Computational Models of Opinion Formation in Social Networks and Their Dimensions
Subject Areas : ICT
1 -
Keywords: Opinion Formation, Opinion Dynamics, Modeling, Computational Social Science,
Abstract :
Opinion formation is a propagation process in social networks, examining the dynamics of people's opinion dynamics under the influence of others. Several computational opinion formation models have been proposed to study the dynamics of opinion and the process of creating situations such as consensus, bipolarity/multi-polarization, or the diversity of opinions in a society. Due to the growing trend of online social networks and considering the speed and convenience of producing and publishing content in these networks, an appropriate opinion formation model should be used in related studies. This study surveys the major opinion formation models and introduces a set of dimensions distinguishing opinion formation models. These dimensions are comprised of 1) opinion space, 2) discrete/continuous time, 3) interaction network, 4) interaction limitation, 5) degree of influence, 6) time dependency, and 7) linearity of model. Moreover, some conditions could be considered on the models that affect opinion formation model, including 1) homogeneity/heterogeneity of interacting people, 2) the number of dimensions of opinion space, 3) first impression, and 4) deterministic/noisy modeling. The results of this study help the researchers in the field of opinion formation to choose the appropriate opinion formation model according to the conditions and characteristics of the subject under investigation, and even to expand opinion formation models, if necessary.
References:
[1] B. Liu and L. Zhang, "A survey of opinion mining and sentiment analysis," in Mining text data, ed: Springer, 2012, pp. 415-463.
[2] M. Jalili, "Social power and opinion formation in complex networks," Physica A: Statistical Mechanics and its Applications, vol. 392, pp. 959-966, 2013.
[3] I. N. Lymperopoulos and G. D. Ioannou, "Understanding and modeling the complex dynamics of the online social networks: a scalable conceptual approach," Evolving Systems, vol. 7, pp. 207-232, 2016.
[4] M. S. Granovetter, "The strength of weak ties," American journal of sociology, vol. 78, pp. 1360-1380, 1973.
[5] J. A. Holyst, K. Kacperski, and F. Schweitzer, "Social impact models of opinion dynamics," Annual reviews of computational physics, vol. 9, pp. 253-273, 2002.
[6] Y. Dong, M. Zhan, G. Kou, Z. Ding, and H. Liang, "A survey on the fusion process in opinion dynamics," Information Fusion, vol. 43, pp. 57-65, 2018.
[7] H. Noorazar, "Recent advances in opinion propagation dynamics: A 2020 survey," The European Physical Journal Plus, vol. 135, pp. 1-20, 2020.
[8] D. Lazer, A. Pentland, L. Adamic, S. Aral, A.-L. Barabási, D. Brewer, et al., "Computational social science," Science, vol. 323, pp. 721-723, 2009.
[9] H. Lietz, A. Schmitz, and J. Schaible, "Social Network Analysis with Digital Behavioral Data," easy_social_sciences, pp. 41-48, 2021.
[10] R. Urena, G. Kou, Y. Dong, F. Chiclana, and E. Herrera-Viedma, "A review on trust propagation and opinion dynamics in social networks and group decision making frameworks," Information sciences, vol. 478, pp. 461-475, 2019.
[11] K. Lichtenegger and T. Hadzibeganovic, "The interplay of self-reflection, social interaction and random events in the dynamics of opinion flow in two-party democracies," International Journal of Modern Physics C, vol. 27, p. 1650065, 2016.
[12] A. Hanifa, C. Debora, M. F. Hasani, and P. Wicaksono, "Analyzing Views on Presidential Candidates for Election 2024 Based on the Instagram and X Platforms with Text Clustering," Procedia Computer Science, vol. 245, pp. 730-739, 2024.
[13] S. Hong and S. H. Kim, "Political polarization on twitter: Implications for the use of social media in digital governments," Government Information Quarterly, vol. 33, pp. 777-782, 2016.
[14] A. Mansouri, M. Mahmoudi, M. Farhoodi, and S. M. Mirsarraf, "Persian Rumor Detection Using a MultiClassifier Fusion Approach," International Journal of Information and Communication Technology Research, vol. 16, pp. 33-43, 2024.
[15] A. Bondielli and F. Marcelloni, "A survey on fake news and rumour detection techniques," Information sciences, vol. 497, pp. 38-55, 2019.
[16] K. Sharma, F. Qian, H. Jiang, N. Ruchansky, M. Zhang, and Y. Liu, "Combating fake news: A survey on identification and mitigation techniques," ACM transactions on intelligent systems and technology (TIST), vol. 10, pp. 1-42, 2019.
[17] X. Zhou and R. Zafarani, "A survey of fake news: Fundamental theories, detection methods, and opportunities," ACM Computing Surveys (CSUR), vol. 53, pp. 1-40, 2020.
[18] C. Castellano, S. Fortunato, and V. Loreto, "Statistical physics of social dynamics," Reviews of modern physics, vol. 81, p. 591, 2009.
[19] P. Sobkowicz, "Modelling opinion formation with physics tools: Call for closer link with reality," Journal of Artificial Societies and Social Simulation, vol. 12, p. 11, 2009.
[20] F. Klügl and A. L. Bazzan, "Agent-based modeling and simulation," AI Magazine, vol. 33, p. 29, 2012.
[21] C. M. Macal and M. J. North, "Tutorial on agent-based modelling and simulation," Journal of simulation, vol. 4, pp. 151-162, 2010.
[22] C. Macal and M. North, "Introductory tutorial: Agent-based modeling and simulation," in Proceedings of the 2014 Winter Simulation Conference, 2014, pp. 6-20.
[23] F. Schweitzer, T. Krivachy, and D. Garcia, "How emotions drive opinion polarization: An agent-based model," arXiv preprint arXiv:1908.11623, 2019.
[24] M. Tomaiuolo, G. Lombardo, M. Mordonini, S. Cagnoni, and A. Poggi, "A Survey on Troll Detection," Future Internet, vol. 12, p. 31, 2020.
[25] L. Mastroeni, P. Vellucci, and M. Naldi, "Agent-based models for opinion formation: A bibliographic survey," IEEE Access, vol. 7, pp. 58836-58848, 2019.
[26] O. Abid, S. Jamoussi, and Y. B. Ayed, "Deterministic models for opinion formation through communication: A survey," Online Social Networks and Media, vol. 6, pp. 1-17, 2018.
[27] J. Lorenz, "Continuous opinion dynamics under bounded confidence: A survey," International Journal of Modern Physics C, vol. 18, pp. 1819-1838, 2007.
[28] C. A. Devia and G. Giordano, "A framework to analyze opinion formation models," Scientific Reports, vol. 12, p. 13441, 2022.
[29] C. A. Devia and G. Giordano, "Probabilistic analysis of agent-based opinion formation models," Scientific Reports, vol. 13, p. 20152, 2023.
[30] I. V. Kozitsin, "A general framework to link theory and empirics in opinion formation models," Scientific reports, vol. 12, p. 5543, 2022.
[31] N. E. Friedkin, "A formal theory of social power," Journal of Mathematical Sociology, vol. 12, pp. 103-126, 1986.
[32] R. P. Abelson, "Mathematical models of the distribution of attitudes under controversy," Contributions to mathematical psychology, vol. 14, pp. 1-160, 1964.
[33] R. Hegselmann and U. Krause, "Opinion dynamics and bounded confidence models, analysis, and simulation," Journal of Artificial Societies and Social Simulation, vol. 5, 2002.
[34] M. Taylor, "towards a mathematical theory of Influence and attitude change," Human Relations, vol. 21, pp. 121-139, 1968.
[35] M. H. DeGroot, "Reaching a consensus," Journal of the American Statistical Association, vol. 69, pp. 118-121, 1974.
[36] 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.
[37] N. E. Friedkin and E. C. Johnsen, "Social influence and opinions," Journal of Mathematical Sociology, vol. 15, pp. 193-206, 1990.
[38] N. E. Friedkin and E. C. Johnsen, "Social influence networks and opinion change," Advances in Group Processes, vol. 16, pp. 1-29, 1999.
[39] K. Sznajd-Weron and J. Sznajd, "Opinion evolution in closed community," International Journal of Modern Physics C, vol. 11, pp. 1157-1165, 2000.
[40] K. Sznajd-Weron, "Sznajd model and its applications," arXiv preprint physics/0503239, 2005.
[41] 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, pp. 1239-1245, 2000.
[42] G. Deffuant, D. Neau, F. Amblard, and G. Weisbuch, "Mixing beliefs among interacting agents," Advances in Complex Systems, vol. 3, pp. 87-98, 2000.
[43] 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, 2002.
[44] G. Deffuant, F. Amblard, and G. Weisbuch, "Modelling group opinion shift to extreme: the smooth bounded confidence model," arXiv preprint cond-mat/0410199, 2004.
[45] A. Nowak, J. Szamrej, and B. Latané, "From private attitude to public opinion: A dynamic theory of social impact," Psychological review, vol. 97, p. 362, 1990.
[46] S. E. Asch, "Opinions and social pressure," Scientific american, vol. 193, pp. 31-35, 1955.
[47] S. E. Asch, "Studies of independence and conformity: I. A minority of one against a unanimous majority," Psychological monographs: General and applied, vol. 70, p. 1, 1956.
[48] S. Galam, "Minority opinion spreading in random geometry," The European Physical Journal B-Condensed Matter and Complex Systems, vol. 25, pp. 403-406, 2002.
[49] C. Altafini, "Dynamics of opinion forming in structurally balanced social networks," PloS one, vol. 7, p. e38135, 2012.
[50] C. Altafini, "Consensus problems on networks with antagonistic interactions," IEEE transactions on automatic control, vol. 58, pp. 935-946, 2013.
[51] C. Altafini and G. Lini, "Predictable dynamics of opinion forming for networks with antagonistic interactions," IEEE Transactions on Automatic Control, vol. 60, pp. 342-357, 2015.
[52] X. Chen, P. Tsaparas, J. Lijffijt, and T. De Bie, "Opinion dynamics with backfire effect and biased assimilation," PloS one, vol. 16, p. e0256922, 2021.
[53] P. Erdős and A. Rényi, "On random graphs I," Publ. Math. Debrecen, vol. 6, pp. 290-297, 1959.
[54] D. J. Watts and S. H. Strogatz, "Collective dynamics of ‘small-world’networks," nature, vol. 393, pp. 440-442, 1998.
[55] A.-L. Barabási and R. Albert, "Emergence of scaling in random networks," science, vol. 286, pp. 509-512, 1999.
[56] U. Krause, "A discrete nonlinear and non-autonomous model of consensus formation," Communications in difference equations, pp. 227-236, 2000.
[57] D. N. Sotiropoulos, C. Bilanakos, and G. M. Giaglis, "Opinion formation in social networks: a time-variant and non-linear model," Complex & Intelligent Systems, vol. 2, pp. 269-284, 2016.
[58] E. Kurmyshev and H. A. Juárez, "What is a leader of opinion formation in bounded confidence models?," arXiv preprint arXiv:1305.4677, 2013.
[59] S. Wongkaew, M. Caponigro, and A. Borzi, "On the control through leadership of the Hegselmann–Krause opinion formation model," Mathematical Models and Methods in Applied Sciences, vol. 25, pp. 565-585, 2015.
[60] J. Lorenz, "Continuous opinion dynamics of multidimensional allocation problems under bounded confidence: More dimensions lead to better chances for consensus," arXiv preprint arXiv:0708.2923, 2007.
[61] P. Liu and X. Chen, "An overview on opinion spreading model," Journal of Applied Mathematics and Physics, vol. 3, p. 449, 2015.
[62] E. Alraddadi, "Opinion formation among mobile agents," Cardiff University, 2021.
[63] R. Chhimpa and A. C. Yadav, "$1/f $ noise in the Ising model," arXiv preprint arXiv:2503.04105, 2025.
[64] 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, p. 3, 2020.
[65] A. Mansouri and F. Taghiyareh, "Phase transition in the social impact model of opinion formation in log-normal networks," Journal of Information Systems and Telecommunication (JIST), vol. 1, pp. 1-14, 2021.
[66] A. Mansouri and F. Taghiyareh, "Effect of segregation on the dynamics of noise-free social impact model of opinion formation through agent-based modeling," International Journal of Web Research, vol. 2, pp. 36-44, 2019.
[67] 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, pp. 199-210, 2000.
[1] B. Liu and L. Zhang, "A survey of opinion mining and sentiment analysis," in Mining text data, ed: Springer, 2012, pp. 415-463.
[2] M. Jalili, "Social power and opinion formation in complex networks," Physica A: Statistical Mechanics and its Applications, vol. 392, pp. 959-966, 2013.
[3] I. N. Lymperopoulos and G. D. Ioannou, "Understanding and modeling the complex dynamics of the online social networks: a scalable conceptual approach," Evolving Systems, vol. 7, pp. 207-232, 2016.
[4] M. S. Granovetter, "The strength of weak ties," American journal of sociology, vol. 78, pp. 1360-1380, 1973.
[5] J. A. Holyst, K. Kacperski, and F. Schweitzer, "Social impact models of opinion dynamics," Annual reviews of computational physics, vol. 9, pp. 253-273, 2002.
[6] Y. Dong, M. Zhan, G. Kou, Z. Ding, and H. Liang, "A survey on the fusion process in opinion dynamics," Information Fusion, vol. 43, pp. 57-65, 2018.
[7] H. Noorazar, "Recent advances in opinion propagation dynamics: A 2020 survey," The European Physical Journal Plus, vol. 135, pp. 1-20, 2020.
[8] D. Lazer, A. Pentland, L. Adamic, S. Aral, A.-L. Barabási, D. Brewer, et al., "Computational social science," Science, vol. 323, pp. 721-723, 2009.
[9] H. Lietz, A. Schmitz, and J. Schaible, "Social Network Analysis with Digital Behavioral Data," easy_social_sciences, pp. 41-48, 2021.
[10] R. Urena, G. Kou, Y. Dong, F. Chiclana, and E. Herrera-Viedma, "A review on trust propagation and opinion dynamics in social networks and group decision making frameworks," Information sciences, vol. 478, pp. 461-475, 2019.
[11] K. Lichtenegger and T. Hadzibeganovic, "The interplay of self-reflection, social interaction and random events in the dynamics of opinion flow in two-party democracies," International Journal of Modern Physics C, vol. 27, p. 1650065, 2016.
[12] A. Hanifa, C. Debora, M. F. Hasani, and P. Wicaksono, "Analyzing Views on Presidential Candidates for Election 2024 Based on the Instagram and X Platforms with Text Clustering," Procedia Computer Science, vol. 245, pp. 730-739, 2024.
[13] S. Hong and S. H. Kim, "Political polarization on twitter: Implications for the use of social media in digital governments," Government Information Quarterly, vol. 33, pp. 777-782, 2016.
[14] A. Mansouri, M. Mahmoudi, M. Farhoodi, and S. M. Mirsarraf, "Persian Rumor Detection Using a MultiClassifier Fusion Approach," International Journal of Information and Communication Technology Research, vol. 16, pp. 33-43, 2024.
[15] A. Bondielli and F. Marcelloni, "A survey on fake news and rumour detection techniques," Information sciences, vol. 497, pp. 38-55, 2019.
[16] K. Sharma, F. Qian, H. Jiang, N. Ruchansky, M. Zhang, and Y. Liu, "Combating fake news: A survey on identification and mitigation techniques," ACM transactions on intelligent systems and technology (TIST), vol. 10, pp. 1-42, 2019.
[17] X. Zhou and R. Zafarani, "A survey of fake news: Fundamental theories, detection methods, and opportunities," ACM Computing Surveys (CSUR), vol. 53, pp. 1-40, 2020.
[18] C. Castellano, S. Fortunato, and V. Loreto, "Statistical physics of social dynamics," Reviews of modern physics, vol. 81, p. 591, 2009.
[19] P. Sobkowicz, "Modelling opinion formation with physics tools: Call for closer link with reality," Journal of Artificial Societies and Social Simulation, vol. 12, p. 11, 2009.
[20] F. Klügl and A. L. Bazzan, "Agent-based modeling and simulation," AI Magazine, vol. 33, p. 29, 2012.
[21] C. M. Macal and M. J. North, "Tutorial on agent-based modelling and simulation," Journal of simulation, vol. 4, pp. 151-162, 2010.
[22] C. Macal and M. North, "Introductory tutorial: Agent-based modeling and simulation," in Proceedings of the 2014 Winter Simulation Conference, 2014, pp. 6-20.
[23] F. Schweitzer, T. Krivachy, and D. Garcia, "How emotions drive opinion polarization: An agent-based model," arXiv preprint arXiv:1908.11623, 2019.
[24] M. Tomaiuolo, G. Lombardo, M. Mordonini, S. Cagnoni, and A. Poggi, "A Survey on Troll Detection," Future Internet, vol. 12, p. 31, 2020.
[25] L. Mastroeni, P. Vellucci, and M. Naldi, "Agent-based models for opinion formation: A bibliographic survey," IEEE Access, vol. 7, pp. 58836-58848, 2019.
[26] O. Abid, S. Jamoussi, and Y. B. Ayed, "Deterministic models for opinion formation through communication: A survey," Online Social Networks and Media, vol. 6, pp. 1-17, 2018.
[27] J. Lorenz, "Continuous opinion dynamics under bounded confidence: A survey," International Journal of Modern Physics C, vol. 18, pp. 1819-1838, 2007.
[28] C. A. Devia and G. Giordano, "A framework to analyze opinion formation models," Scientific Reports, vol. 12, p. 13441, 2022.
[29] C. A. Devia and G. Giordano, "Probabilistic analysis of agent-based opinion formation models," Scientific Reports, vol. 13, p. 20152, 2023.
[30] I. V. Kozitsin, "A general framework to link theory and empirics in opinion formation models," Scientific reports, vol. 12, p. 5543, 2022.
[31] N. E. Friedkin, "A formal theory of social power," Journal of Mathematical Sociology, vol. 12, pp. 103-126, 1986.
[32] R. P. Abelson, "Mathematical models of the distribution of attitudes under controversy," Contributions to mathematical psychology, vol. 14, pp. 1-160, 1964.
[33] R. Hegselmann and U. Krause, "Opinion dynamics and bounded confidence models, analysis, and simulation," Journal of Artificial Societies and Social Simulation, vol. 5, 2002.
[34] M. Taylor, "towards a mathematical theory of Influence and attitude change," Human Relations, vol. 21, pp. 121-139, 1968.
[35] M. H. DeGroot, "Reaching a consensus," Journal of the American Statistical Association, vol. 69, pp. 118-121, 1974.
[36] 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.
[37] N. E. Friedkin and E. C. Johnsen, "Social influence and opinions," Journal of Mathematical Sociology, vol. 15, pp. 193-206, 1990.
[38] N. E. Friedkin and E. C. Johnsen, "Social influence networks and opinion change," Advances in Group Processes, vol. 16, pp. 1-29, 1999.
[39] K. Sznajd-Weron and J. Sznajd, "Opinion evolution in closed community," International Journal of Modern Physics C, vol. 11, pp. 1157-1165, 2000.
[40] K. Sznajd-Weron, "Sznajd model and its applications," arXiv preprint physics/0503239, 2005.
[41] 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, pp. 1239-1245, 2000.
[42] G. Deffuant, D. Neau, F. Amblard, and G. Weisbuch, "Mixing beliefs among interacting agents," Advances in Complex Systems, vol. 3, pp. 87-98, 2000.
[43] 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, 2002.
[44] G. Deffuant, F. Amblard, and G. Weisbuch, "Modelling group opinion shift to extreme: the smooth bounded confidence model," arXiv preprint cond-mat/0410199, 2004.
[45] A. Nowak, J. Szamrej, and B. Latané, "From private attitude to public opinion: A dynamic theory of social impact," Psychological review, vol. 97, p. 362, 1990.
[46] S. E. Asch, "Opinions and social pressure," Scientific american, vol. 193, pp. 31-35, 1955.
[47] S. E. Asch, "Studies of independence and conformity: I. A minority of one against a unanimous majority," Psychological monographs: General and applied, vol. 70, p. 1, 1956.
[48] S. Galam, "Minority opinion spreading in random geometry," The European Physical Journal B-Condensed Matter and Complex Systems, vol. 25, pp. 403-406, 2002.
[49] C. Altafini, "Dynamics of opinion forming in structurally balanced social networks," PloS one, vol. 7, p. e38135, 2012.
[50] C. Altafini, "Consensus problems on networks with antagonistic interactions," IEEE transactions on automatic control, vol. 58, pp. 935-946, 2013.
[51] C. Altafini and G. Lini, "Predictable dynamics of opinion forming for networks with antagonistic interactions," IEEE Transactions on Automatic Control, vol. 60, pp. 342-357, 2015.
[52] X. Chen, P. Tsaparas, J. Lijffijt, and T. De Bie, "Opinion dynamics with backfire effect and biased assimilation," PloS one, vol. 16, p. e0256922, 2021.
[53] P. Erdős and A. Rényi, "On random graphs I," Publ. Math. Debrecen, vol. 6, pp. 290-297, 1959.
[54] D. J. Watts and S. H. Strogatz, "Collective dynamics of ‘small-world’networks," nature, vol. 393, pp. 440-442, 1998.
[55] A.-L. Barabási and R. Albert, "Emergence of scaling in random networks," science, vol. 286, pp. 509-512, 1999.
[56] U. Krause, "A discrete nonlinear and non-autonomous model of consensus formation," Communications in difference equations, pp. 227-236, 2000.
[57] D. N. Sotiropoulos, C. Bilanakos, and G. M. Giaglis, "Opinion formation in social networks: a time-variant and non-linear model," Complex & Intelligent Systems, vol. 2, pp. 269-284, 2016.
[58] E. Kurmyshev and H. A. Juárez, "What is a leader of opinion formation in bounded confidence models?," arXiv preprint arXiv:1305.4677, 2013.
[59] S. Wongkaew, M. Caponigro, and A. Borzi, "On the control through leadership of the Hegselmann–Krause opinion formation model," Mathematical Models and Methods in Applied Sciences, vol. 25, pp. 565-585, 2015.
[60] J. Lorenz, "Continuous opinion dynamics of multidimensional allocation problems under bounded confidence: More dimensions lead to better chances for consensus," arXiv preprint arXiv:0708.2923, 2007.
[61] P. Liu and X. Chen, "An overview on opinion spreading model," Journal of Applied Mathematics and Physics, vol. 3, p. 449, 2015.
[62] E. Alraddadi, "Opinion formation among mobile agents," Cardiff University, 2021.
[63] R. Chhimpa and A. C. Yadav, "$1/f $ noise in the Ising model," arXiv preprint arXiv:2503.04105, 2025.
[64] 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, p. 3, 2020.
[65] A. Mansouri and F. Taghiyareh, "Phase transition in the social impact model of opinion formation in log-normal networks," Journal of Information Systems and Telecommunication (JIST), vol. 1, pp. 1-14, 2021.
[66] A. Mansouri and F. Taghiyareh, "Effect of segregation on the dynamics of noise-free social impact model of opinion formation through agent-based modeling," International Journal of Web Research, vol. 2, pp. 36-44, 2019.
[67] 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, pp. 199-210, 2000.
