Abstract
This work explores models of opinion dynamics with opinion-dependent connectivity. Our starting point is that individuals have limited capabilities to engage in interactions with their peers. Motivated by this observation, we propose an opinion dynamics model such that interactions take place with a limited number of peers: we refer to these interactions as topological, as opposed to metric interactions that are postulated in classical bounded-confidence models.
Supported in part by MITI CNRS via 80 PRIME grant DOOM and by ANR via project HANDY, number ANR-18-CE40-0010.
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References
Angeli, D., Manfredi, S.: A Petri net approach to consensus in networks with joint-agent interactions. Automatica 110, 108466 (2019)
Aydoğdu, A., et al.: Interaction network, state space, and control in social dynamics. In: Bellomo, N., Degond, P., Tadmor, E. (eds.) Active Particles, Volume 1. MSSET, pp. 99–140. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-49996-3_3
Aydoğdu, A., et al.: Modeling birds on wires. J. Theor. Biol. 415, 102–112 (2017)
Balister, P., Bollobás, B., Sarkar, A., Walters, M.: Connectivity of random k-nearest-neighbour graphs. Adv. Appl. Probab. 37(1), 1–24 (2005)
Ballerini, M.: Interaction ruling animal collective behavior depends on topological rather than metric distance: evidence from a field study. Proc. Natl. Acad. Sci. 105(4), 1232–1237 (2008)
Blanchet, A., Degond, P.: Topological interactions in a Boltzmann-type framework. J. Stat. Phys. 163(1), 41–60 (2016). https://doi.org/10.1007/s10955-016-1471-6
Blondel, V.D., Hendrickx, J.M., Tsitsiklis, J.N.: On Krause’s multi-agent consensus model with state-dependent connectivity. IEEE Trans. Autom. Control 54(11), 2586–2597 (2009)
Blondel, V.D., Hendrickx, J.M., Tsitsiklis, J.N.: Continuous-time average-preserving opinion dynamics with opinion-dependent communications. SIAM J. Control. Optim. 48(8), 5214–5240 (2010)
Canuto, C., Fagnani, F., Tilli, P.: An Eulerian approach to the analysis of Krause’s consensus models. SIAM J. Control. Optim. 50(1), 243–265 (2012)
Ceragioli, F., Frasca, P.: Continuous and discontinuous opinion dynamics with bounded confidence. Nonlinear Anal. Appl. B 13(3), 1239–1251 (2012)
Ceragioli, F., Frasca, P.: Discontinuities, generalized solutions, and (dis)agreement in opinion dynamics. In: Tarbouriech, S., Girard, A., Hetel, L. (eds.) Control Subject to Computational and Communication Constraints: Current Challenges. LNCS, vol. 475, pp. 287–309. Springer, Heidelberg (2018). https://doi.org/10.1007/978-3-319-78449-6_14
Chazelle, B., Wang, C.: Inertial Hegselmann-Krause systems. IEEE Trans. Autom. Control 62(8), 3905–3913 (2017)
Chen, C., Chen, G., Guo, L.: On the minimum number of neighbors needed for consensus of flocks. Control Theory Technol. 15(4), 327–339 (2017). https://doi.org/10.1007/s11768-017-7097-7
Chen, G., Su, W., Mei, W., Bullo, F.: Convergence properties of the heterogeneous Deffuant-Weisbuch model. Automatica 114, 108825 (2020)
Cristiani, E., Frasca, P., Piccoli, B.: Effects of anisotropic interactions on the structure of animal groups. J. Math. Biol. 62(4), 569–588 (2011). https://doi.org/10.1007/s00285-010-0347-7
Deffuant, G., Neau, D., Amblard, F., Weisbuch, G.: Mixing beliefs among interacting agents. Adv. Complex Syst. 03(01n04), 87–98 (2000)
Degond, P., Pulvirenti, M.: Propagation of chaos for topological interactions. Ann. Appl. Probab. 29(4), 2594–2612 (2019)
Dunbar, R.: Neocortex size as a constraint on group size in primates. J. Hum. Evol. 22(6), 469–493 (1992)
Fagnani, F., Frasca, P.: Introduction to Averaging Dynamics over Networks. Lecture Notes in Control and Information Sciences, Springer, Heidelberg (2017). https://doi.org/10.1007/978-3-319-68022-4
Giardina, I.: Collective behavior in animal groups: theoretical models and empirical studies. HFSP J. 2(4), 205–219 (2008). pMID: 19404431
Gonçalves, B., Perra, N., Vespignani, A.: Modeling users’ activity on Twitter networks: validation of Dunbar’s number. PloS ONE 6(8), e22656 (2011)
Krause, U.: A discrete nonlinear and non-autonomous model of consensus formation. In: Communications in Difference Equations, pp. 227–236 (2000)
Lazer, D.: The rise of the social algorithm. Science 348(6239), 1090–1091 (2015)
Martin, S.: Multi-agent flocking under topological interactions. Syst. Control Lett. 69, 53–61 (2014)
Mirtabatabaei, A., Bullo, F.: Opinion dynamics in heterogeneous networks: convergence conjectures and theorems. SIAM J. Control. Optim. 50(5), 2763–2785 (2012)
Proskurnikov, A., Tempo, R.: A tutorial on modeling and analysis of dynamic social networks. Part II. Ann. Rev. Control 45, 166–190 (2018)
Proskurnikov, A.V., Tempo, R.: A tutorial on modeling and analysis of dynamic social networks. Part I. Ann. Rev. Control 43, 65–79 (2017)
Rossi, W.S., Frasca, P.: Asynchronous opinion dynamics on the \(k\)-nearest-neighbors graph. In: IEEE Conference on Decision and Control, pp. 3648–3653 (2018)
Rossi, W.S., Frasca, P.: Opinion dynamics with topological gossiping: asynchronous updates under limited attention. IEEE Control Syst. Lett. 4(3), 566–571 (2020)
Sethi, R.: Evolutionary stability and social norms. J. Econ. Behav. Organ. 29(1), 113–140 (1996)
Shvydkoy, R., Tadmor, E.: Topological models for emergent dynamics with short-range interactions. arXiv preprint (2018)
Simmel, G.: The persistence of social groups. Am. J. Sociol. 3(5), 662–698 (1898)
Van de Waal, E., Borgeaud, C., Whiten, A.: Potent social learning and conformity shape a wild primate’s foraging decisions. Science 340(6131), 483–485 (2013)
Acknowledgements
The authors are grateful to Emiliano Cristiani, Julien Hendrickx, Samuel Martin, Benedetto Piccoli and Tommaso Venturini for fruitful discussions that, along the years, have shaped their point of view on the topic of this paper.
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Ceragioli, F., Frasca, P., Rossi, W.S. (2021). Modeling Limited Attention in Opinion Dynamics by Topological Interactions. In: Lasaulce, S., Mertikopoulos, P., Orda, A. (eds) Network Games, Control and Optimization. NETGCOOP 2021. Communications in Computer and Information Science, vol 1354. Springer, Cham. https://doi.org/10.1007/978-3-030-87473-5_24
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