Journal of Systems Science and Complexity

, Volume 31, Issue 6, pp 1498–1509 | Cite as

Rebels Lead to the Doctrine of the Mean: A Heterogeneous DeGroot Model

  • Zhigang Cao
  • Fengliang Jiao
  • Xinglong Qu
  • Wen-Xu Wang
  • Mingmin Yang
  • Xiaoguang Yang
  • Boyu ZhangEmail author


The DeGroot model is one of the most classical models in the field of opinion dynamics. The standard DeGroot model assumes that agents are homogeneous and update their opinions in the direction of a weighted average of their neighbors’ opinions. One natural question is whether a second type of agents could significantly change the main properties of the model. The authors address this question by introducing rebels, who update their opinions toward the opposite of their neighbors’ weighted average. The authors find that the existence of rebels remarkably affects the opinion dynamics. Under certain mild conditions, the existence of a few rebels will lead the group opinion to the golden mean, regardless of the initial opinions of the agents and the structure of the learning network. This result is completely different from that of the standard DeGroot model, where the final consensus opinion is determined by both the initial opinions and the learning topology. The study then provides new insights into understanding how heterogeneous individuals in a group reach consensus and why the golden mean is so common in human society.


Golden mean network opinion dynamics rebel 


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A preliminary version of this paper appears in Proceedings of The 6th International Conference on Knowledge, Information and Creativity Support Systems, Beijing, 2011. The authors acknowledge the valuable suggestions and comments received from that conference.


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Copyright information

© Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Zhigang Cao
    • 1
  • Fengliang Jiao
    • 2
  • Xinglong Qu
    • 3
  • Wen-Xu Wang
    • 4
  • Mingmin Yang
    • 5
  • Xiaoguang Yang
    • 5
  • Boyu Zhang
    • 6
    Email author
  1. 1.Department of Economics, School of Economics and ManagementBeijing Jiaotong UniversityBeijingChina
  2. 2.Department of Information EngineeringWeifang Business Vocational CollegeZhuchengChina
  3. 3.The Research Center of Information Technology & Economic and Social DevelopmentHangzhou Dianzi UniversityHangzhouChina
  4. 4.School of Systems ScienceBeijing Normal UniversityBeijingChina
  5. 5.MADIS, Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijingChina
  6. 6.Laboratory of Mathematics and Complex Systems, Ministry of Education, School of Mathematical SciencesBeijing Normal UniversityBeijingChina

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