Authors

Dong Xue, Sandra Hirche, Ming Cao

Abstract

Both interpersonal communication and media contact are important information sources and play a significant role in shaping public opinions of large populations. In this paper, we investigate how the opinion-forming process evolves over social networks under the media influence. In addition to being affected by the opinions of their connected peers, the media cooperate and/or compete mutually with each other. Networks with mixed cooperative and competitive interactions are said to be coopetitive. In this endeavor, a novel mathematical model of opinion dynamics is introduced, which captures the information diffusion process under consideration, makes use of the community-based network structure, and takes into account personalized biases among individuals in social networks. By employing port-Hamiltonian system theory to analyze the modeled opinion dynamics, we predict how public opinions evolve in the long run through social entities and find applications in political strategy science. A key technical observation is that as a result of the port-Hamiltonian formulation, the mathematical passivity property of individuals’ self-dynamics facilitates the convergence analysis of opinion evolution. We explain how to steer public opinions towards consensus, polarity, or neutrality, and investigate how an autocratic media coalition might emerge regardless of public views. We also assess the role of interpersonal communication and media exposure, which in itself is an essential topic in mathematical sociology.

Citation

  • Journal: IEEE Transactions on Network Science and Engineering
  • Year: 2020
  • Volume: 7
  • Issue: 3
  • Pages: 961–974
  • Publisher: Institute of Electrical and Electronics Engineers (IEEE)
  • DOI: 10.1109/tnse.2019.2894565

BibTeX

@article{Xue_2020,
  title={{Opinion Behavior Analysis in Social Networks Under the Influence of Coopetitive Media}},
  volume={7},
  ISSN={2334-329X},
  DOI={10.1109/tnse.2019.2894565},
  number={3},
  journal={IEEE Transactions on Network Science and Engineering},
  publisher={Institute of Electrical and Electronics Engineers (IEEE)},
  author={Xue, Dong and Hirche, Sandra and Cao, Ming},
  year={2020},
  pages={961--974}
}

Download the bib file

References

  • Jha, C. K. & Sarangi, S. Does social media reduce corruption? Information Economics and Policy vol. 39 60–71 (2017) – 10.1016/j.infoecopol.2017.04.001
  • Lazer, D. M. J. et al. The science of fake news. Science vol. 359 1094–1096 (2018) – 10.1126/science.aao2998
  • Leonard, N. E. Multi-agent system dynamics: Bifurcation and behavior of animal groups. Annual Reviews in Control vol. 38 171–183 (2014) – 10.1016/j.arcontrol.2014.09.002
  • Golubitsky, M. & Stewart, I. Recent advances in symmetric and network dynamics. Chaos: An Interdisciplinary Journal of Nonlinear Science vol. 25 (2015) – 10.1063/1.4918595
  • Fiore, D., Russo, G. & di Bernardo, M. Exploiting Nodes Symmetries to Control Synchronization and Consensus Patterns in Multiagent Systems. IEEE Control Systems Letters vol. 1 364–369 (2017) – 10.1109/lcsys.2017.2718840
  • Han, X. et al. Emergence of communities and diversity in social networks. Proceedings of the National Academy of Sciences vol. 114 2887–2891 (2017) – 10.1073/pnas.1608164114
  • Asch, S. E. Opinions and Social Pressure. Scientific American vol. 193 31–35 (1955) – 10.1038/scientificamerican1155-31
  • asch, Effects of Group Pressure Upon the Modification and Distortion of Judgment in (1951)
  • boudin, Modelling Opinion Formation by Means of Kinetic Equations (2010)
  • Srivastava, V., Moehlis, J. & Bullo, F. On Bifurcations in Nonlinear Consensus Networks. Journal of Nonlinear Science vol. 21 875–895 (2011) – 10.1007/s00332-011-9103-4
  • Mirtabatabaei, A., Jia, P. & Bullo, F. Eulerian Opinion Dynamics with Bounded Confidence and Exogenous Inputs. SIAM Journal on Applied Dynamical Systems vol. 13 425–446 (2014) – 10.1137/130934040
  • Trentelman, H. L., Stoorvogel, A. A. & Hautus, M. Control Theory for Linear Systems. Communications and Control Engineering (Springer London, 2001). doi:10.1007/978-1-4471-0339-4 – 10.1007/978-1-4471-0339-4
  • Russo, G. & Shorten, R. On common noise-induced synchronization in complex networks with state-dependent noise diffusion processes. Physica D: Nonlinear Phenomena vol. 369 47–54 (2018) – 10.1016/j.physd.2018.01.003
  • Quattrociocchi, W., Caldarelli, G. & Scala, A. Opinion dynamics on interacting networks: media competition and social influence. Scientific Reports vol. 4 (2014) – 10.1038/srep04938
  • Olfati-Saber, R., Fax, J. A. & Murray, R. M. Consensus and Cooperation in Networked Multi-Agent Systems. Proceedings of the IEEE vol. 95 215–233 (2007) – 10.1109/jproc.2006.887293
  • Hu, J. & Zheng, W. X. Emergent collective behaviors on coopetition networks. Physics Letters A vol. 378 1787–1796 (2014) – 10.1016/j.physleta.2014.04.070
  • toth, Rationality and irrationality in understanding human behaviors: An evaluation of the methodological consequence of conceptualising irrationality. Journal of Comparative Research in Anthropology and Sociology (2013)
  • Altafini, C. Consensus Problems on Networks With Antagonistic Interactions. IEEE Transactions on Automatic Control vol. 58 935–946 (2013) – 10.1109/tac.2012.2224251
  • Xia, W., Cao, M. & Johansson, K. H. Structural Balance and Opinion Separation in Trust–Mistrust Social Networks. IEEE Transactions on Control of Network Systems vol. 3 46–56 (2016) – 10.1109/tcns.2015.2437528
  • Young, K. Handbook of Social Psychology. (Routledge, 2016). doi:10.4324/9781315008189 – 10.4324/9781315008189
  • michels, New York: Hearst’s International Library Co. Political Parties A Sociological Study of the Oligarchical Tendencies of Modern Democracy (1915)
  • Liu, F., Xue, D., Hirche, S. & Buss, M. Polarizability, Consensusability, and Neutralizability of Opinion Dynamics on Coopetitive Networks. IEEE Transactions on Automatic Control vol. 64 3339–3346 (2019) – 10.1109/tac.2018.2879599
  • Rotoli, M., Russo, G. & di Bernardo, M. Stabilizing Quorum-Sensing Networks via Noise. IEEE Transactions on Circuits and Systems II: Express Briefs vol. 65 647–651 (2018) – 10.1109/tcsii.2018.2820815
  • Zhai, S. Modulus synchronization in a network of nonlinear systems with antagonistic interactions and switching topologies. Communications in Nonlinear Science and Numerical Simulation vol. 33 184–193 (2016) – 10.1016/j.cnsns.2015.09.010
  • Proskurnikov, A. V. & Tempo, R. A tutorial on modeling and analysis of dynamic social networks. Part II. Annual Reviews in Control vol. 45 166–190 (2018) – 10.1016/j.arcontrol.2018.03.005
  • Russo, G. & Slotine, J. J. E. Global convergence of quorum-sensing networks. Physical Review E vol. 82 (2010) – 10.1103/physreve.82.041919
  • Girvan, M. & Newman, M. E. J. Community structure in social and biological networks. Proceedings of the National Academy of Sciences vol. 99 7821–7826 (2002) – 10.1073/pnas.122653799
  • Danino, T., Mondragón-Palomino, O., Tsimring, L. & Hasty, J. A synchronized quorum of genetic clocks. Nature vol. 463 326–330 (2010) – 10.1038/nature08753
  • Friedkin, N., Jia, P. & Bullo, F. A Theory of the Evolution of Social Power: Natural Trajectories of Interpersonal Influence Systems along Issue Sequences. Sociological Science vol. 3 444–472 (2016) – 10.15195/v3.a20
  • DellaVigna, S. & Kaplan, E. The Fox News Effect: Media Bias and Voting. The Quarterly Journal of Economics vol. 122 1187–1234 (2007) – 10.1162/qjec.122.3.1187
  • Proskurnikov, A. V. & Tempo, R. A tutorial on modeling and analysis of dynamic social networks. Part I. Annual Reviews in Control vol. 43 65–79 (2017) – 10.1016/j.arcontrol.2017.03.002
  • Hegselmann, R. & Krause, U. Opinion dynamics under the influence of radical groups, charismatic leaders, and other constant signals: A simple unifying model. Networks & Heterogeneous Media vol. 10 477–509 (2015) – 10.3934/nhm.2015.10.477
  • The Problem of Social Control and Coordination of Complex Systems in Sociology: A Look at the Community Cleavage Problem. IEEE Control Systems vol. 35 40–51 (2015) – 10.1109/mcs.2015.2406655
  • Bollobás, B. Modern Graph Theory. Graduate Texts in Mathematics (Springer New York, 1998). doi:10.1007/978-1-4612-0619-4 – 10.1007/978-1-4612-0619-4
  • Proskurnikov, A. V., Matveev, A. S. & Cao, M. Opinion Dynamics in Social Networks With Hostile Camps: Consensus vs. Polarization. IEEE Transactions on Automatic Control vol. 61 1524–1536 (2016) – 10.1109/tac.2015.2471655
  • Godsil, C. & Royle, G. Algebraic Graph Theory. Graduate Texts in Mathematics (Springer New York, 2001). doi:10.1007/978-1-4613-0163-9 – 10.1007/978-1-4613-0163-9
  • Hatanaka, T., Chopra, N., Fujita, M. & Spong, M. W. Passivity-Based Control and Estimation in Networked Robotics. Communications and Control Engineering (Springer International Publishing, 2015). doi:10.1007/978-3-319-15171-7 – 10.1007/978-3-319-15171-7
  • van der Schaft, A. & Jeltsema, D. Port-Hamiltonian Systems Theory: An Introductory Overview. (2014) doi:10.1561/978160198787710.1561/9781601987877
  • Wieland, P., Sepulchre, R. & Allgöwer, F. An internal model principle is necessary and sufficient for linear output synchronization. Automatica vol. 47 1068–1074 (2011) – 10.1016/j.automatica.2011.01.081
  • Russo, G., Wirth, F. & Shorten, R. On Synchronization in Continuous-Time Networks of Nonlinear Nodes With State-Dependent and Degenerate Noise Diffusion. IEEE Transactions on Automatic Control vol. 64 389–395 (2019) – 10.1109/tac.2018.2829462
  • Francis, B. A. & Wonham, W. M. The internal model principle of control theory. Automatica vol. 12 457–465 (1976) – 10.1016/0005-1098(76)90006-6
  • Liu, Z., Zhang, M., Saberi, A. & Stoorvogel, A. A. State synchronization of multi-agent systems via static or adaptive nonlinear dynamic protocols. Automatica vol. 95 316–327 (2018) – 10.1016/j.automatica.2018.05.034
  • Wang, S.-W., Huang, C.-Y. & Sun, C.-T. Modeling self-perception agents in an opinion dynamics propagation society. SIMULATION vol. 90 238–248 (2013) – 10.1177/0037549713515029
  • Proskurnikov, A. V. & Cao, M. Polarization in coopetitive networks of heterogeneous nonlinear agents. 2016 IEEE 55th Conference on Decision and Control (CDC) 6915–6920 (2016) doi:10.1109/cdc.2016.7799334 – 10.1109/cdc.2016.7799334
  • Governance and Knowledge. (2012) doi:10.4324/9780203118450 – 10.4324/9780203118450
  • Mäs, M., Flache, A. & Helbing, D. Individualization as Driving Force of Clustering Phenomena in Humans. PLoS Computational Biology vol. 6 e1000959 (2010) – 10.1371/journal.pcbi.1000959