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Social interactions between agents that disagree on a proposition can be introduced in order to see how, in the long term, social norms and competing belief systems build up in a population. Among other metrics, entropy is used to characterize the diversity of belief systems.<\/jats:p>","DOI":"10.3390\/e27040358","type":"journal-article","created":{"date-parts":[[2025,3,28]],"date-time":"2025-03-28T13:36:49Z","timestamp":1743169009000},"page":"358","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A Model for the Formation of Beliefs and Social Norms Based on the Satisfaction Problem (SAT)"],"prefix":"10.3390","volume":"27","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6638-0945","authenticated-orcid":false,"given":"Bastien","family":"Chopard","sequence":"first","affiliation":[{"name":"Computer Science Department, University of Geneva, 7 Route de Drize, 1227 Carouge, Switzerland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6667-7370","authenticated-orcid":false,"given":"Franck","family":"Raynaud","sequence":"additional","affiliation":[{"name":"Computer Science Department, University of Geneva, 7 Route de Drize, 1227 Carouge, Switzerland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Julien","family":"Stalhandske","sequence":"additional","affiliation":[{"name":"Computer Science Department, University of Geneva, 7 Route de Drize, 1227 Carouge, Switzerland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,3,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Galam, S. 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Sci."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"72","DOI":"10.4018\/jkss.2011100106","article-title":"Opinion dynamics: A multidisciplinary review and perspective on future research","volume":"2","author":"Xia","year":"2011","journal-title":"Int. J. Knowl. Syst. Sci. (IJKSS)"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"101115","DOI":"10.1016\/j.jocs.2020.101115","article-title":"Influence measurement in a complex dynamical model: An information theoretic approach","volume":"44","author":"Toupance","year":"2020","journal-title":"J. Comput. Sci."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"129829","DOI":"10.1016\/j.physa.2024.129829","article-title":"N-player game formulation of the majority-vote model of opinion dynamics","volume":"643","author":"Soares","year":"2024","journal-title":"Phys. Stat. Mech. Its Appl."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1080\/0022250X.1971.9989794","article-title":"Dynamic models of segregation","volume":"1","author":"Schelling","year":"1971","journal-title":"J. Math. Sociol."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"473","DOI":"10.1140\/epjb\/e2007-00181-8","article-title":"Ising, Schelling and self-organising segregation","volume":"57","author":"Stauffer","year":"2007","journal-title":"Eur. Phys. J."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Rodrigues, N., Bollen, J., and Ahn, Y.Y. (2016). Collective Dynamics of Belief Evolution under Cognitive Coherence and Social Conformity. PLoS ONE, 11.","DOI":"10.1371\/journal.pone.0165910"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"066103","DOI":"10.1103\/PhysRevE.67.066103","article-title":"Relaxation and metastability in a local search procedure for the random satisfiability problem","volume":"67","author":"Semerjian","year":"2003","journal-title":"Phys. Rev. E"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Monasson, R. (2006). Introduction to Phase Transitions in Random Optimization Problems, Laboratoire de Physique Th\u00e9orique de l\u2019ENS. Technical Report.","DOI":"10.1016\/S0924-8099(07)80008-4"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Chopard, B., and Tomassini, M. (2018). An Introduction to Metaheuristics for Optimization, Springer.","DOI":"10.1007\/978-3-319-93073-2"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Nooteboom, B. (2000). Learning and Innovation in Organizations and Economies, Oxford University Press.","DOI":"10.1093\/acprof:oso\/9780199241002.001.0001"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1016\/j.jebo.2004.03.019","article-title":"Empirical tests of optimal cognitive distance","volume":"58","author":"Wuyts","year":"2005","journal-title":"J. Econ. Behav. Organ."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1016","DOI":"10.1016\/j.respol.2007.04.003","article-title":"Optimal cognitive distance and absorptive capacity","volume":"36","author":"Nooteboom","year":"2007","journal-title":"Res. Policy"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"435","DOI":"10.1017\/S0140525X00057046","article-title":"Explanatory Coherence","volume":"12","author":"Thagard","year":"1989","journal-title":"Behav. Brain Sci."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Thagard, P. (2000). Coherence in Thought and Action, The MIT Press.","DOI":"10.7551\/mitpress\/1900.001.0001"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"282","DOI":"10.1207\/S15327957PSPR0604_03","article-title":"Structural Dynamics of Cognition: From consistency theories to constraint satisfaction","volume":"6","author":"Simon","year":"2002","journal-title":"Personal. Soc. Psychol. Rev."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1017\/S1930297500002424","article-title":"Modeling Option and Strategy Choices with Connectionist Networks: Towards an integrative model of automatic and deliberate decision making","volume":"3","author":"Gloeckner","year":"2008","journal-title":"Judgm. Decis. Mak."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Kauffman, S.A. (1993). The Origins of Order, Oxford University Press.","DOI":"10.1093\/oso\/9780195079517.001.0001"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1111\/j.0956-7976.2004.00678.x","article-title":"Construction of Preferences by Constraint Satisfaction","volume":"15","author":"Simon","year":"2004","journal-title":"Psychol. Sci."},{"key":"ref_23","unstructured":"Montgomery, H. (1989). Cognition to Action: The search for dominance in decision making. Human Decision Making, John Wiley & Sons."},{"key":"ref_24","first-page":"79","article-title":"A free energy principle for the brain","volume":"100","author":"Friston","year":"2006","journal-title":"J. Physiol."},{"key":"ref_25","unstructured":"Papadimitriou, C. (1991, January 1\u20134). On selecting a satisfying truth assignment. Proceedings of the 32nd Annual IEEE Symposium on Foundations of Computer Science, San Juan, PR, USA."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"M\u00e9zard, M., Parisi, G., and Virasoro, M. (1987). 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