The noisy Hegselmann-Krause model for opinion dynamics. (English) Zbl 1518.91197
Summary: In the model for continuous opinion dynamics introduced by Hegselmann and Krause, each individual moves to the average opinion of all individuals within an area of confidence. In this work we study the effects of noise in this system. With certain probability, individuals are given the opportunity to change spontaneously their opinion to another one selected randomly inside the opinion space with different rules. If the random jump does not occur, individuals interact through the Hegselmann-Krause’s rule. We analyze two cases, one where individuals can carry out opinion random jumps inside the whole opinion space, and other where they are allowed to perform jumps just inside a small interval centered around the current opinion. We found that these opinion random jumps change the model behavior inducing interesting phenomena. Using pattern formation techniques, we obtain approximate analytical results for critical conditions of opinion cluster formation. Finally, we compare the results of this work with the noisy version of the Deffuant et al. model [G. Deffuant et al., Adv. Complex Syst. 3, 87–98 (2000; doi:10.1142/S0219525900000078)] for continuous-opinion dynamics.
MSC:
| 91D10 | Models of societies, social and urban evolution |
Keywords:
statistical and nonlinear physicsReferences:
| [1] | Stauffer, D., No article title, AIP Conf. Proc., 779, 56 (2005) · doi:10.1063/1.2008591 |
| [2] | Castellano, C.; Fortunato, S.; Loreto, V., No article title, Rev. Mod. Phys., 81, 592 (2009) · doi:10.1103/RevModPhys.81.591 |
| [3] | Lorenz, J., No article title, Int. J. Mod. Phys. C, 18, 119 (2007) · Zbl 1151.91076 · doi:10.1142/S0129183107011789 |
| [4] | Lorenz, J., No article title, Complexity, 15, 43 (2010) |
| [5] | Deffuant, G.; Neu, D.; Amblard, F.; Weisbuch, G., No article title, Adv. Compl. Syst., 3, 87 (2000) · doi:10.1142/S0219525900000078 |
| [6] | U. Krause, in Commun. Difference Equations, edited by S. Elyadi, G. Ladas, J. Popenda, J. Rakowski (Gordon and Breach Pub., Amsterdam, 2000), pp. 227-236 |
| [7] | Hegselmann, R.; Krause, U., No article title, J. Artif. Soc. Soc. Simul., 5, 2 (2002) |
| [8] | Fortunato, F., No article title, Int. J. Mod. Phys. C, 16, 259 (2005) · Zbl 1112.91353 · doi:10.1142/S0129183105007078 |
| [9] | Slanina, F., No article title, Eur. Phys. J. B, 79, 99 (2011) · doi:10.1140/epjb/e2010-10568-y |
| [10] | Granovetter, M., No article title, Am. J. Sociol., 83, 1420 (1978) · doi:10.1086/226707 |
| [11] | Axelrod, R., No article title, J. Conflict Res., 41, 203 (1997) · doi:10.1177/0022002797041002001 |
| [12] | Urbig, D.; Lorenz, J.; Herzberg, H., No article title, J. Artif. Soc. Soc. Simul., 11, 4 (2008) |
| [13] | Laguna, M. F.; Abramson, G.; Zanette, D. H., No article title, Complexity, 9, 31 (2004) · doi:10.1002/cplx.20018 |
| [14] | Porfiri, M.; Bolt, E. M.; Stilwell, D. J., No article title, Eur. Phys. J. D, 57, 481 (2007) · doi:10.1140/epjb/e2007-00186-3 |
| [15] | Ben-Naim, E.; Krapivsky, P. L.; Redner, S., No article title, Physica D, 183, 190 (2003) · Zbl 1058.91069 · doi:10.1016/S0167-2789(03)00171-4 |
| [16] | Pineda, M.; Toral, R.; Hernández-García, E., No article title, J. Stat. Mech., 2009, p08001 (2009) · Zbl 1459.91144 · doi:10.1088/1742-5468/2009/08/P08001 |
| [17] | Pineda, M.; Toral, R.; Hernández-García, E., No article title, Eur. Phys. J. D, 62, 109 (2011) · doi:10.1140/epjd/e2010-00227-0 |
| [18] | Grauwin, S.; Jensen, P., No article title, Phys. Rev. E, 85, 066113 (2012) · doi:10.1103/PhysRevE.85.066113 |
| [19] | Carletti, T.; Fanelli, D.; Guarino, A.; Bagnoli, F.; Guazzini, A., No article title, Eur. Phys. J. B, 64, 285 (2008) · Zbl 1189.91175 · doi:10.1140/epjb/e2008-00297-3 |
| [20] | Török, J.; Iniguez, G.; Yasseri, T.; San Miguel, M. S.; Kaski, K.; Kertesz, J., No article title, Phys. Rev. Lett., 110, 088701 (2013) · doi:10.1103/PhysRevLett.110.088701 |
| [21] | Douven, I., No article title, Logic Journal of the IGPL, 18, 323 (2010) · doi:10.1093/jigpal/jzp059 |
| [22] | N. Friedkin, A structural Theory of Social Influence (Cambridge University Press, Cambridge, 1998) |
| [23] | Fortunato, S.; Latora, V.; Pluchino, A.; Rapisarda, A., No article title, Int. J. Mod. Phys. C, 16, 1535 (2005) · Zbl 1125.82315 · doi:10.1142/S0129183105008126 |
| [24] | Lorenz, J., No article title, J. Artif. Soc. Soc. Simul., 9, 8 (2006) |
| [25] | Sznajd-Weron, K.; Tabiszewski, M.; Timpanaro, A. M., No article title, Europhys. Lett., 96, 48002 (2011) · doi:10.1209/0295-5075/96/48002 |
| [26] | Ben-Naim, E., No article title, Europhys. Lett., 69, 671 (2005) · doi:10.1209/epl/i2004-10421-1 |
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