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

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Abstract

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.

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Acknowledgements

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.

Author information

Authors and Affiliations

  1. Department of Economics, School of Economics and Management, Beijing Jiaotong University, Beijing, 100044, China

    Zhigang Cao

  2. Department of Information Engineering, Weifang Business Vocational College, Zhucheng, 262234, China

    Fengliang Jiao

  3. The Research Center of Information Technology & Economic and Social Development, Hangzhou Dianzi University, Hangzhou, 310018, China

    Xinglong Qu

  4. School of Systems Science, Beijing Normal University, Beijing, 100088, China

    Wen-Xu Wang

  5. MADIS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Mingmin Yang & Xiaoguang Yang

  6. Laboratory of Mathematics and Complex Systems, Ministry of Education, School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, China

    Boyu Zhang

Authors
  1. Zhigang Cao
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  2. Fengliang Jiao
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  3. Xinglong Qu
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  4. Wen-Xu Wang
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  5. Mingmin Yang
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  6. Xiaoguang Yang
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  7. Boyu Zhang
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Corresponding author

Correspondence to Boyu Zhang.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant Nos. 71771026, 71701058, 11471326.

This paper was recommended for publication by Editor HONG Yiguang.

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Cao, Z., Jiao, F., Qu, X. et al. Rebels Lead to the Doctrine of the Mean: A Heterogeneous DeGroot Model. J Syst Sci Complex 31, 1498–1509 (2018). https://doi.org/10.1007/s11424-018-7136-6

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  • DOI: https://doi.org/10.1007/s11424-018-7136-6

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