Modeling public opinion control by a charismatic leader. (English) Zbl 07901962
Summary: We study the average long-time behavior of the binary opinions of a social group with peer-to-peer interactions under the influence of an external bias and a persuadable leader, a strongly-biased agent with a dynamic opinion with the intention of spreading it across the system. We use a generalized, fully-connected Ising model, with each spin representing the binary opinion of an agent at a given time and a single, super spin representing the opinion of the leader. External fields and interaction constants model the opinion bias and peer-to-peer interactions, respectively, while the temperature \(T\) models an idealized social climate, representing an authoritarian regime if \(T\) is low or a liberal one if \(T\) is high. We derive a mean-field solution for the average magnetization \(m\), the “social mood”, and investigate how \(m\) and the super spin magnetization vary as a function of \(T\). We find that, depending on the initial conditions, due to the presence of metastable states, the sign of the average magnetization depends on the temperature. Finally, we verify that this effect is also present even if we consider only nearest-neighbor interactions within the social group.
MSC:
| 82-XX | Statistical mechanics, structure of matter |
References:
| [1] | Galam, S.; Gefen (Feigenblat), Y.; Shapir, Y., Sociophysics: A new approach of sociological collective behaviour, I. mean-behaviour description of a strike, J. Math. Sociol., 9, 1, 1-13, 1982 · Zbl 0496.92015 |
| [2] | Jones, F., Simulation models of group segregation, Aust. N. Zeal. J. Sociol., 21, 3, 431-444, 1985 |
| [3] | Castellano, C.; Fortunato, S.; Loreto, V., Statistical physics of social dynamics, Rev. Modern Phys., 81, 2, 591-646, 2009 |
| [4] | Weidlich, W., The statistical description of polarization phenomena in society, Br. J. Math. Stat. Psychol., 24, 2, 251-266, 1971 · Zbl 0225.92004 |
| [5] | Baldassarri, S.; Gallo, A.; Jacquier, V.; Zocca, A., Ising model on clustered networks: A model for opinion dynamics, Phys. A, 623, Article 128811 pp., 2023 · Zbl 1519.91195 |
| [6] | Schelling, T. C., Dynamic models of segregation, J. Math. Sociol., 1, 2, 143-186, 1971 · Zbl 1355.91061 |
| [7] | Axelrod, R., The dissemination of culture: A model with local convergence and global polarization, J. Conflict Resolut., 41, 2, 203-226, 1997 |
| [8] | Clifford, P.; Sudbury, A., A model for spatial conflict, Biometrika, 60, 3, 581-588, 1973 · Zbl 0272.60072 |
| [9] | Holley, R. A.; Liggett, T. M., Ergodic theorems for weakly interacting infinite systems and the voter model, Ann. Probab., 3, 4, 643-663, 1975 · Zbl 0367.60115 |
| [10] | Redner, S., Reality-inspired voter models: A mini-review, C. R. Phys., 20, 4, 275-292, 2019 |
| [11] | Sznajd-Weron, K.; Sznajd, J., Opinion evolution in closed community, Internat. J. Modern Phys. C, 11, 06, 1157-1165, 2000 |
| [12] | Sznajd-Weron, K., Sznajd model and its applications, 2005, arXiv:physics/0503239 |
| [13] | de Oliveira, M. J., Isotropic majority-vote model on a square lattice, J. Stat. Phys., 66, 1, 273-281, 1992 · Zbl 0925.82179 |
| [14] | Vilela, A. L.M.; Wang, C.; Nelson, K. P.; Stanley, H. E., Majority-vote model for financial markets, Phys. A, 515, 762-770, 2019 |
| [15] | Kacperski, K.; Hołyst, J. A., Opinion formation model with strong leader and external impact: A mean field approach, Phys. A, 269, 2, 511-526, 1999 |
| [16] | Mobilia, M., Does a single zealot affect an infinite group of voters?, Phys. Rev. Lett., 91, 2, Article 028701 pp., 2003 |
| [17] | Yildiz, E.; Acemoglu, D.; Ozdaglar, A. E.; Saberi, A.; Scaglione, A., Discrete opinion dynamics with Stubborn agents, 2011 |
| [18] | Verma, G.; Swami, A.; Chan, K., The impact of competing zealots on opinion dynamics, Phys. A, 395, 310-331, 2014 · Zbl 1402.91606 |
| [19] | Khalil, N.; San Miguel, M.; Toral, R., Zealots in the mean-field noisy voter model, Phys. Rev. E, 97, 1, Article 012310 pp., 2018 |
| [20] | Mobilia, M.; Petersen, A.; Redner, S., On the role of zealotry in the voter model, J. Stat. Mech. Theory Exp., 2007, 08, P08029, 2007 · Zbl 1456.91047 |
| [21] | Klamser, P. P.; Wiedermann, M.; Donges, J. F.; Donner, R. V., Zealotry effects on opinion dynamics in the adaptive voter model, Phys. Rev. E, 96, 5, Article 052315 pp., 2017 |
| [22] | Toral, R.; Tessone, C. J., Finite size effects in the dynamics of opinion formation, Commun. Comput. Phys., 2, 177-195, 2007 |
| [23] | Ritchie, H.; Rodés-Guirao, L.; Mathieu, E.; Gerber, M.; Ortiz-Ospina, E.; Hasell, J.; Roser, M., Population growth, 2023, https://ourworldindata.org/population-growth |
| [24] | Castellani, T.; Cavagna, A., Spin-glass theory for pedestrians, J. Stat. Mech. Theory Exp., 2005, 05, P05012, 2005 · Zbl 1456.82490 |
| [25] | Böttcher, L.; Herrmann, H. J., Computational Statistical Physics, 2021, Cambridge University Press: Cambridge University Press Cambridge · Zbl 1473.82001 |
| [26] | Corberi, F.; Castellano, C., Kinetics of the one-dimensional voter model with long-range interactions, J. Phys.: Complex., 5, 2, Article 025021 pp., 2024 |
| [27] | Helfmann, L.; Djurdjevac Conrad, N.; Lorenz-Spreen, P.; Schütte, C., Modelling opinion dynamics under the impact of influencer and media strategies, Sci. Rep., 13, 1, 19375, 2023 |
| [28] | Meyer, P. G.; Metzler, R., Time scales in the dynamics of political opinions and the voter model, New J. Phys., 26, 2, Article 023040 pp., 2024 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
