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.
Similar content being viewed by others
References
French J R P, A formal theory of social power, Psychological Review, 1956, 63: 181–194.
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.
De Groot M H, Reaching a consensus, Journal of American Statistical Association, 1974, 69: 118–121.
Lehere K, When rational disagreement is impossible, Nous, 1976, 10(3): 327–332.
Lehere K, Social consensus and rational agnoiology, Synthese, 1975, 31: 141–160.
Lehere K, Consensus and comparison: A theory of social rationality, Foundations and Applications of Decision Theory, 1978, 13: 283–309.
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.
Friedkin N E and Johnsen E C, Social influence networks and opinion change, Advaances in Group Processes, 1999, 16: 1–29.
Acemglu D, Como G, Fagnani F, et al., Opinion fluctuations and disagreement in social networks, Mathematics of Operations Research, 2013, 38: 1–27.
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.
Deffuant G, Neau D, Amblard F, et al., Mixing beliefs among interacting agents, Advances in Complex Systems, 2000, 3: 1–4.
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.
Galam S, Sociophysics: A mean behavior model for the process of strike, The Journal of Mathematical Sociology, 1982, 9(2): 1–13.
Weron S and Sznajd K J, Opinion evolution in closed community, International Journal of Modern Physics C, 2000, 11(6): 1157–1165.
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.
Jackson M O, Social and Economic Networks, Princeton University Press, Princeton, 2008.
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.
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.
Acemogluy D and Ozdaglar A, Opinion dynamics and learning in social networks, Dynamic Games and Applications, 2011, 1(1): 3–49.
Mobilia M, Does a single zealot affect an infinite group of voters, Physical Review Letters, 2003, 91(2): 2409–2428.
Mobilia M, Petersen A, and Redner S, On the role of zealotry in the voter model, Journal of Statistical Mechanics, 2007, 8: 1742–5468.
Hughes M, Buzz marketing, Sales and Service Excellence, 2005, 5(7): 16.
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.
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.
Han J and Wang L, Nondestructive intervention to multi-agent systems through an intelligent agent, PLoS ONE, 2013, 8(5).
Wang X, Han J, and Han H, Special agents can promote cooperation in population, PLoS ONE, 2011, 6(12): e61542.
Seneta E, Non-Negative Matrices and Markov Chains, Springer, 1981.
Watts D J and Strogatz S H, Collective dynamics of ‘small-world’ networks, Nature, 1998, 393(6684): 440–442.
Barabsi A L and Albert R, Emergence of scaling in random networks, Science, 1999, 286(5439): 509–512.
Author information
Authors and Affiliations
Corresponding author
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
About this article
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
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11424-017-5186-9