership in opinion dynamics, Information Sciences 397/398 (2017) 187–205.

    Article  Google Scholar 

  18. Y. Dong, Q. Zha, H. Zhang, F. Herrera, Consensus reaching and strategic manipulation in group decision making with trust relationships, IEEE Transactions on Systems, Man and Cybernetics: Systems 51 (2021) 6304–6318.

    Article  Google Scholar 

  19. Y. Dong, M. Zhan, G. Kou, Z. Ding, H. Liang, A survey on the fusion process in opinion dynamics, Information Fusion 43 (2018) 57–65.

    Article  Google Scholar 

  20. Y. Dong, X. Chen, F. Herrera, Minimizing adjusted simple terms in the consensus reaching process with hesitant linguistic assessments in group decision making, Information Sciences 297 (2015) 95–117.

    Article  Google Scholar 

  21. Y. Dong, C. Li, Y. Xu, X. Gu, Consensus-based group decision making under multi-granular unbalanced 2-tuple linguistic preference relations, Group Decision Negotiation 24 (2015) 217–242.

    Article  Google Scholar 

  22. Y. Dong, Y. Xu, H. Li, B. Feng, The OWA-based consensus operator under linguistic representation models using position indexes, European Journal of Operational Research 203 (2010) 455–463.

    Article  Google Scholar 

  23. P. Erdős, A. Rényi, On random graphs I, Publicationes Mathematicae 6 (1959) 290–297.

    Article  Google Scholar 

  24. N. Friedkin, E. Johnsen, Social influence and opinions, Journal of Mathematical Sociology 15 (1990) 193–206.

    Article  Google Scholar 

  25. N. Friedkin, E. Johnsen, Social influence networks and opinion change, Advances in Group Processes 16 (1999) 1–29.

    Google Scholar 

  26. Y. Gao, Z. Zhang, Consensus reaching with non-cooperative behavior management for personalized individual semantics-based social network group decision making, Journal of the Operational Research Society 73 (2022) 2518–2535.

    Article  Google Scholar 

  27. G. Gilardoni, M. Clayton, On reaching a consensus using Degroot’s iterative pooling, Annals of Statistics 21 (1993) 391–401.

    Article  Google Scholar 

  28. D. Hartfiel, C. Meyer, On the structure of stochastic matrices with a subdominant eigenvalue near 1, Linear Algebra and Its Applications 272 (1998) 193–203.

    Article  Google Scholar 

  29. R. Hegselmann, U. Krause, Opinion dynamics and bounded confidence models, analysis and simulation, Journal of Artificial Societies and Social Simulation 5 (2002).

    Google Scholar 

  30. E. Herrera-Viedma, F. Cabrerizo, J. Kacprzyk, W. Pedrycz, A review of soft consensus models in a fuzzy environment, Information Fusion 17 (2014) 4–13.

    Article  Google Scholar 

  31. R. Horn , C. Johnson, Matrix Analysis(2nd ed), Cambridge University Press, 1994.

    Google Scholar 

  32. M. Jackson, Social and Economic networks, Princeton University Press, 2008.

    Google Scholar 

  33. C. Li, Y. Dong, F. Herrera, E. Herrera-Viedma, L. Martínez, Personalized individual semantics in computing with words for supporting linguistic group decision making. An application on consensus reaching, Information Fusion 33 (2017) 29–40.

    Google Scholar 

  34. R. Olfatisaber, R. Murray, Consensus problems in networks of agents with switching topology and time-delays, IEEE Transactions on Automatic Control 49 (2004) 1520–1533.

    Article  Google Scholar 

  35. I. Palomares, F. Estrella, L. Martínez, F. Herrera, Consensus under a fuzzy context: Taxonomy, analysis framework AFRYCA and experimental case of study, Information Fusion 20 (2014) 252–271.

    Article  Google Scholar 

  36. I. Palomares, L. Martínez, A semisupervised multiagent system model to support consensus reaching processes, IEEE Transactions on Fuzzy Systems 22 (2014) 762–777.

    Article  Google Scholar 

  37. I. Palomares, L. Martínez, F. Herrera, A consensus model to detect and manage non-cooperative behaviors in large scale group decision making, IEEE Transactions on Fuzzy System 22 (2014) 516–530.

    Article  Google Scholar 

  38. I. Palomares, R. Rodríguez, L. Martínez, An attitude-driven web consensus support system for heterogeneous group decision making, Expert Systems With Applications 40 (2013) 139–149.

    Article  Google Scholar 

  39. S. Robbins, T. Judge, Organizational behavior(16th ed), Pearson Education,Inc., 2016.

    Google Scholar 

  40. E. Seneta, Non-negative matrices and markov chains, Springer, 2006.

    Google Scholar 

  41. Tuma N, Hannan M (1984) Social dynamics: models and methods. Journal of the American Statistical Association 80:775

    Google Scholar 

  42. R. Varga, Geršgorin and his circles, Springer, 2004.

    Google Scholar 

  43. Watts D, Strogatz S, Collective dynamics of “small-world" networks. Nature 393 (1998) 440–442.

    Google Scholar 

  44. J. Wu, F. Chiclana, E. Herrera-Viedma, Trust based consensus model for social network in an incomplete linguistic information context, Applied Soft Computing 35 (2015) 827–839.

    Article  Google Scholar 

  45. Q. Zha, Y. Dong, H. Zhang, F. Herrera, E. Herrera-Viedma, A personalized feedback mechanism based on bounded confidence learning to support consensus reaching in group decision making, IEEE Transactions on Systems, Man and Cybernetics: Systems 51 (2019) 3900–3910.

    Article  Google Scholar 

  46. Q. Zha, H. Liang, G. Kou, Y. Dong, S. Yu, Feedback mechanism with bounded confidence-based optimization approach for consensus reaching in multiple attribute large-scale group decision making, IEEE Transactions on Computational Social Systems 6 (2019) 994–1006.

    Article  Google Scholar 

  47. Z. Zhang, Z. Li, Personalized individual semantics-based consistency control and consensus reaching in linguistic group decision making, IEEE Transactions on Systems, Man, and Cybernetics: Systems 52 (2022) 5623–5635.

    Article  Google Scholar 

  48. Z. Zhang, Z. Li, Y. Gao, Consensus reaching for group decision making with multi-granular unbalanced linguistic information: A bounded confidence and minimum adjustment-based approach, Information Fusion 74 (2021) 96–110.

    Article  Google Scholar 

  49. K. Zollman, Social network structure and the achievement of consensus, Politics, Philosophy & Economics 11 (2012) 26–44.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Yucheng Dong .

Rights and permissions

Reprints and permissions

Copyright information

© 2024 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Dong, Y., Ding, Z., Kou, G. (2024). Social Network DeGroot Model: Consensus and Convergence Speed. In: Social Network DeGroot Model. Springer, Singapore. https://doi.org/10.1007/978-981-97-0421-7_2

Download citation

Publish with us

Policies and ethics

Navigation