Hydrodynamic Models of Preference Formation in Multi-agent Societies
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In this paper, we discuss the passage to hydrodynamic equations for kinetic models of opinion formation. The considered kinetic models feature an opinion density depending on an additional microscopic variable, identified with the personal preference. This variable describes an opinion-driven polarisation process, leading finally to a choice among some possible options, as it happens, e.g. in referendums or elections. Like in the kinetic theory of rarefied gases, the derivation of hydrodynamic equations is based on the computation of the local equilibrium distribution of the opinions from the underlying kinetic model. Several numerical examples validate the resulting model, shedding light on the crucial role played by the distinction between opinion and preference formation on the choice processes in multi-agent societies.
KeywordsOpinion and preference formation Choice processes Kinetic modelling Hydrodynamic equations
Mathematics Subject Classification35L65 35Q20 35Q70 35Q91 82B21
This research was partially supported by the Italian Ministry of Education, University and Research (MIUR) through the “Dipartimenti di Eccellenza” Programme (2018–2022)—Department of Mathematics “F. Casorati”, University of Pavia and Department of Mathematical Sciences “G. L. Lagrange”, Politecnico di Torino (CUP: E11G18000350001) and through the PRIN 2017 Project (No. 2017KKJP4X) “Innovative numerical methods for evolutionary partial differential equations and applications”. This work is also part of the activities of the Starting Grant “Attracting Excellent Professors” funded by “Compagnia di San Paolo” (Torino) and promoted by Politecnico di Torino. L.P. is member of GNCS (Gruppo Nazionale per il Calcolo Scientifico) of INdAM (Istituto Nazionale di Alta Matematica), Italy. G.T, A.T. and M.Z. are members of GNFM (Gruppo Nazionale per la Fisica Matematica) of INdAM, Italy.
- Albi, G., Pareschi, L., Toscani, G., Zanella, M.: Recent advances in opinion modeling: control and social influence. In: Bellomo, N., Degond, P., Tadmor, E. (eds.) Active Particles Volume 1, Theory, Methods, and Applications, Modeling and Simulation in Science, Engineering and Technology. Birkhäuser, Basel (2016)Google Scholar
- Chatterjee, A.: Socio-economic inequalities: a statistical physics perspective. In: Abergel, F., Aoyama, H., Chakrabarti, B., Chakraborti, A., Ghosh, A. (eds.) Econophysics and Data Driven Modelling of Market Dynamics, New Economic Windows, pp. 287–324. Springer, Berlin (2015)Google Scholar
- Deffuant, G., Amblard, F., Weisbuch, G., Faure, T.: How can extremism prevail? A study on the relative agreement interaction model. JASSS 5(4) (2002). http://jasss.soc.surrey.ac.uk/5/4/1.html
- Hegselmann, R., Krause, U.: Opinion dynamics and bounded confidence: models, analysis, and simulation. J. Artif. Soc. Soc. Simulat. 5(3), 1–33 (2002)Google Scholar
- Pareschi, L., Zanella, M.: Structure preserving schemes for mean-field equations of collective behavior. In: Westdickenberg, M., Klingenberg, C. (eds.) Theory, Numerics and Applications of Hyperbolic Problems II, HYP 2016, Volume 237 of Springer Proceedings in Mathematics and Statistics, pp. 405–421. Springer, Cham (2018a)Google Scholar
- Stella, L., Bagagiolo, F., Bauso, D., Como, G.: Opinion dynamics and stubbornness through mean-field games. In: 52nd IEEE Conference on Decision and Control, Florence, Italy, pp. 2519–2524 (2013)Google Scholar