Skip to main content
SpringerLink
Log in

Consensus on Social Influence Network Model

  • Conference paper
  • First Online:
Computational Social Networks (CSoNet 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9197))

Included in the following conference series:

Abstract

Many studies show that opinions formation displays multiple patterns, from consensus to polarization. Under the framework of the social influence network by Friedkin and Johnsen (1999) and based on random walk on graph, we rigorously prove that for a social group influence system, with static social influence structure, the group consensus is almost a quite certain result. In addition, we prove the lower bounds on the convergence time m for random walk \(P^{m}\) to be close to its final average consensus (wisdom group decision making) state, given an arbitrary initial opinions profile vector and one small positive error \(\epsilon \). Although our explanations are purely based on mathematic deduction, it shows that the latent social influence structure is the key factor for the persistence of disagreement and formation of opinions convergence or consensus in the real world social group.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. DeGroot, M.: Reaching a consensus. Journal of the American Statistical Association 69(345), 118–121 (1974)

    Article  MATH  Google Scholar 

  2. Friedkin, N.E., Johnsen, E.C.: Social influence networks and opinion change. In: Lawler, E.J., Macy, M.W. (eds.) Advances in Group Processes vol. 16, pp. 1–29 (1999)

    Google Scholar 

  3. Friedkin, N.E.: A formal theory of reflected appraisals in the evolution of power. Administrative Science Quarterly 56(4), 501–529 (2011)

    Article  Google Scholar 

  4. French, J.: A formal theory of social power. Psychological Review 63, 181–194 (1956)

    Article  MathSciNet  Google Scholar 

  5. Jadbabaie, A., Lin, J., Morse, A.S.: Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Transactions on Automatic Control 48(6), 988–1001 (2003)

    Article  MathSciNet  Google Scholar 

  6. Blondel, V., Hendrickx, J.M., Olshevsky, A., et al.: Convergence in multiagent coordination, consensus, and flocking. In: The 44th IEEE Conference on Decision and Control and the European Control Conference 2005, pp. 2996–3000 (2005)

    Google Scholar 

  7. Olfati-Saber, R., Murray, R.M.: Consensus problems in networks of agents with switching topology and time-delays. IEEE Transactions on Automatic Control 49(9), 1520–1533 (2004)

    Article  MathSciNet  Google Scholar 

  8. Moreau, L.: Stability of multiagent systems with time-dependent communication links. IEEE Transactions on Automatic Control 50(2), 169–182 (2005)

    Article  MathSciNet  Google Scholar 

  9. Fagnani, F., Zampieri, S.: Randomized consensus algorithms over large scale networks. IEEE Journal on Selected Areas in Communications 26(4), 634–649 (2008)

    Article  Google Scholar 

  10. Tsitsiklis, J.N.: Problems in decentralized decision making and computation. Ph.D. Dissertation, Massachusetts Institute of Technology (1985)

    Google Scholar 

  11. Kempe, D., Dobra, A., Gehrke, J.: Gossip-based computation of aggregate information. In: Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science, pp. 482–491. IEEE (2003)

    Google Scholar 

  12. Intanagonwiwat, C., Govindan, R., Estrin, D.: Directed diffusion: a scalable and robust communication paradigm for sensor networks. In: Proceedings of the 6th Annual International Conference on Mobile Computing and Networking, pp. 56–67. ACM (2000)

    Google Scholar 

  13. Zhao, J., Govindan, R., Estrin, D.: Computing aggregates for monitoring wireless sensor networks. In: Proceedings of the First IEEE International Workshop on Sensor Network Protocols and Applications, pp. 139–148. IEEE (2003)

    Google Scholar 

  14. Xiao, L., Boyd, S., Lall, S.: A scheme for robust distributed sensor fusion based on average consensus. In: The 4th International Symposium on Information Processing in Sensor Networks, 63–70. IEEE (2005)

    Google Scholar 

  15. Dimakis, A.G., Sarwate, A.D., Wainwright, M.J.: Geographic gossip: efficient aggregation for sensor networks. In: Proceedings of the 5th International Conference on Information Processing in Sensor Networks, pp. 69–76. ACM (2006)

    Google Scholar 

  16. Galam, S.: From 2000 bush-gore to 2006 italian elections: voting at fifty-fifty and the contrarian effect. Quality and Quantity Journal 41, 579–589 (2007)

    Article  Google Scholar 

  17. Arrow, K.J.: Social Choice and Individual Values. Wiley, New York (1951)

    Google Scholar 

  18. Frasca, P., Ravazzi, C., Tempo, R., et al.: Gossips and prejudices: Ergodic randomized dynamics in social networks. arXiv:1304.2268 (2013)

  19. Yardi, S., Boyd, D.: Dynamic Debates: An Analysis of Group Polarization Over Time on Twitter. Bulletin of Science, Technology & Society 30(5), 316–327 (2010)

    Article  Google Scholar 

  20. Chung, F.R.K.: Spectral graph theory. American Mathematical Soc. 92 (1997)

    Google Scholar 

  21. Ishii, H., Tempo, R.: Distributed randomized algorithms for the PageRank computation. IEEE Transactions on Automatic Control 55(9), 1987–2002 (2010)

    Article  MathSciNet  Google Scholar 

  22. Golub, B., Jackson, M.O.: Naive learning in social networks and the wisdom of crowds. American Economic Journal: Microeconomics, 112–149 (2010)

    Google Scholar 

  23. Touri, B., Nedic, A.: On ergodicity, infinite flow, and consensus in random models. IEEE Transactions on Automatic Control 56(7), 1593–1605 (2011)

    Article  MathSciNet  Google Scholar 

  24. Bertsekas, D., Tsitsiklis, J.N.: Parallel and Distributed Computation: Numerical Methods. Prentice Hall (1989)

    Google Scholar 

  25. Nedic, A., Ozdaglar, A.: Distributed subgradient methods for multi-agent optimization. IEEE Transactions on Automatic Control 54(1), 48–61 (2009)

    Article  MathSciNet  Google Scholar 

  26. Olshevsky, A., John, N.: Tsitsiklis. Convergence Speed in Distributed Consensus and Averaging. SIAM Journal on Control and Optimization 48(1), 33–55 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  27. Kemeny, J.G., Snell, J.L.: Finite Markov Chains. Springer (1960)

    Google Scholar 

  28. Boyd, S., et al.: Randomized gossip algorithms. IEEE Trans. Information Theory 52(6), 2508–2530 (2006)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Applied Statistics, Dali University, Dali, 671003, China

    Zhenpeng Li

  2. Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing, 100190, China

    Xijin Tang

Authors
  1. Zhenpeng Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xijin Tang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xijin Tang .

Editor information

Editors and Affiliations

  1. Computer and Information Science and Engineering, University of Florida, Gainesville, Florida, USA

    My T. Thai

  2. Towsen University, Towson, Maryland, USA

    Nam P. Nguyen

  3. Chinese Academy of Sciences, Beijing, China

    Huawei Shen

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Li, Z., Tang, X. (2015). Consensus on Social Influence Network Model. In: Thai, M., Nguyen, N., Shen, H. (eds) Computational Social Networks. CSoNet 2015. Lecture Notes in Computer Science(), vol 9197. Springer, Cham. https://doi.org/10.1007/978-3-319-21786-4_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-21786-4_7

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-21785-7

  • Online ISBN: 978-3-319-21786-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation