Skip to main content
Log in

Soft-control for collective opinion of weighted DeGroot model

  • Published:
Journal of Systems Science and Complexity Aims and scope Submit manuscript

Abstract

The DeGroot model is a classic model to study consensus of opinion in a group of individuals (agents). Consensus can be achieved under some circumstances. But when the group reach consensus with a convergent opinion value which is not what we expect, how can we intervene the system and change the convergent value? In this paper a mechanism named soft control is first introduced in opinion dynamics to guide the group’s opinion when the population are given and evolution rules are not allowed to change. According to the idea of soft control, one or several special agents, called shills, are added and connected to one or several normal agents in the original group. Shills act and are treated as normal agents. The authors prove that the change of convergent opinion value is decided by the initial opinion and influential value of the shill, as well as how the shill connects to normal agents. An interesting and counterintuitive phenomenon is discovered: Adding a shill with an initial opinion value which is smaller (or larger) than the original convergent opinion value dose not necessarily decrease (or increase) the convergent opinion value under some conditions. These conditions are given through mathematical analysis and they are verified by the numerical tests. The authors also find out that the convergence speed of the system varies when a shill is connected to different normal agents. Our simulations show that it is positively related to the degree of the connected normal agent in scale-free networks.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. French J R P, A formal theory of social power, Psychological Review, 1956, 63: 181–194.

    Article  Google Scholar 

  2. Harary F, A criterion for unanimity in French’s theory of social power, Studies in Social Power, ed. by Cartwright D, Institute for social Research, Ann Arbor, 1959.

    Google Scholar 

  3. De Groot M H, Reaching a consensus, Journal of American Statistical Association, 1974, 69: 118–121.

    Article  MATH  Google Scholar 

  4. Lehere K, When rational disagreement is impossible, Nous, 1976, 10(3): 327–332.

    Article  MathSciNet  Google Scholar 

  5. Lehere K, Social consensus and rational agnoiology, Synthese, 1975, 31: 141–160.

    Article  Google Scholar 

  6. Lehere K, Consensus and comparison: A theory of social rationality, Foundations and Applications of Decision Theory, 1978, 13: 283–309.

    Google Scholar 

  7. Abelson R P, Mathematical models of the distribution of attitudes under controversy, Contributions to Mathematical Psychology, eds. by Frederiksen N and Gulliksen H, New York, NY: Holt, Rinehart, and Winston, 1964.

    Google Scholar 

  8. Friedkin N E and Johnsen E C, Social influence networks and opinion change, Advaances in Group Processes, 1999, 16: 1–29.

    Google Scholar 

  9. Acemglu D, Como G, Fagnani F, et al., Opinion fluctuations and disagreement in social networks, Mathematics of Operations Research, 2013, 38: 1–27.

    Article  MathSciNet  MATH  Google Scholar 

  10. Krause U, A discrete nonlinear and non-autonomous model of consensus formation, Communications in Difference Equations, eds. by Elaydi S, Ldas G, Popenda J, et al., Amsterdam, Gordon and Breach Publ., 2000, 227–236.

    Chapter  Google Scholar 

  11. Deffuant G, Neau D, Amblard F, et al., Mixing beliefs among interacting agents, Advances in Complex Systems, 2000, 3: 1–4.

    Article  Google Scholar 

  12. Holley R A and Liggett T M, Ergodic theorems for weakly interacting infinite systems and the voter model, Annals of Probability, 1975, 3: 643–663.

    Article  MathSciNet  MATH  Google Scholar 

  13. Galam S, Sociophysics: A mean behavior model for the process of strike, The Journal of Mathematical Sociology, 1982, 9(2): 1–13.

    Article  Google Scholar 

  14. Weron S and Sznajd K J, Opinion evolution in closed community, International Journal of Modern Physics C, 2000, 11(6): 1157–1165.

    Article  Google Scholar 

  15. Golub B and Jackson M O, Naive learning in social networks and the wisdom of crowds, American Economic Journal: Microeconomics, 2007, 2(1): 112–149.

    Google Scholar 

  16. Jackson M O, Social and Economic Networks, Princeton University Press, Princeton, 2008.

    MATH  Google Scholar 

  17. Hegselmann R and Krause U, Truth and Cognitive division of labour first steps towards a computer aided social epistemology, Journal of Artificial Societies and Social Simulation, 2006, 9(3): 10–38.

    Google Scholar 

  18. Chandrasekhar A G, Rreguy H, and Xandari J P, Testing models of social learning on networksevidence from a lab experiment in the field, Working Paper, 2014.

    Google Scholar 

  19. Acemogluy D and Ozdaglar A, Opinion dynamics and learning in social networks, Dynamic Games and Applications, 2011, 1(1): 3–49.

    Article  MathSciNet  MATH  Google Scholar 

  20. Mobilia M, Does a single zealot affect an infinite group of voters, Physical Review Letters, 2003, 91(2): 2409–2428.

    Article  Google Scholar 

  21. Mobilia M, Petersen A, and Redner S, On the role of zealotry in the voter model, Journal of Statistical Mechanics, 2007, 8: 1742–5468.

    Google Scholar 

  22. Hughes M, Buzz marketing, Sales and Service Excellence, 2005, 5(7): 16.

    Google Scholar 

  23. Kelly J A, St Lawrence J S, Diaz Y E, et al., HIV risk behavior reduction following intervention with key opinion leaders of population: An experimental analysis, American Journal of Public Health, 1991, 81(2): 168–171.

    Article  Google Scholar 

  24. Han J, Li M, and Guo L, Soft control on a collective behavior of a group of autonomous agents by a Shill agent, Journal of Systems Science and Complexity, 2005, 19(1): 54–62.

    Article  MathSciNet  Google Scholar 

  25. Han J and Wang L, Nondestructive intervention to multi-agent systems through an intelligent agent, PLoS ONE, 2013, 8(5).

    Google Scholar 

  26. Wang X, Han J, and Han H, Special agents can promote cooperation in population, PLoS ONE, 2011, 6(12): e61542.

    Article  Google Scholar 

  27. Seneta E, Non-Negative Matrices and Markov Chains, Springer, 1981.

    Book  MATH  Google Scholar 

  28. Watts D J and Strogatz S H, Collective dynamics of ‘small-world’ networks, Nature, 1998, 393(6684): 440–442.

    Article  Google Scholar 

  29. Barabsi A L and Albert R, Emergence of scaling in random networks, Science, 1999, 286(5439): 509–512.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jing Han.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant No. 61374168.

This paper was recommended for publication by Editor WANG Xiaofan.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Han, H., Qiang, C., Wang, C. et al. Soft-control for collective opinion of weighted DeGroot model. J Syst Sci Complex 30, 550–567 (2017). https://doi.org/10.1007/s11424-017-5186-9

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11424-017-5186-9

Keywords

Navigation