{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T04:02:31Z","timestamp":1776830551677,"version":"3.51.2"},"reference-count":57,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2022,1,26]],"date-time":"2022-01-26T00:00:00Z","timestamp":1643155200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004569","name":"Ministry of Science and Higher Education","doi-asserted-by":"publisher","award":["DI2019 0008 49"],"award-info":[{"award-number":["DI2019 0008 49"]}],"id":[{"id":"10.13039\/501100004569","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Our agent-based model of opinion dynamics concerns the current vast divisions in modern societies. It examines the process of social polarization, understood here as the partition of a community into two opposing groups with contradictory opinions. Our goal is to measure how mutual animosities between parties may lead to their radicalization. We apply a double-clique topology with both positive and negative ties to the model of binary opinions. Individuals are subject to social pressure; they conform to the opinions of their own clique (positive links) and oppose those from the other one (negative links). There is also a chance of acting independently, which alters the system\u2019s behavior in various ways, depending on its magnitude. The results, obtained with both Monte-Carlo simulations and the mean-field approach, lead to two main conclusions: in such a system, there exists a critical quantity of negative relations that are needed for polarization to occur, and (rather surprisingly) independent actions actually support the process, unless their frequency is too high, in which case the system falls into total disorder.<\/jats:p>","DOI":"10.3390\/e24020185","type":"journal-article","created":{"date-parts":[[2022,1,27]],"date-time":"2022-01-27T04:49:51Z","timestamp":1643258991000},"page":"185","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Opinion Evolution in Divided Community"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1141-5095","authenticated-orcid":false,"given":"Tomasz","family":"Weron","sequence":"first","affiliation":[{"name":"Hugo Steinhaus Center, Faculty of Pure and Applied Mathematics, Wroc\u0142aw University of Science and Technology, 50-370 Wroc\u0142aw, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6992-3634","authenticated-orcid":false,"given":"Janusz","family":"Szwabi\u0144ski","sequence":"additional","affiliation":[{"name":"Hugo Steinhaus Center, Faculty of Pure and Applied Mathematics, Wroc\u0142aw University of Science and Technology, 50-370 Wroc\u0142aw, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,1,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"690","DOI":"10.1086\/230995","article-title":"Have American\u2019s Social Attitudes Become More Polarized?","volume":"102","author":"DiMaggio","year":"1996","journal-title":"Am. J. Sociol."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"M\u00e4s, M., and Flache, A. (2013). Differentiation without Distancing. Explaining Bi-Polarization of Opinions without Negative Influence. PLoS ONE, 8.","DOI":"10.1371\/journal.pone.0074516"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1141","DOI":"10.1037\/0022-3514.50.6.1141","article-title":"Group polarization: A critical review and meta-analysis","volume":"50","author":"Isenberg","year":"1986","journal-title":"J. Personal. Soc. Psychol."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1111\/1467-9760.00148","article-title":"The Law of Group Polarization","volume":"10","author":"Sunstein","year":"2002","journal-title":"J. Political Philos."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"9216","DOI":"10.1073\/pnas.1804840115","article-title":"Exposure to opposing views on social media can increase political polarization","volume":"115","author":"Bail","year":"2018","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_6","unstructured":"(2017). The Global Risk Report 2017, World Economic Forum."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"913","DOI":"10.1086\/320294","article-title":"Culture Wars and Opinion Polarization: The Case of Abortion","volume":"106","author":"Mouw","year":"2001","journal-title":"Am. J. Sociol."},{"key":"ref_8","first-page":"2001","article-title":"The politization of climate change and polarization in the American public\u2019s views of global warming","volume":"52","author":"McCright","year":"2011","journal-title":"Sociol. Q."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1002\/1944-2866.POI354","article-title":"Investigating Political Polarization on Twitter: A Canadian Perspective","volume":"6","author":"Gruzd","year":"2014","journal-title":"Policy Internet"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Adamic, L.A., and Glance, N. (2005, January 21\u201325). The political blogosphere and the 2004 US election: Divided they blog. Proceedings of the 3rd International Workshop on Link Discovery (LinkKDD \u201905), Chicago, IL, USA.","DOI":"10.1145\/1134271.1134277"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1816","DOI":"10.1177\/0022343306065720","article-title":"Network Polarization, Network Interdependence, and International Conflict","volume":"43","author":"Maoz","year":"2006","journal-title":"J. Peace Res."},{"key":"ref_12","unstructured":"Waugh, A., Pei, L., Fowler, J.H., Mucha, P.J., and Porter, M.A. (2011). Party Polarization in Congress: A Network Science Approach. arXiv."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Pariser, E. (2011). The Filter Bubble. What the Internet Is Hiding from You?, Penguin Press.","DOI":"10.3139\/9783446431164"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1177\/0022002797041002001","article-title":"The Dissemination of Culture. A Model with Local Convergence and Global Polarization","volume":"41","author":"Axelrod","year":"1997","journal-title":"J. Confl. Resolut."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"415","DOI":"10.1146\/annurev.soc.27.1.415","article-title":"Birds of a Feather: Homophily in Social Networks","volume":"27","author":"McPherson","year":"2001","journal-title":"Annu. Rev. Sociol."},{"key":"ref_16","first-page":"1","article-title":"Opinion dynamics and bounded confidence: Models, analysis and simulation","volume":"5","author":"Hengselmann","year":"2002","journal-title":"J. Artif. Soc. Soc. Simul."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1142\/S0219525900000078","article-title":"Mixing beliefs among interacting agents","volume":"03","author":"Deffuant","year":"2000","journal-title":"Adv. Complex Syst."},{"key":"ref_18","unstructured":"Breiger, R., Carley, K., and Pattison, P. (2003). Polarization and Dynamic Networks. A Hopfield Model of Emergent Structure. Dynamic Social Network Modeling and Analysis: Workshop Summary and Papers, The National Academies Press."},{"key":"ref_19","first-page":"13","article-title":"A Continuous Opinion Dynamics Model Based on the Principle of Meta-Contrast","volume":"9","author":"Salzarulo","year":"2006","journal-title":"J. Artif. Soc. Soc. Simul."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Traag, V.A., Dooren, P.V., and Leenheer, P.D. (2013). Dynamical Models Explaining Social Balance and Evolution of Cooperation. PLoS ONE, 8.","DOI":"10.1371\/journal.pone.0060063"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"9","DOI":"10.18564\/jasss.3203","article-title":"The interplay between conformity and anticonformity and its polarizing effect on society","volume":"19","author":"Siedlecki","year":"2016","journal-title":"J. Artif. Soc. Soc. Simul."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Krueger, T., Szwabi\u0144ski, J., and Weron, T. (2017). Conformity, anticonformity and polarization of opinions: Insights from a mathematical model of opinion dynamics. Entropy, 19.","DOI":"10.3390\/e19070371"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"030101","DOI":"10.1103\/PhysRevE.75.030101","article-title":"Majority model on a network with communities","volume":"75","author":"Lambiotte","year":"2007","journal-title":"Phys. Rev. E"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"031110","DOI":"10.1103\/PhysRevE.80.031110","article-title":"Bistable-monostable transition in the Ising model on two connected complex networks","volume":"80","author":"Suchecki","year":"2009","journal-title":"Phys. Rev. E"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"617","DOI":"10.1142\/S0129183108012339","article-title":"Continuous Opinions and Discrete Actions in Opinion Dynamics Problems","volume":"19","author":"Martins","year":"2008","journal-title":"Int. J. Mod. Phys. C"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"042807","DOI":"10.1103\/PhysRevE.87.042807","article-title":"Building up of individual inflexibility in opinion dynamics","volume":"87","author":"Martins","year":"2013","journal-title":"Phys. Rev. E"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"76","DOI":"10.1080\/0022250X.2018.1517761","article-title":"Opinion polarization by learning from social feedback","volume":"43","author":"Banisch","year":"2019","journal-title":"J. Math. Sociol."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"190","DOI":"10.1037\/0033-2909.100.2.190","article-title":"Toward an integration of some models and theories of social response","volume":"100","author":"Nail","year":"1986","journal-title":"Psychol. Bull."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"454","DOI":"10.1037\/0033-2909.126.3.454","article-title":"Proposal of a Four Dimensional Model of Social Response","volume":"126","author":"Nail","year":"2000","journal-title":"Psychol. Bull."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"174","DOI":"10.1007\/s10955-013-0701-4","article-title":"Anticonformity or Independence?\u2014Insights from Statistical Physics","volume":"151","author":"Nyczka","year":"2013","journal-title":"J. Stat. Phys."},{"key":"ref_31","unstructured":"Conover, M., Ratkiewicz, J., Francisco, M., Gon\u00e7alves, B., Flammini, A., and Menczer, F. (2011, January 17\u201321). Political Polarization on Twitter. Proceedings of the Fifth International AAAI Conference on Weblogs and Social Media (ICWSM), Barcelona, Spain."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"8577","DOI":"10.1073\/pnas.0601602103","article-title":"Modularity and community structure in networks","volume":"103","author":"Newman","year":"2006","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"452","DOI":"10.1086\/jar.33.4.3629752","article-title":"An Information Flow Model for Conflict and Fission in Small Groups","volume":"33","author":"Zachary","year":"1977","journal-title":"J. Anthropol. Res."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"041121","DOI":"10.1103\/PhysRevE.77.041121","article-title":"Voter models on heterogeneous networks","volume":"77","author":"Sood","year":"2008","journal-title":"Phys. Rev. E"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"441","DOI":"10.1086\/518527","article-title":"Influentials, Networks, and Public Opinion Formation","volume":"34","author":"Watts","year":"2007","journal-title":"J. Consum. Res."},{"key":"ref_36","unstructured":"Guerra, P.H.C., Meira, M., Cardie, C., and Kleinberg, R. (2013, January 8\u201311). A Measure of Polarization on Social Media Networks Based on Community Boundaries. Proceedings of the Seventh International AAAI Conference on Web and Social Media, Cambridge, MA, USA."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"041129","DOI":"10.1103\/PhysRevE.80.041129","article-title":"Nonlinear q-voter model","volume":"80","author":"Castellano","year":"2009","journal-title":"Phys. Rev. E"},{"key":"ref_38","unstructured":"Myers, D.G. (2013). Social Psychology, Freeman Press. [11th ed.]."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1177\/1368430205056464","article-title":"Group Size and Conformity","volume":"8","author":"Bond","year":"2005","journal-title":"Group Process. Intergroup Relat."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1038\/scientificamerican1155-31","article-title":"Opinions and Social Pressure","volume":"193","author":"Asch","year":"1955","journal-title":"Sci. Am."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"011105","DOI":"10.1103\/PhysRevE.86.011105","article-title":"Phase transitions in the q-voter model with two types of stochastic driving","volume":"86","author":"Nyczka","year":"2012","journal-title":"Phys. Rev. E"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1371\/journal.pone.0209620","article-title":"Conformity in numbers\u2014Does criticality in social responses exist?","volume":"13","author":"Nyczka","year":"2018","journal-title":"PLoS ONE"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"1450004","DOI":"10.1142\/S0219525914500040","article-title":"Diffusion of innovation within an agent-based model: Spinsons, independence and advertising","volume":"17","author":"Weron","year":"2014","journal-title":"Adv. Complex Syst."},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Sznajd-Weron, K., Szwabi\u0144ski, J., and Weron, R. (2014). Is the Person-Situation Debate Important for Agent-Based Modeling and Vice-Versa?. PLoS ONE, 9.","DOI":"10.1371\/journal.pone.0112203"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"110","DOI":"10.1016\/j.physa.2015.11.005","article-title":"Mapping the q-voter model: From a single chain to complex networks","volume":"446","year":"2016","journal-title":"Phys. A"},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"J\u0119drzejewski, A., and Sznajd-Weron, K. (2017). Person-Situation Debate Revisited: Phase Transitions with Quenched and Annealed Disorders. Entropy, 19.","DOI":"10.3390\/e19080415"},{"key":"ref_47","first-page":"1","article-title":"Think then act or act then think?","volume":"13","author":"Marcjasz","year":"2018","journal-title":"PLoS ONE"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"306","DOI":"10.1016\/j.physa.2018.03.077","article-title":"Impact of memory on opinion dynamics","volume":"505","year":"2018","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1002\/ejsp.2420210105","article-title":"Towards a theory of collective phenomena: Consensus and attitude changes in groups","volume":"21","author":"Galam","year":"1991","journal-title":"Eur. J. Soc. Psychol."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"66","DOI":"10.1016\/S0378-4371(96)00456-6","article-title":"Rational group decision making: A random field Ising model at T = 0","volume":"238","author":"Galam","year":"1997","journal-title":"Phys. A"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"366","DOI":"10.1016\/j.physa.2007.03.034","article-title":"The role of inflexible minorities in the breaking of democratic opinion dynamics","volume":"381","author":"Galam","year":"2007","journal-title":"Phys. A"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"028701","DOI":"10.1103\/PhysRevLett.91.028701","article-title":"Does a Single Zealot Affect an Infinite Group of Voters?","volume":"91","author":"Mobilia","year":"2003","journal-title":"Phys. Rev. Lett."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1037\/a0030997","article-title":"Proposal of a Double Diamond Model of Social Response","volume":"17","author":"Nail","year":"2013","journal-title":"Rev. Gen. Psychol."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"453","DOI":"10.1016\/j.physa.2003.10.041","article-title":"Contrarian deterministic effects on opinion dynamics: \u201cThe hung elections scenario\u201d","volume":"333","author":"Galam","year":"2004","journal-title":"Phys. A"},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"48002","DOI":"10.1209\/0295-5075\/96\/48002","article-title":"Phase transition in the Sznajd model with independence","volume":"96","author":"Tabiszewski","year":"2011","journal-title":"Europhys. Lett."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"061905","DOI":"10.1103\/PhysRevE.72.061905","article-title":"Quantification of the differences between quenched and annealed averaging for RNA secondary structures","volume":"72","author":"Liu","year":"2005","journal-title":"Phys. Rev. E"},{"key":"ref_57","doi-asserted-by":"crossref","unstructured":"Strogatz, S.H. (1994). Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering, Addison-Wesley.","DOI":"10.1063\/1.4823332"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/2\/185\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T22:08:32Z","timestamp":1760134112000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/2\/185"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,1,26]]},"references-count":57,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2022,2]]}},"alternative-id":["e24020185"],"URL":"https:\/\/doi.org\/10.3390\/e24020185","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,1,26]]}}}