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Qiannan","award":["2020XK05ST"],"award-info":[{"award-number":["2020XK05ST"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The last decade has witnessed a great number of opinion formation models that depict the evolution of opinions within a social group and make predictions about the evolution process. In the traditional formulation of opinion evolution such as the DeGroot model, an agent\u2019s opinion is represented as a real number and updated by taking a weighted average of its neighbour\u2019s opinions. In this paper, we adopt a hybrid representation of opinions that integrate both the discrete and continuous nature of an opinion. Basically, an agent has a \u2018Yes\u2019, \u2018Neutral\u2019 or \u2018No\u2019 opinion on some issues of interest and associates with its Yes opinion a support degree which captures how strongly it supports the opinion. With such a rich representation, not only can we study the evolution of opinion but also that of support degree. After all, an agent\u2019s opinion can stay the same but become more or less supportive of it. Changes in the support degree are progressive in nature and only a sufficient accumulation of such a progressive change will result in a change of opinion say from Yes to No. Hence, in our formulation, after an agent interacts with another, its support degree is either strengthened or weakened by a predefined amount and a change of opinion may occur as a consequence of such progressive changes. We carry out simulations to evaluate the impacts of key model parameters including (1) the number of agents, (2) the distribution of initial support degrees and (3) the amount of change of support degree changes in a single interaction. Last but not least, we present several extensions to the hybrid and progressive model which lead to opinion polarization.<\/jats:p>","DOI":"10.3390\/e24111692","type":"journal-article","created":{"date-parts":[[2022,11,21]],"date-time":"2022-11-21T03:07:23Z","timestamp":1669000043000},"page":"1692","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A Hybrid Opinion Formation and Polarization Model"],"prefix":"10.3390","volume":"24","author":[{"given":"Baizhong","family":"Yang","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistic, Guizhou University, Guiyang 550025, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Quan","family":"Yu","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistic, Qiannan Normal University for Nationalities, Duyun 558000, China"},{"name":"Key Laboratory of Complex Systems and Intelligent Optimization of Guizhou Province, Duyun 558000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yi","family":"Fan","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistic, Qiannan Normal University for Nationalities, Duyun 558000, China"},{"name":"Key Laboratory of Complex Systems and Intelligent Optimization of Guizhou Province, Duyun 558000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,11,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Srbu, A., Loreto, V., Servedio, V., and Tria, F. (2017). Opinion Dynamics: Models, Extensions and External Effects, Springer International Publishing.","DOI":"10.1007\/978-3-319-25658-0_17"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"884","DOI":"10.1016\/j.procs.2015.05.146","article-title":"Simulating Opinion Dynamics on Stakeholders\u2019 Networks through Agent-based Modeling for Collective Transport Decisions","volume":"52","author":"Inturri","year":"2015","journal-title":"Procedia Comput. Sci."},{"key":"ref_3","first-page":"066101","article-title":"Strategy of Competition between Two Groups based on an Inflexible Contrarian Opinion Model","volume":"86","author":"Li","year":"2012","journal-title":"Am. Phys. Soc."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Varma, V.S., Morarescu, I.C., Lasaulce, S., and Martin, S. (2017, January 12\u201315). Opinion dynamics aware marketing strategies in duopolies. Proceedings of the 2017 IEEE 56th Annual Conference on Decision and Control (CDC), Melbourne, VIC, Australia.","DOI":"10.1109\/CDC.2017.8264227"},{"key":"ref_5","unstructured":"Kozuki, A., and Mahmassani, H.S. (2009, January 11\u201315). Information Acquisition and Social Interaction Mechanisms in Opinion Formation and Market Adoption of Transportation Services. Proceedings of the 88th Annual Meeting of the Transportation Research Board, Washington, DC, USA."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1729","DOI":"10.1016\/j.physa.2011.11.038","article-title":"Effects of mass media on opinion spreading in the Sznajd sociophysics model","volume":"391","author":"Crokidakis","year":"2011","journal-title":"Phys. Stat. Mech. Its Appl."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1763","DOI":"10.1109\/TVCG.2014.2346920","article-title":"Opinion Flow: Visual Analysis of Opinion Diffusion on Social Media","volume":"20","author":"Wu","year":"2014","journal-title":"Vis. Comput. Graph. IEEE Trans."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"617","DOI":"10.1016\/j.procs.2016.07.154","article-title":"An opinion control rule with minimum adjustments to support the consensus reaching in bounded confidence model","volume":"91","author":"Ding","year":"2016","journal-title":"Procedia Comput. Sci."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Bravo-Marquez, F., Gayo-Avello, D., Mendoza, M., and Poblete, B. (2012, January 25\u201327). Opinion Dynamics of Elections in Twitter. Proceedings of the 2012 Eighth Latin American Web Congress, Cartagena, Colombia.","DOI":"10.1109\/LA-WEB.2012.11"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2394","DOI":"10.1109\/TSMC.2017.2695158","article-title":"Opinion Dynamics-Based Group Recommender Systems","volume":"48","author":"Castro","year":"2018","journal-title":"IEEE Trans. Syst. Man Cybern. Syst."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2142","DOI":"10.1109\/TITS.2017.2724852","article-title":"Opinion Dynamics-Based Vehicle Velocity Estimation and Diagnosis","volume":"19","author":"Hashemi","year":"2018","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1126\/science.aag2624","article-title":"Network science on belief system dynamics under logic constraints","volume":"354","author":"Friedkin","year":"2016","journal-title":"Science"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"eabg8068","DOI":"10.1126\/sciadv.abg8068","article-title":"Achieving consensus in multilateral international negotiations: The case study of the 2015 Paris Agreement on climate change","volume":"7","author":"Bernardo","year":"2021","journal-title":"Sci. Adv."},{"key":"ref_14","unstructured":"Montroll, E.W., and Badger, W.W. (1974). Introduction to Quantitative Aspects of Social Phenomena, Gordon & Breach."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"032144","DOI":"10.1103\/PhysRevE.98.032144","article-title":"Hysteresis in the zero-temperature random-field Ising model on directed random graphs","volume":"98","author":"Shukla","year":"2018","journal-title":"Phys. Rev. E"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"433","DOI":"10.1016\/j.physa.2019.03.011","article-title":"Binary opinion dynamics on signed networks based on Ising model","volume":"525","author":"Li","year":"2019","journal-title":"Phys. Stat. Mech. Appl."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Dom\u00ednguez, A.R., Arroyo-Duarte, R., Rinc\u00f3n-Vieyra, F., and Alvarado-Mentado, M. (2022). Modeling cancer immunoediting in tumor microenvironment with system characterization through the ising-model Hamiltonian. BMC Bioinform., 23.","DOI":"10.1186\/s12859-022-04731-w"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Takabatake, K., Yanagisawa, K., and Akiyama, Y. (2022). Solving Generalized Polyomino Puzzles Using the Ising Model. Entropy, 24.","DOI":"10.3390\/e24030354"},{"key":"ref_19","unstructured":"Zukovic, M. (June, January 30). Massive Degeneracy And Anomalous Thermodynamics in a Highly Frustrated Ising Model On Honeycomb Lattice. Proceedings of the International ECMS Conference on Modelling and Simulation, Alesund, Norway."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1157","DOI":"10.1142\/S0129183100000936","article-title":"Opinion evolution in closed community","volume":"11","author":"Sznajd","year":"2000","journal-title":"Int. J. Mod. Phys."},{"key":"ref_21","first-page":"e3","article-title":"Non Local Effects in the Sznajd Model: Stochastic resonance aspects","volume":"1","author":"Revelli","year":"2012","journal-title":"EAI Endorsed Trans. Complex Syst."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Chen, H., and Shu, J. (2016). Sznajd2: A Community-Aware Opinion Dynamics Model, IEEE.","DOI":"10.1109\/TrustCom.2016.0231"},{"key":"ref_23","first-page":"643","article-title":"Ergodic Theorems for Weakly Interacting Infinite Systems and the Voter Model","volume":"3","author":"Liggett","year":"1975","journal-title":"Ann. Probab."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"014301","DOI":"10.1103\/PhysRevE.106.014301","article-title":"Adversarial attacks on voter model dynamics in complex networks","volume":"106","author":"Chiyomaru","year":"2021","journal-title":"Phys. Rev. E"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1080\/0022250X.2019.1625349","article-title":"Voter models and external influence","volume":"44","author":"Majmudar","year":"2020","journal-title":"J. Math. Sociol."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"014121","DOI":"10.1103\/PhysRevE.106.014121","article-title":"Curvature-driven growth and interfacial noise in the voter model with self-induced zealots","volume":"106","author":"Latoski","year":"2022","journal-title":"Phys. Rev. E"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Doniec, M., Lipiecki, A., and Sznajd-Weron, K. (2022). Consensus, Polarization and Hysteresis in the Three-State Noisy q-Voter Model with Bounded Confidence. Entropy, 24.","DOI":"10.3390\/e24070983"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"302","DOI":"10.1007\/978-3-030-77967-2_25","article-title":"The Evolution of Political Views Within the Model with Two Binary Opinions","volume":"Volume 12744","author":"Golebiowska","year":"2021","journal-title":"Lecture Notes in Computer Science"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"132","DOI":"10.1016\/S0378-4371(99)00320-9","article-title":"Application of statistical physics to politics","volume":"274","author":"Galam","year":"1999","journal-title":"Phys. Stat. Mech. Appl."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"440","DOI":"10.1016\/j.physleta.2016.12.001","article-title":"Ising percolation in a three-state majority vote model","volume":"381","author":"Balankin","year":"2017","journal-title":"Phys. Lett. A"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"125450","DOI":"10.1016\/j.physa.2020.125450","article-title":"Majority-vote model with limited visibility: An investigation into filter bubbles","volume":"563","author":"Vilela","year":"2021","journal-title":"Phys. Stat. Mech. Appl."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"062311","DOI":"10.1103\/PhysRevE.102.062311","article-title":"Non-Markovian majority-vote model","volume":"102","author":"Chen","year":"2020","journal-title":"Phys. Rev. E"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Neshov, N.N., Tonchev, K., Velchev, Y., Manolova, A., and Poulkov, V. (2022). SoftVotingSleepNet: Majority Vote of Deep Learning Models for Sleep Stage Classification from Raw Single EEG Channel, IEEE.","DOI":"10.1109\/BlackSeaCom54372.2022.9858199"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1142\/S0219525900000078","article-title":"Mixing beliefs among interacting agents","volume":"3","author":"Deffuant","year":"2000","journal-title":"Adv. Complex Syst."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"5289","DOI":"10.1016\/j.physa.2013.07.014","article-title":"Opinion evolution analysis for short-range and long-range Deffuant\u2013Weisbuch models","volume":"392","author":"Zhang","year":"2013","journal-title":"Phys. Stat. Mech. Appl."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"127095","DOI":"10.1016\/j.physa.2022.127095","article-title":"Adapted Deffuant\u2013Weisbuch model with implicit and explicit opinions","volume":"596","author":"Luo","year":"2022","journal-title":"Phys. Stat. Mech. Appl."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"108825","DOI":"10.1016\/j.automatica.2020.108825","article-title":"Convergence properties of the heterogeneous Deffuant-Weisbuch model","volume":"114","author":"Chen","year":"2020","journal-title":"Automatica"},{"key":"ref_38","first-page":"1","article-title":"Opinion dynamics and bounded confidence: Models, analysis and simulation","volume":"5","author":"Hegselmann","year":"2002","journal-title":"J. Artif. Soc. Soc. Simul."},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Xu, H., Cai, H., Wu, S., Ai, K., and Xu, M. (2020, January 11\u201314). HKML: A Novel Opinion Dynamics Hegselmann-Krause Model with Media Literacy. Proceedings of the 2020 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2020, Toronto, ON, Canada.","DOI":"10.1109\/SMC42975.2020.9283055"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"129202:1","DOI":"10.1007\/s11432-019-2788-5","article-title":"Social conformity creates consensus and strong diversity of Hegselmann-Krause opinion dynamics","volume":"65","author":"Cheng","year":"2022","journal-title":"Sci. China Inf. Sci."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"102671","DOI":"10.1016\/j.ipm.2021.102671","article-title":"Fuzzy inference based Hegselmann-Krause opinion dynamics for group decision-making under ambiguity","volume":"58","author":"Zhao","year":"2021","journal-title":"Inf. Process. Manag."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"676","DOI":"10.1016\/j.matcom.2021.01.012","article-title":"Bifurcation analysis of Friedkin-Johnsen and Hegselmann-Krause models with a nonlinear interaction potential","volume":"185","author":"Atas","year":"2021","journal-title":"Math. Comput. Simul."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.inffus.2019.09.006","article-title":"Opinion dynamics model based on the cognitive dissonance: An agent-based simulation","volume":"56","author":"Li","year":"2020","journal-title":"Inf. Fusion"},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Baccelli, F., Chatterjee, A., and Vishwanath, S. (May, January 26). Pairwise stochastic bounded confidence opinion dynamics: Heavy tails and stability. Proceedings of the IEEE INFOCOM 2015\u2014IEEE Conference on Computer Communications, Hong Kong, China.","DOI":"10.1109\/INFOCOM.2015.7218565"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1016\/j.ins.2019.03.044","article-title":"A hybrid group decision making framework for achieving agreed solutions based on stable opinions","volume":"490","author":"Dong","year":"2019","journal-title":"Inf. Sci."},{"key":"ref_46","first-page":"20210169","article-title":"Opinion dynamics: Public and private","volume":"380","author":"Roy","year":"2022","journal-title":"Philos. Trans. R. Soc. Math. Phys. Eng. Sci."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"17719","DOI":"10.1038\/s41598-021-97155-0","article-title":"Discontinuous phase transitions in the q-voter model with generalized anticonformity on random graphs","volume":"11","author":"Lipiecki","year":"2021","journal-title":"Sci. Rep."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"056112","DOI":"10.1103\/PhysRevE.82.056112","article-title":"Opinion formation in kinetic exchange models: Spontaneous symmetry-breaking transition","volume":"82","author":"Lallouache","year":"2010","journal-title":"Phys. Rev. E"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1093\/ijpor\/13.1.25","article-title":"Perceptions of \u2018Public Opinion\u2019 and \u2018Public\u2019 Opinion Expression","volume":"13","author":"Scheufele","year":"2001","journal-title":"Int. J. Public Opin. Res."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"112","DOI":"10.1016\/j.inffus.2015.08.010","article-title":"The fusion process of interval opinions based on the dynamic bounded confidence","volume":"29","author":"Liang","year":"2016","journal-title":"Inf. Fusion"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"2150006:1","DOI":"10.1142\/S0219525921500065","article-title":"Detecting Opinion-based Groups and polarization in Survey-based attitude Networks and estimating Question Relevance","volume":"24","author":"Dinkelberg","year":"2021","journal-title":"Adv. Complex Syst."},{"key":"ref_52","doi-asserted-by":"crossref","unstructured":"Gaitonde, J., Kleinberg, J.M., and Tardos, \u00c9. (2021, January 18\u201323). Polarization in Geometric Opinion Dynamics. Proceedings of the EC \u201821: 22nd ACM Conference on Economics and Computation, Budapest, Hungary.","DOI":"10.1145\/3465456.3467633"},{"key":"ref_53","unstructured":"Biondi, E., Boldrini, C., Passarella, A., and Conti, M. (2022). Dynamics of opinion polarization. arXiv."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"108337","DOI":"10.1016\/j.cie.2022.108337","article-title":"Managing minority opinions in large-scale group decision making based on community detection and group polarization","volume":"170","author":"Wu","year":"2022","journal-title":"Comput. Ind. Eng."},{"key":"ref_55","doi-asserted-by":"crossref","unstructured":"Zafeiris, A. (2022). Opinion Polarization in Human Communities Can Emerge as a Natural Consequence of Beliefs Being Interrelated. Entropy, 24.","DOI":"10.3390\/e24091320"},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1016\/j.ins.2022.07.086","article-title":"Opinion influence maximization problem in online social networks based on group polarization effect","volume":"609","author":"Dai","year":"2022","journal-title":"Inf. Sci."},{"key":"ref_57","doi-asserted-by":"crossref","unstructured":"Ye, Y., Zhang, R., Zhao, Y., Yu, Y., Du, W., and Chen, T. (2022). A Novel Public Opinion Polarization Model Based on BA Network. Systems, 10.","DOI":"10.3390\/systems10020046"},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"134","DOI":"10.1016\/S0965-2299(95)80052-2","article-title":"The Barnum effect in complementary medicine","volume":"3","author":"Ernst","year":"1995","journal-title":"Complement. Ther. Med."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/11\/1692\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:21:50Z","timestamp":1760145710000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/11\/1692"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,11,19]]},"references-count":58,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2022,11]]}},"alternative-id":["e24111692"],"URL":"https:\/\/doi.org\/10.3390\/e24111692","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,11,19]]}}}