{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,25]],"date-time":"2026-03-25T01:48:17Z","timestamp":1774403297542,"version":"3.50.1"},"reference-count":74,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2022,10,18]],"date-time":"2022-10-18T00:00:00Z","timestamp":1666051200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"European Union\u2019s Horizon 2020 research","award":["732942"],"award-info":[{"award-number":["732942"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>What are the mechanisms by which groups with certain opinions gain public voice and force others holding a different view into silence? Furthermore, how does social media play into this? Drawing on neuroscientific insights into the processing of social feedback, we develop a theoretical model that allows us to address these questions. In repeated interactions, individuals learn whether their opinion meets public approval and refrain from expressing their standpoint if it is socially sanctioned. In a social network sorted around opinions, an agent forms a distorted impression of public opinion enforced by the communicative activity of the different camps. Even strong majorities can be forced into silence if a minority acts as a cohesive whole. On the other hand, the strong social organisation around opinions enabled by digital platforms favours collective regimes in which opposing voices are expressed and compete for primacy in public. This paper highlights the role that the basic mechanisms of social information processing play in massive computer-mediated interactions on opinions.<\/jats:p>","DOI":"10.3390\/e24101484","type":"journal-article","created":{"date-parts":[[2022,10,18]],"date-time":"2022-10-18T21:18:02Z","timestamp":1666127882000},"page":"1484","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Modelling Spirals of Silence and Echo Chambers by Learning from the Feedback of Others"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1263-580X","authenticated-orcid":false,"given":"Sven","family":"Banisch","sequence":"first","affiliation":[{"name":"Institute of Technology Futures, Karlsruhe Institute of Technology, 76133 Karlsruhe, Germany"},{"name":"Max Planck Institute for Mathematics in the Sciences, 04103 Leipzig, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Felix","family":"Gaisbauer","sequence":"additional","affiliation":[{"name":"Max Planck Institute for Mathematics in the Sciences, 04103 Leipzig, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3987-1271","authenticated-orcid":false,"given":"Eckehard","family":"Olbrich","sequence":"additional","affiliation":[{"name":"Max Planck Institute for Mathematics in the Sciences, 04103 Leipzig, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,10,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2566","DOI":"10.1073\/pnas.012582999","article-title":"Random graph models of social networks","volume":"99","author":"Newman","year":"2002","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_2","unstructured":"Newman, M.E., Barab\u00e1si, A.L.E., and Watts, D.J. (2006). The Structure and Dynamics of Networks, Princeton University Press."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"892","DOI":"10.1126\/science.1165821","article-title":"Network analysis in the social sciences","volume":"323","author":"Borgatti","year":"2009","journal-title":"Science"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"421","DOI":"10.1016\/j.shpsc.2005.03.010","article-title":"Explanation: A mechanist alternative","volume":"36","author":"Bechtel","year":"2005","journal-title":"Stud. Hist. Philos. Sci. Part C Stud. Hist. Philos. Biol. Biomed. Sci."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1146\/annurev.soc.012809.102632","article-title":"Causal mechanisms in the social sciences","volume":"36","author":"Ylikoski","year":"2010","journal-title":"Annu. Rev. Sociol."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"69","DOI":"10.2307\/271045","article-title":"Threshold models of diversity: Chinese restaurants, residential segregation, and the spiral of silence","volume":"18","author":"Granovetter","year":"1988","journal-title":"Sociol. Methodol."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1007\/BF00116762","article-title":"Sparks and prairie fires: A theory of unanticipated political revolution","volume":"61","author":"Kuran","year":"1989","journal-title":"Public Choice"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"655","DOI":"10.1111\/1467-6419.00128","article-title":"Collective Action Cascades: An Informational Rationale for the Power in Numbers","volume":"14","author":"Lohmann","year":"2000","journal-title":"J. Econ. Surv."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1269","DOI":"10.1126\/science.1207055","article-title":"An experimental study of homophily in the adoption of health behavior","volume":"334","author":"Centola","year":"2011","journal-title":"Science"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1038\/nature11421","article-title":"A 61-million-person experiment in social influence and political mobilization","volume":"489","author":"Bond","year":"2012","journal-title":"Nature"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"556","DOI":"10.1002\/sim.5408","article-title":"Social contagion theory: Examining dynamic social networks and human behavior","volume":"32","author":"Christakis","year":"2013","journal-title":"Stat. Med."},{"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":"1116","DOI":"10.1126\/science.aas8827","article-title":"Experimental evidence for tipping points in social convention","volume":"360","author":"Centola","year":"2018","journal-title":"Science"},{"key":"ref_14","unstructured":"Locke, J. (1860). An Essay Concerning Human Understanding: And a Treatise on the Conduct of the Understanding. Complete in One Volume with the Author\u2019s Last Additions and Corrections, Hayes & Zell."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1111\/j.1460-2466.1974.tb00367.x","article-title":"The spiral of silence a theory of public opinion","volume":"24","year":"1974","journal-title":"J. Commun."},{"key":"ref_16","unstructured":"Noelle-Neumann, E. (1996). \u00d6ffentliche Meinung: Die Entdeckung der Schweigespirale, Ullstein."},{"key":"ref_17","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_18","unstructured":"Noelle-Neumann, E., and Petersen, T. (2004). The spiral of silence and the social nature of man. Handbook of Political Communication Research, Routledge."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"387","DOI":"10.1177\/1073858414521869","article-title":"Social rewards and social networks in the human brain","volume":"20","author":"Fareri","year":"2014","journal-title":"Neuroscientist"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"549","DOI":"10.1038\/nrn3776","article-title":"The neurobiology of rewards and values in social decision making","volume":"15","author":"Ruff","year":"2014","journal-title":"Nat. Rev. Neurosci."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"4","DOI":"10.1007\/s10588-018-09291-0","article-title":"Multi-scale resolution of neural, cognitive and social systems","volume":"25","author":"Orr","year":"2019","journal-title":"Comput. Math. Organ. Theory"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1593","DOI":"10.1126\/science.275.5306.1593","article-title":"A neural substrate of prediction and reward","volume":"275","author":"Schultz","year":"1997","journal-title":"Science"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"4","DOI":"10.1038\/npp.2009.129","article-title":"The reward circuit: Linking primate anatomy and human imaging","volume":"35","author":"Haber","year":"2010","journal-title":"Neuropsychopharmacology"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1160","DOI":"10.1126\/science.1169694","article-title":"The computation of social behavior","volume":"324","author":"Behrens","year":"2009","journal-title":"Science"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"343","DOI":"10.3758\/CABN.9.4.343","article-title":"Reinforcement learning, conditioning, and the brain: Successes and challenges","volume":"9","author":"Maia","year":"2009","journal-title":"Cogn. Affect. Behav. Neurosci."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1016\/S0896-6273(03)00169-7","article-title":"Temporal difference models and reward-related learning in the human brain","volume":"38","author":"Dayan","year":"2003","journal-title":"Neuron"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"505","DOI":"10.1038\/nn.4506","article-title":"Motivational neural circuits underlying reinforcement learning","volume":"20","author":"Averbeck","year":"2017","journal-title":"Nat. Neurosci."},{"key":"ref_28","first-page":"1","article-title":"Rationality as process and as product of thought","volume":"68","author":"Simon","year":"1978","journal-title":"Am. Econ. Rev."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1027","DOI":"10.1177\/0956797616645673","article-title":"The power of the like in adolescence: Effects of peer influence on neural and behavioral responses to social media","volume":"27","author":"Sherman","year":"2016","journal-title":"Psychol. Sci."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"699","DOI":"10.1093\/scan\/nsy051","article-title":"What the brain \u2018Likes\u2019: Neural correlates of providing feedback on social media","volume":"13","author":"Sherman","year":"2018","journal-title":"Soc. Cogn. Affect. Neurosci."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1344","DOI":"10.1126\/science.1145463","article-title":"Evolution in the social brain","volume":"317","author":"Dunbar","year":"2007","journal-title":"Science"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"178","DOI":"10.1002\/(SICI)1520-6505(1998)6:5<178::AID-EVAN5>3.0.CO;2-8","article-title":"The social brain hypothesis","volume":"6","author":"Dunbar","year":"1998","journal-title":"Evol. Anthropol. Issues News Rev. Issues News Rev."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1007\/s13752-018-0313-y","article-title":"Toward a Macroevolutionary Theory of Human Evolution: The Social Protocell","volume":"14","author":"Andersson","year":"2019","journal-title":"Biol. Theory"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1016\/j.tics.2005.12.004","article-title":"Can cognitive processes be inferred from neuroimaging data?","volume":"10","author":"Poldrack","year":"2006","journal-title":"Trends Cogn. Sci."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"148","DOI":"10.3389\/fnins.2012.00148","article-title":"Effects of direct social experience on trust decisions and neural reward circuitry","volume":"6","author":"Fareri","year":"2012","journal-title":"Front. Neurosci."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"284","DOI":"10.1016\/j.neuron.2008.03.020","article-title":"Processing of social and monetary rewards in the human striatum","volume":"58","author":"Izuma","year":"2008","journal-title":"Neuron"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"140","DOI":"10.1016\/j.neuron.2008.11.027","article-title":"Reinforcement learning signal predicts social conformity","volume":"61","author":"Klucharev","year":"2009","journal-title":"Neuron"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1165","DOI":"10.1016\/j.cub.2010.04.055","article-title":"How the opinion of others affects our valuation of objects","volume":"20","author":"Bach","year":"2010","journal-title":"Curr. Biol."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"621","DOI":"10.1162\/jocn.2009.21228","article-title":"Processing of the incentive for social approval in the ventral striatum during charitable donation","volume":"22","author":"Izuma","year":"2010","journal-title":"J. Cogn. Neurosci."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1146\/annurev.psych.121208.131647","article-title":"The neuroscience of social decision-making","volume":"62","author":"Rilling","year":"2011","journal-title":"Annu. Rev. Psychol."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1177\/1088868313495594","article-title":"Action, outcome, and value: A dual-system framework for morality","volume":"17","author":"Cushman","year":"2013","journal-title":"Personal. Soc. Psychol. Rev."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"268","DOI":"10.1038\/nrn1884","article-title":"Meeting of minds: The medial frontal cortex and social cognition","volume":"7","author":"Amodio","year":"2006","journal-title":"Nat. Rev. Neurosci."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1016\/j.neures.2012.01.003","article-title":"The social neuroscience of reputation","volume":"72","author":"Izuma","year":"2012","journal-title":"Neurosci. Res."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1109\/37.126844","article-title":"Reinforcement learning is direct adaptive optimal control","volume":"12","author":"Sutton","year":"1992","journal-title":"IEEE Control Syst. Mag."},{"key":"ref_45","unstructured":"Sutton, R.S., and Barto, A.G. (2018). Reinforcement Learning: An Introduction, MIT Press."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"304","DOI":"10.1038\/1124","article-title":"Dopamine neurons report an error in the temporal prediction of reward during learning","volume":"1","author":"Hollerman","year":"1998","journal-title":"Nat. Neurosci."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"769","DOI":"10.1016\/j.conb.2004.10.016","article-title":"Reward representations and reward-related learning in the human brain: Insights from neuroimaging","volume":"14","year":"2004","journal-title":"Curr. Opin. Neurobiol."},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Gaisbauer, F., Olbrich, E., and Banisch, S. (2019). The dynamics of opinion expression. arXiv.","DOI":"10.1103\/PhysRevE.102.042303"},{"key":"ref_49","doi-asserted-by":"crossref","unstructured":"Wasserman, S., and Faust, K. (1994). Social Network Analysis: Methods and Applications, Cambridge University Press.","DOI":"10.1017\/CBO9780511815478"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1111\/1467-937X.00121","article-title":"Contagion","volume":"67","author":"Morris","year":"2000","journal-title":"Rev. Econ. Stud."},{"key":"ref_51","doi-asserted-by":"crossref","unstructured":"Tuyls, K., Verbeeck, K., and Lenaerts, T. (2003, January 14\u201318). A selection-mutation model for q-learning in multi-agent systems. Proceedings of the Second International Joint Conference on Autonomous Agents and Multiagent Systems, Melbourne, Australia.","DOI":"10.1145\/860575.860687"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"015206","DOI":"10.1103\/PhysRevE.67.015206","article-title":"Coupled replicator equations for the dynamics of learning in multiagent systems","volume":"67","author":"Sato","year":"2003","journal-title":"Phys. Rev. E"},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"041145","DOI":"10.1103\/PhysRevE.85.041145","article-title":"Dynamics of Boltzmann Q learning in two-player two-action games","volume":"85","author":"Kianercy","year":"2012","journal-title":"Phys. Rev. E"},{"key":"ref_54","first-page":"17","article-title":"On the evolution of random graphs","volume":"5","author":"Erdos","year":"1960","journal-title":"Publ. Math. Inst. Hung. Acad. Sci."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"1141","DOI":"10.1214\/aoms\/1177706098","article-title":"Random graphs","volume":"30","author":"Gilbert","year":"1959","journal-title":"Ann. Math. Stat."},{"key":"ref_56","unstructured":"Lazarsfeld, P.F., Berelson, B., and Gaudet, H. (1944). The People\u2019s Choice. How the Voter Makes Up Their Mind in a Presidential Campaign, Columbia University Press."},{"key":"ref_57","first-page":"100","article-title":"US extremism on Telegram","volume":"15","author":"Walther","year":"2021","journal-title":"Perspect. Terror."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"2218","DOI":"10.1177\/1461444819888746","article-title":"(((They))) rule: Memetic antagonism and nebulous othering on 4chan","volume":"22","author":"Tuters","year":"2020","journal-title":"New Media Soc."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"1078","DOI":"10.1038\/s41562-019-0677-4","article-title":"Homophily and minority-group size explain perception biases in social networks","volume":"3","author":"Lee","year":"2019","journal-title":"Nat. Hum. Behav."},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1111\/pops.12407","article-title":"Ideological asymmetries and the essence of political psychology","volume":"38","author":"Jost","year":"2017","journal-title":"Political Psychol."},{"key":"ref_61","unstructured":"Gaisbauer, F., Pournaki, A., Banisch, S., and Olbrich, E. (2020). How Twitter affects the perception of public opinion: Two case studies. arXiv."},{"key":"ref_62","unstructured":"Hume, D. (1963). Essays: Moral, Political and Literary, Oxford University Press."},{"key":"ref_63","unstructured":"The Gettysburg Address Delivered by Abraham Lincoln Nov (1970, January 01). 19 1863 at the Dedication Services on the Battle Field, Available online: https:\/\/www.loc.gov\/item\/2004671506\/."},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"429","DOI":"10.3758\/CABN.8.4.429","article-title":"Decision theory, reinforcement learning, and the brain","volume":"8","author":"Dayan","year":"2008","journal-title":"Cogn. Affect. Behav. Neurosci."},{"key":"ref_65","unstructured":"Glimcher, P.W., and Fehr, E. (2013). Neuroeconomics: Decision Making and the Brain, Academic Press."},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1177\/0038038588022001007","article-title":"Social network analysis","volume":"22","author":"Scott","year":"1988","journal-title":"Sociology"},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"721","DOI":"10.1126\/science.1167742","article-title":"Computational social science","volume":"323","author":"Lazer","year":"2009","journal-title":"Science"},{"key":"ref_68","unstructured":"Conover, M.D., Ratkiewicz, J., Francisco, M., Gon\u00e7alves, B., Menczer, F., and Flammini, A. (2011, January 17\u201321). Political polarization on twitter. Proceedings of the Fifth International AAAI Conference on Weblogs and Social Media, Barcelona, Spain."},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1145\/3140565","article-title":"Quantifying controversy on social media","volume":"1","author":"Garimella","year":"2018","journal-title":"ACM Trans. Soc. Comput."},{"key":"ref_70","doi-asserted-by":"crossref","unstructured":"Gaumont, N., Panahi, M., and Chavalarias, D. (2018). Reconstruction of the socio-semantic dynamics of political activist Twitter networks\u2014Method and application to the 2017 French presidential election. PLoS ONE, 13.","DOI":"10.1371\/journal.pone.0201879"},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"7","DOI":"10.2307\/2010422","article-title":"Now out of never: The element of surprise in the East European revolution of 1989","volume":"44","author":"Kuran","year":"1991","journal-title":"World Politics"},{"key":"ref_72","doi-asserted-by":"crossref","unstructured":"Festinger, L. (1957). A Theory of Cognitive Dissonance, Stanford University Press.","DOI":"10.1515\/9781503620766"},{"key":"ref_73","doi-asserted-by":"crossref","unstructured":"Hughes, B.L., Leong, J.K., Shiv, B., and Zaki, J. (2018). Wanting to like: Motivation influences behavioral and neural responses to social feedback. bioRxiv, 300657.","DOI":"10.1101\/300657"},{"key":"ref_74","doi-asserted-by":"crossref","first-page":"4375","DOI":"10.1073\/pnas.1802176115","article-title":"Neural precursors of future liking and affective reciprocity","volume":"115","author":"Zerubavel","year":"2018","journal-title":"Proc. Natl. Acad. Sci. USA"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/10\/1484\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:56:26Z","timestamp":1760144186000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/10\/1484"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,10,18]]},"references-count":74,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2022,10]]}},"alternative-id":["e24101484"],"URL":"https:\/\/doi.org\/10.3390\/e24101484","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,10,18]]}}}