Phase Transition in the Social Impact Model of Opinion Formation in Log-Normal Networks
محورهای موضوعی : Complex Networks
Alireza Mansouri
1
,
Fattaneh Taghiyareh
2
1 - ICT Research Institute Information Technology
2 - Tehran University
کلید واژه: Social Network, Segregation, Opinion Formation, Opinion Dynamics, Agent-Based Modeling,
چکیده مقاله :
People may change their opinions as a consequence of interacting with others. In the literature, this phenomenon is expressed as opinion formation and has a wide range of applications, including predicting social movements, predicting political voting results, and marketing. The interactions could be face-to-face or via online social networks. The social opinion phases are categorized into consensus, majority, and non-majority. In this research, we study phase transitions due to interactions between connected people with various noise levels using agent-based modeling and a computational social science approach. Two essential factors affect opinion formations: the opinion formation model and the network topology. We assumed the social impact model of opinion formation, a discrete binary opinion model, appropriate for both face-to-face and online interactions for opinion formation. For the network topology, scale-free networks have been widely used in many studies to model real social networks, while recent studies have revealed that most social networks fit log-normal distributions, which we considered in this study. Therefore, the main contribution of this study is to consider the log-normal distribution network topology in phase transitions in the social impact model of opinion formation. The results reveal that two parameters affect the phase transition: noise level and segregation. A non-majority phase happens in equilibrium in high enough noise level, regardless of the network topology, and a majority phase happens in equilibrium in lower noise levels. However, the segregation, which depends on the network topology, affects opinion groups’ population. A comparison with the scale-free network topology shows that in the scale-free network, which have a more segregated topology, resistance of segregated opinion groups against opinion change causes a slightly different phase transition at low noise levels. EI (External-Internal) index has been used to measure segregations, which is based on the difference between between-group (External) links and within-group (Internal) links.
People may change their opinions as a consequence of interacting with others. In the literature, this phenomenon is expressed as opinion formation and has a wide range of applications, including predicting social movements, predicting political voting results, and marketing. The interactions could be face-to-face or via online social networks. The social opinion phases are categorized into consensus, majority, and non-majority. In this research, we study phase transitions due to interactions between connected people with various noise levels using agent-based modeling and a computational social science approach. Two essential factors affect opinion formations: the opinion formation model and the network topology. We assumed the social impact model of opinion formation, a discrete binary opinion model, appropriate for both face-to-face and online interactions for opinion formation. For the network topology, scale-free networks have been widely used in many studies to model real social networks, while recent studies have revealed that most social networks fit log-normal distributions, which we considered in this study. Therefore, the main contribution of this study is to consider the log-normal distribution network topology in phase transitions in the social impact model of opinion formation. The results reveal that two parameters affect the phase transition: noise level and segregation. A non-majority phase happens in equilibrium in high enough noise level, regardless of the network topology, and a majority phase happens in equilibrium in lower noise levels. However, the segregation, which depends on the network topology, affects opinion groups’ population. A comparison with the scale-free network topology shows that in the scale-free network, which have a more segregated topology, resistance of segregated opinion groups against opinion change causes a slightly different phase transition at low noise levels. EI (External-Internal) index has been used to measure segregations, which is based on the difference between between-group (External) links and within-group (Internal) links.
[1] P. Hedström, and P. Bearman, “What is analytical sociology all about? An introductory essay,” The Oxford handbook of analytical sociology, pp. 3-24, 2009.#
[2] M. Keuschnigg, N. Lovsjö, and P. Hedström, “Analytical sociology and computational social science,” Journal of Computational Social Science, vol. 1, no. 1, pp. 3-14, 2018.#
[3] L. Mastroeni, P. Vellucci, and M. Naldi, “Agent-based models for opinion formation: A bibliographic survey,” IEEE Access, vol. 7, pp. 58836-58848, 2019.#
[4] B. D. Anderson, and M. Ye, “Recent advances in the modelling and analysis of opinion dynamics on influence networks,” International Journal of Automation and Computing, vol. 16, no. 2, pp. 129-149, 2019.#
[5] C. Castellano, S. Fortunato, and V. Loreto, “Statistical physics of social dynamics,” Reviews of modern physics, vol. 81, no. 2, pp. 591, 2009.#
[6] J. R. French Jr, “A formal theory of social power,” Psychological review, vol. 63, no. 3, pp. 181, 1956.#
[7] J. A. Hołyst, K. Kacperski, and F. Schweitzer, “Social impact models of opinion dynamics,” Annual reviews of computational physics, vol. 9, pp. 253-273, 2001.#
[8] B. Latané, “The psychology of social impact,” American psychologist, vol. 36, no. 4, pp. 343-356, 1981.#
[9] S. Hobolt, T. J. Leeper, and J. Tilley, “Divided by the vote: affective polarization in the wake of the Brexit referendum,” British Journal of Political Science, 2020.#
[10] M. Pineda, R. Toral, and E. Hernandez-Garcia, “Noisy continuous-opinion dynamics,” Journal of Statistical Mechanics: Theory and Experiment, vol. 2009, no. 08, pp. P08001, 2009.#
[11] L. P. Kadanoff, “More is the same; phase transitions and mean field theories,” Journal of Statistical Physics, vol. 137, no. 5-6, pp. 777, 2009.#
[12] A. Mansouri, and F. Taghiyareh, “Phase Transition in the Social Impact Model of Opinion Formation in Scale-Free Networks: The Social Power Effect,” Journal of Artificial Societies and Social Simulation, vol. 23, no. 2, pp. 3, 2020.#
[13] J. A. Hołyst, K. Kacperski, and F. Schweitzer, “Phase transitions in social impact models of opinion formation,” Physica A: Statistical Mechanics and its Applications, vol. 285, no. 1-2, pp. 199-210, 2000.#
[14] G. Jaeger, “The Ehrenfest classification of phase transitions: introduction and evolution,” Archive for history of exact sciences, vol. 53, no. 1, pp. 51-81, 1998.#
[15] M. Li, and H. Dankowicz, “Impact of temporal network structures on the speed of consensus formation in opinion dynamics,” Physica A: Statistical Mechanics and its Applications, vol. 523, pp. 1355-1370, 2019.#
[16] A.-L. Barabási, and R. Albert, “Emergence of scaling in random networks,” science, vol. 286, no. 5439, pp. 509-512, 1999.#
[17] T. Johansson, “Generating artificial social networks,” The Quantitative Methods for Psychology, vol. 15, no. 2, pp. 56-74, 2019.#
[18] A. D. Broido, and A. Clauset, “Scale-free networks are rare,” Nature communications, vol. 10, no. 1, pp. 1-10, 2019.#
[19] K. Sun, “Explanation of log-normal distributions and power-law distributions in biology and social science,” Tech. Report, Department of Physics, 2004.#
[20] C. Cioffi-Revilla, “Computational social science,” Wiley Interdisciplinary Reviews: Computational Statistics, vol. 2, no. 3, pp. 259-271, 2010.#
[21] P. Y.-z. Wan, “Analytical sociology: A Bungean appreciation,” Science & Education, vol. 21, no. 10, pp. 1545-1565, 2012.#
[22] N. Gilbert, and K. Troitzsch, Simulation for the social scientist: McGraw-Hill Education (UK), 2005.#
[23] J. Hauke, I. Lorscheid, and M. Meyer, “Recent development of social simulation as reflected in JASSS between 2008 and 2014: A citation and co-citation analysis,” Journal of artificial societies and social simulation, vol. 20, no. 1, 2017.#
[24] E. Chattoe-Brown, “Why sociology should use agent based modelling,” Sociological Research Online, vol. 18, no. 3, pp. 1-11, 2013.#
[25] F. Bianchi, and F. Squazzoni, “Agent-based models in sociology,” Wiley Interdisciplinary Reviews: Computational Statistics, vol. 7, no. 4, pp. 284-306, 2015.#
[26] A. Jędrzejewski, and K. Sznajd-Weron, “Statistical physics of opinion formation: is it a spoof?,” Comptes Rendus Physique, 2019.#
[27] R. P. Abelson, “Mathematical models of the distribution of attitudes under controversy,” Contributions to mathematical psychology, vol. 14, pp. 1-160, 1964.#
[28] M. H. DeGroot, “Reaching a consensus,” Journal of the American Statistical Association, vol. 69, no. 345, pp. 118-121, 1974.#
[29] R. A. Holley, and T. M. Liggett, “Ergodic theorems for weakly interacting infinite systems and the voter model,” The annals of probability, pp. 643-663, 1975.#
[30] N. E. Friedkin, and E. C. Johnsen, “Social influence and opinions,” Journal of Mathematical Sociology, vol. 15, no. 3-4, pp. 193-206, 1990.#
[31] N. E. Friedkin, and E. C. Johnsen, “Social influence networks and opinion change,” Advances in Group Processes, vol. 16, pp. 1-29, 1999.#
[32] R. Axelrod, “The dissemination of culture: A model with local convergence and global polarization,” Journal of conflict resolution, vol. 41, no. 2, pp. 203-226, 1997.#
[33] K. Sznajd-Weron, and J. Sznajd, “Opinion evolution in closed community,” International Journal of Modern Physics C, vol. 11, no. 06, pp. 1157-1165, 2000.#
[34] D. Stauffer, A. O. Sousa, and S. M. De Oliveira, “Generalization to square lattice of Sznajd sociophysics model,” International Journal of Modern Physics C, vol. 11, no. 06, pp. 1239-1245, 2000.#
[35] G. Deffuant, D. Neau, F. Amblard, and G. Weisbuch, “Mixing beliefs among interacting agents,” Advances in Complex Systems, vol. 3, no. 01n04, pp. 87-98, 2000.#
[36] G. Deffuant, F. Amblard, G. Weisbuch, and T. Faure, “How can extremism prevail? A study based on the relative agreement interaction model,” Journal of artificial societies and social simulation, vol. 5, no. 4, 2002.#
[37] G. Deffuant, F. Amblard, and G. Weisbuch, “Modelling group opinion shift to extreme: the smooth bounded confidence model,” arXiv preprint cond-mat/0410199, 2004.#
[38] R. Hegselmann, and U. Krause, “Opinion dynamics and bounded confidence models, analysis, and simulation,” Journal of Artificial Societies and Social Simulation, vol. 5, no. 3, 2002.#
[39] S. Galam, “Minority opinion spreading in random geometry,” The European Physical Journal B-Condensed Matter and Complex Systems, vol. 25, no. 4, pp. 403-406, 2002.#
[40] C. Altafini, “Dynamics of opinion forming in structurally balanced social networks,” PloS one, vol. 7, no. 6, pp. e38135, 2012.#
[41] C. Altafini, “Consensus problems on networks with antagonistic interactions,” IEEE transactions on automatic control, vol. 58, no. 4, pp. 935-946, 2013.#
[42] C. Altafini, and G. Lini, “Predictable dynamics of opinion forming for networks with antagonistic interactions,” IEEE Transactions on Automatic Control, vol. 60, no. 2, pp. 342-357, 2015.#
[43] A. Nowak, J. Szamrej, and B. Latané, “From private attitude to public opinion: A dynamic theory of social impact,” Psychological review, vol. 97, no. 3, pp. 362, 1990.#
[44] A. Mansouri, F. Taghiyareh, and J. Hatami, “Improving Opinion Formation Models on Social Media Through Emotions,” in 5th International Conference on Web Research (ICWR), 2019.#
[45] A. Mansouri, F. Taghiyareh, and J. Hatami, “Post-Based Prediction of Users' Opinions Employing the Social Impact Model Improved by Emotion,” International Journal of Web Research, vol. 1, no. 2, pp. 34-42, 2018.#
[46] M. Golosovsky, “Power-law citation distributions are not scale-free,” Physical Review E, vol. 96, no. 3, pp. 032306, 2017.#
[47] A. Clauset, C. R. Shalizi, and M. E. Newman, “Power-law distributions in empirical data,” SIAM review, vol. 51, no. 4, pp. 661-703, 2009.#
[48] K. Binder, “Theory of first-order phase transitions,” Reports on progress in physics, vol. 50, no. 7, pp. 783, 1987.#
[49] A. Barrat, M. Barthelemy, and A. Vespignani, Dynamical processes on complex networks: Cambridge university press, 2008.#
[50] P. Fronczak, A. Fronczak, and J. A. Hołyst, “Phase transitions in social networks,” The European Physical Journal B, vol. 59, no. 1, pp. 133-139, 2007.#
[51] M. Perc, “Phase transitions in models of human cooperation,” Physics Letters A, vol. 380, no. 36, pp. 2803-2808, 2016.#
[52] M. Bojanowski, and R. Corten, “Measuring segregation in social networks,” Social Networks, vol. 39, pp. 14-32, 2014.#
[53] A. Kowalska-Styczeń, and K. Malarz, “Noise induced unanimity and disorder in opinion formation,” Plos one, vol. 15, no. 7, pp. e0235313, 2020.#
[54] S. Grauwin, and P. Jensen, “Opinion group formation and dynamics: Structures that last from nonlasting entities,” Physical Review E, vol. 85, no. 6, pp. 066113, 2012.#
[55] M. Pineda, R. Toral, and E. Hernández-García, “Diffusing opinions in bounded confidence processes,” The European Physical Journal D, vol. 62, no. 1, pp. 109-117, 2011.#
[56] A. Carro, R. Toral, and M. San Miguel, “The role of noise and initial conditions in the asymptotic solution of a bounded confidence, continuous-opinion model,” Journal of Statistical Physics, vol. 151, no. 1-2, pp. 131-149, 2013.#
[57] J. Zhang, and Y. Zhao, “The robust consensus of a noisy deffuant-weisbuch model,” Mathematical Problems in Engineering, vol. 2018, 2018.#
[58] L. Sabatelli, and P. Richmond, “Non-monotonic spontaneous magnetization in a Sznajd-like consensus model,” Physica A: Statistical Mechanics and its Applications, vol. 334, no. 1-2, pp. 274-280, 2004.#
[59] K. Sznajd-Weron, “Sznajd model and its applications,” arXiv preprint physics/0503239, 2005.#
[60] W. Su, G. Chen, and Y. Hong, “Noise leads to quasi-consensus of Hegselmann–Krause opinion dynamics,” Automatica, vol. 85, pp. 448-454, 2017.#
[61] G. Chen, W. Su, S. Ding, and Y. Hong, “Heterogeneous hegselmann-krause dynamics with environment and communication noise,” IEEE Transactions on Automatic Control, 2019.#
[62] M. Pineda, R. Toral, and E. Hernández-García, “The noisy Hegselmann-Krause model for opinion dynamics,” The European Physical Journal B, vol. 86, no. 12, pp. 490, 2013.#
[63] G. Bianconi, and A.-L. Barabási, “Competition and multiscaling in evolving networks,” EPL (Europhysics Letters), vol. 54, no. 4, pp. 436, 2001.#
[64] T. Pham, P. Sheridan, H. Shimodaira, M. T. Pham, and I. Rcpp, “Package ‘PAFit’,” 2020.#
