Hydrodynamic Models of Preference Formation in Multi-agent Societies

  • Lorenzo Pareschi
  • Giuseppe Toscani
  • Andrea TosinEmail author
  • Mattia Zanella


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.


Opinion and preference formation Choice processes Kinetic modelling Hydrodynamic equations 

Mathematics Subject Classification

35L65 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.


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mathematics and Computer SciencesUniversity of FerraraFerraraItaly
  2. 2.Department of Mathematics “F. Casorati”University of PaviaPaviaItaly
  3. 3.Department of Mathematical Sciences “G. L. Lagrange”Politecnico di TorinoTorinoItaly

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