×

Adapted Deffuant-Weisbuch model with implicit and explicit opinions. (English) Zbl 07511837

Summary: It is noted in the psychology literature that a discrepancy may exist between individuals’ implicit opinions and their explicit opinions (or beliefs) on a matter due to political correctness or peer pressures. This study proposes an adaptation of the Deffuant-Weisbuch model that incorporates both implicit and explicit opinions to investigate the evolution of opinions in a population. In our proposed model, we also consider the scenario where an opinion leader exists. We present a theoretical analysis of opinion convergence and consensus in our proposed model and prove a result on the occurrence of “strong diversity” in opinions. We further show that with the existence of an opinion leader, the model will predict a convergence to consensus. Finally, we show the emergence of a strong diversity of opinions in the population for model-based networks and square networks using Monte Carlo simulations.

MSC:

91D30 Social networks; opinion dynamics
37N40 Dynamical systems in optimization and economics
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Flache, A.; Mäs, M.; Feliciani, T.; Chattoe-Brown, E.; Lorenz, J., Models of social influence: Towards the next frontiers, J. Artif. Soc. Soc. Simul., 20, 4 (2017)
[2] Holley, R. A.; Liggett, T. M., Ergodic theorems for weakly interacting infinite systems and the voter model, Ann. Probab., 643-663 (1975) · Zbl 0367.60115
[3] Valente, T. W., Social network thresholds in the diffusion of innovations, Social Networks, 18, 1, 69-89 (1996)
[4] Proskurnikov, A. V.; Tempo, R., A tutorial on modeling and analysis of dynamic social networks, Part II, Annu. Rev. Control, 45, 166-190 (2018)
[5] Anderson, B. D.O.; Ye, M., Recent advances in the modelling and analysis of opinion dynamics on influence networks, Int. J. Automat. Comput., 16, 2, 129-149 (2019)
[6] Chen, Z.; Qin, J.; Li, B., Dynamics of opinions with social biases, Automatica, 106, 374-383 (2019) · Zbl 1429.91258
[7] Friedkin, N. E.; Jia, P.; Bullo, F., A theory of the evolution of social power: Natural trajectories of interpersonal influence systems along issue sequences, Sociol. Sci., 3, 444-472 (2016)
[8] DeGroot, M. H., Reaching a consensus, J. Am. Stat. Assoc., 69, 345, 118-121 (1974) · Zbl 0282.92011
[9] Friedkin, N. E.; Johnsen, E. C., Social influence and opinions, J. Math. Sociol., 15, 3-4, 193-206 (1990) · Zbl 0712.92025
[10] Hegselmann, R.; Krause, U., Opinion dynamics and bounded confidence models, analysis, and simulation, J. Artif. Soc. Soc. Simul., 5, 3, 1-33 (2002)
[11] Deffuant, G.; Neau, D.; Weisbuch, G., Mixing beliefs among interacting agents, Adv. Complex Syst., 3, 1, 87-98 (2000)
[12] Proskurnikov, A. V.; Tempo, R., A tutorial on modeling and analysis of dynamic social networks, Part I, Annu. Rev. Control, 43, 65-79 (2017)
[13] Abelson, R. P., Mathematical models of the distribution of attitudes under controversy, Contrib. Math. Psych. (1964)
[14] Cheng, C.; Yu, C., Social conformity creates consensus and strong diversity of hegselmann-krause opinion dynamics, Inform. Sci., 65, 129202, 1-129202 (2022)
[15] Waters, N. L.; Hans, V. P., A jury of one: Opinion formation, conformity, and dissent on juries, J. Empir. Legal Stud., 6, 3, 513-540 (2009)
[16] Asch, S. E.; Guetzkow, H., Effects of group pressure upon the modification and distortion of judgments, Doc. Gestalt Psychol., 222-236 (1951)
[17] Sherif, M., A study of some social factors in perception, Arch. Psychol. (Columbia University) (1935)
[18] Thrasher, F. M., The Gang: A Study of 1, 313 Gangs in Chicago (2013), University of Chicago Press
[19] Abbink, K.; Gangadharan, L.; Handfield, T., Peer punishment promotes enforcement of bad social norms, Nature Commun., 8, 1, 609 (2017)
[20] Shang, Y., Resilient consensus for expressed and private opinions, IEEE Trans. Cybern., 51, 1, 318-331 (2021)
[21] Huang, C. Y.; Wen, T. H., A novel implicit attitude and public opinion dynamics model for simulating pluralistic ignorance and minority influence, J. Artif. Soc. Soc. Simul., 17, 3, 8 (2014)
[22] Fu, W.; Qin, J.; Wu, J., Interval consensus over random networks, Automatica, 111, Article 108603 pp. (2020) · Zbl 1430.93190
[23] Ye, M.; Qin, Y.; Govaert, A., An influence network model to study discrepancies in explicit and implicit opinions, Automatica, 107, 371-381 (2019) · Zbl 1429.91273
[24] Cheng, C.; Luo, Y.; Yu, C. B., Dynamic mechanism of social bots interfering with public opinion in network, Physica A (2020)
[25] Cheng, C.; Luo, Y.; Yu, C., Consensus for expressed and private opinions under self-persuasion, IFAC-PapersOnLine, 53, 2, 2483-2488 (2020)
[26] Gastner, Michael T.; Oborny, Beáta; Gulyás, Máté, Consensus time in a voter model with concealed and publicly expressed opinions, J. Stat. Mech. (2018) · Zbl 1459.91135
[27] Jedrzejewski, Arkadiusz; Marcjasz, Grzegorz; Nail, Paul R.; Sznajd-Weron, Katarzyna, Think then act or act then think?, PLoS One (2017)
[28] Seneta, E., Non-Negative Matrices and Markov Chains (2006), Springer Science and Business Media · Zbl 1099.60004
[29] Shen, J., A geometric approach to ergodic non-homogeneous Markov chains, Lect. Not. Pure Appl. Math., 341-366 (2000) · Zbl 0968.60065
[30] Lorenz, J., A stabilization theorem for dynamics of continuous opinions, Physica A, 355, 1, 217-223 (2005)
[31] Cao, M.; Morse, A. S.; Anderson, B. D.O., Reaching a consensus in a dynamically changing environment: A graphical approach, SIAM J. Control Optim., 47, 2, 575-600 (2008) · Zbl 1157.93514
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.