Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-23T14:49:08.892Z Has data issue: false hasContentIssue false

A kinetic approach to the study of opinion formation

Published online by Cambridge University Press:  07 February 2009

Laurent Boudin
Affiliation:
UPMC Université Paris 6, UMR 7598, Laboratoire Jacques-Louis Lions, 75005 Paris, France. [email protected]
Francesco Salvarani
Affiliation:
Dipartimento di Matematica, Università Degli Studi di Pavia, Via Ferrata 1, 27100 Pavia, Italy. [email protected]
Get access

Abstract

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.

Type
Research Article
Copyright
© EDP Sciences, SMAI, 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Aletti, G., Naldi, G. and Toscani, G., First-order continuous models of opinion formation. SIAM J. Appl. Math. 67 (2007) 837853 (electronic). CrossRef
Ben-Naim, E., Opinion dynamics: rise and fall of political parties. Europhys. Lett. 69 (2005) 671677. CrossRef
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.
Campiti, M., Metafune, G. and Pallara, D., Degenerate self-adjoint evolution equations on the unit interval. Semigroup Forum 57 (1998) 136. CrossRef
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/.
Cordier, S., Pareschi, L. and Toscani, G., On a kinetic model for a simple market economy. J. Stat. Phys. 120 (2005) 253277. CrossRef
Deffuant, G., Neau, D., Amblard, F. and Weisbuch, G., Mixing beliefs among interacting agents. Adv. Complex Systems 3 (2000) 8798. CrossRef
Feix, M.R., Lepelley, D., Merlin, V. and Rouet, J.-L., The probability of conflicts in a U.S. presidential type election. Econom. Theory 23 (2004) 227257. CrossRef
Galam, S., Rational group decision making: A random field Ising model at $t = 0$ . Phys. A 238 (1997) 6680. CrossRef
Galam, S., Contrarian deterministic effects on opinion dynamics: the hung elections scenario. Phys. A 333 (2004) 453460. CrossRef
Galam, S., Heterogeneous beliefs, segregation, and extremism in the making of public opinions. Phys. Rev. E 71 (2005) 046123. CrossRef
Galam, S. and Moscovici, S., Towards a theory of collective phenomena: consensus and attitude changes in groups. Eur. J. Soc. Psychol. 21 (1991) 4974. CrossRef
Galam, S. and Zucker, J.-D., From individual choice to group decision-making. Phys. A 287 (2000) 644659. CrossRef
Galam, S., Gefen, Y. and Shapir, Y., Sociophysics: A new approach of sociological collective behaviour. I. Mean-behaviour description of a strike. J. Math. Sociol. 9 (1982) 123. CrossRef
R. Hegselmann and U. Krause, Opinion dynamics and bounded confidence: models, analysis and simulation. J. Artif. Soc. Soc. Sim. 5 (2002).
Slanina, F., Inelastically scattering particles and wealth distribution in an open economy. Phys. Rev. E 69 (2004) 046102. CrossRef
Slanina, F. and Lavicka, H., Analytical results for the Sznajd model of opinion formation. Eur. Phys. J. B 35 (2003) 279288. CrossRef
Sznajd-Weron, K. and Sznajd, J., Opinion evolution in closed community. Int. J. Mod. Phys. C 11 (2000) 11571166. CrossRef
Toscani, G., Kinetic models of opinion formation. Commun. Math. Sci. 4 (2006) 481496. CrossRef