Artículo

Pérez-Llanos, M.; Pinasco, J.P.; Saintier, N.; Silva, A. "Opinion formation models with heterogeneous persuasion and zealotry" (2018) SIAM Journal on Mathematical Analysis. 50(5):4812-4837
Estamos trabajando para incorporar este artículo al repositorio
Consulte el artículo en la página del editor
Consulte la política de Acceso Abierto del editor

Abstract:

In this work an opinion formation model with heterogeneous agents is proposed. Each agent is supposed to have a different power of persuasion, as well as his/her own level of zealotry, that is, an individual willingness to be convinced by other agents. In addition, our model includes zealots or stubborn agents, agents that never change opinions. We derive a Bolzmann-like equation for the distribution of agents on the space of opinions, which is approximated by a transport equation with a nonlocal drift term. We study the long-time asymptotic behavior of solutions, characterizing the limit distribution of agents, which consists of the distribution of stubborn agents, plus a delta function at the mean of their opinions, weighted by their power of persuasion. Moreover, explicit bounds on the rate of convergence are given, and the time to convergence is shown to decrease when the number of stubborn agents increases. This is a remarkable fact observed in agent-based simulations in different works. © 2018 Society for Industrial and Applied Mathematics.

Registro:

Documento: Artículo
Título:Opinion formation models with heterogeneous persuasion and zealotry
Autor:Pérez-Llanos, M.; Pinasco, J.P.; Saintier, N.; Silva, A.
Filiación:IMAS UBA-CONICET and Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, 1428, Argentina
Instituto de Matemática Aplicada San Luis, IMASL, Universidad Nacional de San Luis and CONICET, San Luis, D5700, Argentina
Palabras clave:Boltzmann equation; Grazing limit; Nonlocal transport equations; Opinion formation models; Delta functions; Agent based simulation; Grazing limit; Heterogeneous agents; Limit distribution; Nonlocal transport equations; Opinion formation models; Rate of convergence; Transport equation; Boltzmann equation
Año:2018
Volumen:50
Número:5
Página de inicio:4812
Página de fin:4837
DOI: http://dx.doi.org/10.1137/17M1152784
Título revista:SIAM Journal on Mathematical Analysis
Título revista abreviado:SIAM J. Math. Anal.
ISSN:00361410
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00361410_v50_n5_p4812_PerezLlanos

Referencias:

  • Aletti, G., Naldi, G., Toscani, G., First-order continuous models of opinion formation (2007) SIAM J. Appl. Math., 67, pp. 837-853. , https://doi.org/10.1137/060658679
  • Arlotti, L., Bellomo, N., De Angelis, E., Generalized kinetic (Boltzmann) models: Mathematical structures and applications (2002) Math. Models Methods Appl. Sci., 12, pp. 567-591
  • Ash, R.B., Real analysis and probability (1972) Probab. Math. Statist., 11. , Academic Press, New York, London
  • Bellomo, N., (2008) Modeling Complex Living Systems. A Kinetic Theory and Stochastic Game Approach, , Birkhäuser Boston
  • Bellomo, N., Ajmone Marsan, G., Tosin, A., (2013) Complex Systems and Society. Modeling and Simulation, , SpringerBriefs Math., Springer, New York
  • Ben-Naim, E., Krapivsky, P.L., Redner, S., Bifurcations and patterns in compromise processes (2003) Phys. D, 183, pp. 190-204
  • Ben-Naim, E., Krapivsky, P.L., Vazquez, F., Redner, S., Unity and discord in opinion dynamics (2003) Phys. A, 330, pp. 99-106
  • Bolley, F., Guillin, A., Villani, C., Quantitative concentration inequalities for empirical measures on non-compact spaces (2007) Probab. Theory Related Fields, 137, pp. 541-593
  • Brugna, C., Toscani, G., Kinetic models of opinion formation in the presence of personal conviction (2015) Phys. Rev. E, 92, p. 052818
  • Cañizo, J.A., Carrillo, J.A., Rosado, J., A well-posedness theory in measures for some kinetic models of collective motion (2011) Math. Models Methods Appl. Sci., 21, pp. 515-539
  • Capasso, V., Bakstein, D., An introduction to continuous-time stochastic processes (2015) Model. Simul. Sci. Eng. Technol., , Birkhäuser/Springer, New York
  • Chakrabarti, B.K., Chakraborti, A., Chatterjee, A., (2006) Econophysics and Sociophysics: Trends and Perspectives, , Wiley-VCH, Berlin
  • Cercignani, C., Illner, R., Pulvirenti, M., The mathematical theory of dilute gases (1994) Appl. Math. Sci., 106. , Springer-Verlag, New York
  • Deffuant, G., Amblard, F., Weisbuch, G., Faure, T., How can extremism prevail? A study based on the relative agreement interaction model (2002) J. Artif. Soc. Soc. Simul., 5
  • Deffuant, G., Neau, D., Amblard, F., Weisbuch, G., Mixing beliefs among interacting agents (2000) Adv. Complex Syst., 3, pp. 87-98
  • Degond, P., Lucquin-Desreux, B., The Fokker-Planck asymptotics of the Boltzmann collision operator in the Coulomb case (1992) Math. Models Methods Appl. Sci., 2, pp. 167-182
  • Desvillettes, L., On asymptotics of the Boltzmann equation when the collisions become grazing (1992) Transport Theory Statist. Phys., 21, pp. 259-276
  • Desvillettes, L., Ricci, V., A rigorous derivative of a linear kinetic equation of Fokker-Planck type in the limit of grazing collisions (2001) J. Statist. Phys., 104, pp. 1173-1189
  • Düring, B., Markowich, P., Pietschmann, J.-F., Wolfram, M.-T., Boltzmann and Fokker-Planck equations modelling opinion formation in the presence of strong leaders (2009) Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 465, pp. 3687-3708
  • Düring, B., Wolfram, M.T., Opinion dynamics: Inhomogeneous Boltzmann-type equations modelling opinion leadership and political segregation (2015) Proc. A, 471, p. 20150345
  • Embrechts, P., Hofert, M., (2014) A Note on Generalized Inverses, , https://people.math.ethz.ch/-embrecht/ftp/generalizedinverse.pdf, ETH Zurich, Zurich, Switzerland
  • Galam, S., Heterogeneous beliefs, segregation, and extremism in the making of public opinions (2005) Phys. Rev. E, 71, p. 046123
  • Galam, S., (2012) Sociophysics: A Physicist's Modeling of Psycho-political Phenomena, , Springer-Verlag, New York
  • Galam, S., Zucker, J.D., From individual choice to group decision-making (2000) Phys. A, 287, pp. 644-659
  • Ghaderi, J., Srikant, R., Opinion dynamics in social networks with stubborn agents: Equilibrium and convergence rate (2014) Automatica J. IFAC, 50, pp. 3209-3215
  • Krée, P., Soize, C., Mathematics of random phenomena: Random vibrations of mechanical structures (1986) Math. Appl., 32. , D. Reidel Publishing, Dordrecht
  • La Rocca, C., Braunstein, L.A., Vázquez, F., The influence of persuasion in opinion formation and polarization (2014) Europhys. Lett., 106, p. 40004
  • Li, H., Toscani, G., Long-time asymptotics of kinetic models of granular flows (2004) Arch. Ration. Mech. Anal., 172, pp. 407-428
  • Lipowski, A., Lipowska, D., Ferreira, A.L., Agreement dynamics on directed random graphs (2017) J. Stat. Mech. Theory Exp., 2017, p. 063408
  • Milgrom, P., Segal, I., Envelope theorems for arbitrary choice sets (2002) Econometrica, 70, pp. 583-601
  • Mobilia, M., Does a single zealot affect an infinite group of voters? (2003) Phys. Rev. Lett., 91, p. 028701
  • Mobilia, M., Petersen, A., Redner, S., On the role of zealotry in the voter model (2007) J. Stat. Mech. Theory Exp., 2007, p. P08029
  • Naldi, G., Pareschi, L., Toscani, G., Mathematical modeling of collective behavior in socio-economic and life sciences (2010) Model. Simul. Sci. Eng. Technol., , Birkhäuser Boston, Boston
  • Pareschi, L., Toscani, G., (2014) Interacting Multiagent Systems: Kinetic Equations and Monte Carlo Methods, , Oxford University Press, Oxford
  • Sen, P.P., Chakrabarti, B.K., (2014) Sociophysics: An Introduction, , Oxford University Press
  • Slanina, F., (2014) Essentials of Econophysics Modelling, , Oxford University Press
  • Sznajd-Weron, K., Sznajd, J., Opinion evolution in closed community (2000) Internat. J. Modern Phys. C, 11, pp. 1157-1165
  • Stroock, D.W., (1993) Probability Theory An Analytic View, , Cambridge University Press, Cambridge, UK
  • Toscani, G., Kinetic models of opinion formation (2006) Commun. Math. Sci., 4, pp. 481-496
  • Villani, C., On a new class of weak solutions for the spatially homogeneous Boltzmann and Landau equations (1998) Arch. Rational Mech. Anal., 143, pp. 273-307
  • Villani, C., On the spatially homogeneous Landau equation for Maxwellian molecules (1998) Math. Models Methods Appl. Sci., 8, pp. 957-983
  • Villani, C., A review of mathematical topics in collisional kinetic theory (2002) Handbook of Mathematical Fluid Dynamics, 1, pp. 71-305. , S.J. Friedlander and D. Serre, eds., North-Holland, Amsterdam
  • Villani, C., Topics in optimal transportation (2003) Grad. Stud. Math., 58. , American Mathematical Society, Providence, RI
  • Villani, C., Mathematics of granular materials (2006) J. Statist. Phys., 124, pp. 781-822
  • Waagen, A., Verma, G., Chan, K., Swami, A., D'Souza, R., Effect of zealotry in highdimensional opinion dynamics models (2015) Phys. Rev. E, 91, p. 022811
  • Woolcock, A., Connaughton, C., Merali, Y., Vazquez, F., Fitness voter model: Damped oscillations and anomalous consensus (2017) Phys. Rev. E, 96, p. 032313
  • Xie, J., Emenheiser, J., Kirby, M., Sreenivasan, S., Szymanski, B.K., Korniss, G., Evolution of opinions on social networks in the presence of competing committed groups (2012) PLoS ONE, 7, p. e33215
  • Xie, J., Sreenivasan, S., Korniss, G., Zhang, W., Lim, C., Szymanski, B.K., Social consensus through the influence of committed minorities (2011) Phys. Rev. E, 84, p. 011130
  • Yildiz, E., Ozdaglar, A., Acemoglu, D., Saberi, A., Scaglione, A., Binary opinion dynamics with stubborn agents (2013) ACM Trans. Econ. Comput., 1, p. 19

Citas:

---------- APA ----------
Pérez-Llanos, M., Pinasco, J.P., Saintier, N. & Silva, A. (2018) . Opinion formation models with heterogeneous persuasion and zealotry. SIAM Journal on Mathematical Analysis, 50(5), 4812-4837.
http://dx.doi.org/10.1137/17M1152784
---------- CHICAGO ----------
Pérez-Llanos, M., Pinasco, J.P., Saintier, N., Silva, A. "Opinion formation models with heterogeneous persuasion and zealotry" . SIAM Journal on Mathematical Analysis 50, no. 5 (2018) : 4812-4837.
http://dx.doi.org/10.1137/17M1152784
---------- MLA ----------
Pérez-Llanos, M., Pinasco, J.P., Saintier, N., Silva, A. "Opinion formation models with heterogeneous persuasion and zealotry" . SIAM Journal on Mathematical Analysis, vol. 50, no. 5, 2018, pp. 4812-4837.
http://dx.doi.org/10.1137/17M1152784
---------- VANCOUVER ----------
Pérez-Llanos, M., Pinasco, J.P., Saintier, N., Silva, A. Opinion formation models with heterogeneous persuasion and zealotry. SIAM J. Math. Anal. 2018;50(5):4812-4837.
http://dx.doi.org/10.1137/17M1152784