Recent Advances in the Modelling and Analysis of Opinion Dynamics on Influence Networks

Abstract

A fundamental aspect of society is the exchange and discussion of opinions between individuals, occurring in situations as varied as company boardrooms, elementary school classrooms and online social media. After a very brief introduction to the established results of the most fundamental opinion dynamics models, which seek to mathematically capture observed social phenomena, a brief discussion follows on several recent themes pursued by the authors building on the fundamental ideas. In the first theme, we study the way an individual′s self-confidence can develop through contributing to discussions on a sequence of topics, reaching a consensus in each case, where the consensus value to some degree reflects the contribution of that individual to the conclusion. During this process, the individuals in the network and the way they interact can change. The second theme introduces a novel discrete-time model of opinion dynamics to study how discrepancies between an individual′s expressed and private opinions can arise due to stubbornness and a pressure to conform to a social norm. It is also shown that a few extremists can create “pluralistic ignorance”, where people believe there is majority support for a position but in fact the position is privately rejected by the majority. Last, we consider a group of individuals discussing a collection of logically related topics. In particular, we identify that for topics whose logical interdependencies take on a cascade structure, disagreement in opinions can occur if individuals have competing and/or heterogeneous views on how the topics are related, i.e., the logical interdependence structure varies between individuals.

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Acknowledgements

We would like to thank all of our co-authors of related work whose ideas contributed immeasurably to the themes covered in this paper: Chang-Bin Yu, Ji Liu, Tamer Başar, Ming Cao, Hyo-Sung Ahn, Yu-Zhen Qin, Alain Govaert, Minh Hoang Trinh and Young-Hun Lim.

This work was supported by the Australian Research Council (ARC) (No. DP-160104500) and Data61-CSIRO, Australia. This work was also supported in part by the European Research Council (No. ERC-CoG-771687) and the Netherlands Organization for Scientific Research (No. NWO-vidi-14134).

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Correspondence to Brian D. O. Anderson.

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Brian D. O. Anderson received the B. Sc. degree in pure mathematics in 1962, and B. Eng. degree in electrical engineering in 1964, from the University of Sydney, Australia, and the Ph. D. degree in electrical engineering from Stanford University, USA in 1966. He is an emeritus professor at the Australian National University (having retired as distinguished professor in 2016), distinguished professor at Hangzhou Dianzi University, and distinguished researcher in Data61-CSIRO, Australia. His awards include the IEEE Control Systems Award of 1997, the 2001 IEEE James H Mulligan, Jr Education Medal, and the Bode Prize of the IEEE Control System Society in 1992, as well as several IEEE and other best paper prizes. He is a Fellow of the Australian Academy of Science, the Australian Academy of Technological Sciences and Engineering, the Royal Society, and a foreign member of the US National Academy of Engineering. He holds honorary doctorates from a number of universities, including Université Catholique de Louvain, Belgium, and Eidgenoessiche Technische Hochschule (Swiss Federal Institute of Technology), Zurich. He is a past president of the International Federation of Automatic Control and the Australian Academy of Science.

His research interests include distributed control and econometric modelling.

Mengbin Ye received the B. Eng. degree (with First Class Honours) in mechanical engineering from University of Auckland, New Zealand in 2013, and the Ph. D. degree in engineering at the Australian National University, Australia in 2018. He is currently a postdoctoral researcher with the Faculty of Science and Engineering, University of Groningen, the Netherlands.

His research interests include opinion dynamics and social networks, consensus and synchronisation of Euler-Lagrange systems, and localisation using bearing measurements.

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Anderson, B.D.O., Ye, M. Recent Advances in the Modelling and Analysis of Opinion Dynamics on Influence Networks. Int. J. Autom. Comput. 16, 129–149 (2019). https://doi.org/10.1007/s11633-019-1169-8

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Keywords

  • Opinion dynamics
  • social networks
  • influence networks
  • agent-based models
  • multi-agent systems
  • networked systems