A kinetic approach to the study of opinion formation
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 43 (2009) no. 3, p. 507-522
In this work, we use the methods of nonequilibrium statistical mechanics in order to derive an equation which models some mechanisms of opinion formation. After proving the main mathematical properties of the model, we provide some numerical results.
DOI : https://doi.org/10.1051/m2an/2009004
Classification:  91D10,  82C22
@article{M2AN_2009__43_3_507_0,
author = {Boudin, Laurent and Salvarani, Francesco},
title = {A kinetic approach to the study of opinion formation},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
publisher = {EDP-Sciences},
volume = {43},
number = {3},
year = {2009},
pages = {507-522},
doi = {10.1051/m2an/2009004},
zbl = {1163.91537},
mrnumber = {2536247},
language = {en},
url = {http://www.numdam.org/item/M2AN_2009__43_3_507_0}
}

Boudin, Laurent; Salvarani, Francesco. A kinetic approach to the study of opinion formation. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 43 (2009) no. 3, pp. 507-522. doi : 10.1051/m2an/2009004. http://www.numdam.org/item/M2AN_2009__43_3_507_0/

[1] G. Aletti, G. Naldi and G. Toscani, First-order continuous models of opinion formation. SIAM J. Appl. Math. 67 (2007) 837-853 (electronic). | MR 2300313 | Zbl 1128.91043

[2] E. Ben-Naim, Opinion dynamics: rise and fall of political parties. Europhys. Lett. 69 (2005) 671-677.

[3] G.A. Bird, Molecular gas dynamics and the direct simulation of gas flows, Oxford Engineering Science Series 42. The Clarendon Press, Oxford University Press, New York (1995). Corrected reprint of the 1994 original, Oxford Science Publications. | MR 1352466

[4] M. Campiti, G. Metafune and D. Pallara, Degenerate self-adjoint evolution equations on the unit interval. Semigroup Forum 57 (1998) 1-36. | MR 1621852 | Zbl 0915.47029

[5] J.A. Carrillo, S. Cordier and G. Toscani, Over-populated tails for conservative in the mean, inelastic Maxwell models. Discrete Contin. Dyn. Syst. A (to appear). Available at http://hal.archives-ouvertes.fr/hal-00206273/fr/. | MR 2476680 | Zbl 1163.82008

[6] S. Cordier, L. Pareschi and G. Toscani, On a kinetic model for a simple market economy. J. Stat. Phys. 120 (2005) 253-277. | MR 2165531 | Zbl 1133.91474

[7] G. Deffuant, D. Neau, F. Amblard and G. Weisbuch, Mixing beliefs among interacting agents. Adv. Complex Systems 3 (2000) 87-98.

[8] M.R. Feix, D. Lepelley, V. Merlin and J.-L. Rouet, The probability of conflicts in a U.S. presidential type election. Econom. Theory 23 (2004) 227-257. | MR 2034775 | Zbl 1128.91316

[9] S. Galam, Rational group decision making: A random field Ising model at $t=0$. Phys. A 238 (1997) 66-80.

[10] S. Galam, Contrarian deterministic effects on opinion dynamics: the hung elections scenario. Phys. A 333 (2004) 453-460. | MR 2100228

[11] S. Galam, Heterogeneous beliefs, segregation, and extremism in the making of public opinions. Phys. Rev. E 71 (2005) 046123.

[12] S. Galam and S. Moscovici, Towards a theory of collective phenomena: consensus and attitude changes in groups. Eur. J. Soc. Psychol. 21 (1991) 49-74.

[13] S. Galam and J.-D. Zucker, From individual choice to group decision-making. Phys. A 287 (2000) 644-659. | MR 1802421

[14] S. Galam, Y. Gefen and Y. Shapir, Sociophysics: A new approach of sociological collective behaviour. I. Mean-behaviour description of a strike. J. Math. Sociol. 9 (1982) 1-23. | Zbl 0496.92015

[15] R. Hegselmann and U. Krause, Opinion dynamics and bounded confidence: models, analysis and simulation. J. Artif. Soc. Soc. Sim. 5 (2002).

[16] F. Slanina, Inelastically scattering particles and wealth distribution in an open economy. Phys. Rev. E 69 (2004) 046102.

[17] F. Slanina and H. Lavicka, Analytical results for the Sznajd model of opinion formation. Eur. Phys. J. B 35 (2003) 279-288.

[18] K. Sznajd-Weron and J. Sznajd, Opinion evolution in closed community. Int. J. Mod. Phys. C 11 (2000) 1157-1166.

[19] G. Toscani, Kinetic models of opinion formation. Commun. Math. Sci. 4 (2006) 481-496. | MR 2247927 | Zbl pre05124907