{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T13:45:30Z","timestamp":1773841530666,"version":"3.50.1"},"reference-count":51,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2023,5,24]],"date-time":"2023-05-24T00:00:00Z","timestamp":1684886400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"EU H2020 ICT48 project \u201cHumane AI Net\u201d","award":["952026"],"award-info":[{"award-number":["952026"]}]},{"name":"EU H2020 ICT48 project \u201cHumane AI Net\u201d","award":["871042"],"award-info":[{"award-number":["871042"]}]},{"name":"EU H2020 ICT48 project \u201cHumane AI Net\u201d","award":["I 5205"],"award-info":[{"award-number":["I 5205"]}]},{"name":"European Union\u2013Horizon 2020 Program under the scheme \u201cINFRAIA-01-2018-2019\u2013Integrating Activities for Advanced Communities\u201d","award":["952026"],"award-info":[{"award-number":["952026"]}]},{"name":"European Union\u2013Horizon 2020 Program under the scheme \u201cINFRAIA-01-2018-2019\u2013Integrating Activities for Advanced Communities\u201d","award":["871042"],"award-info":[{"award-number":["871042"]}]},{"name":"European Union\u2013Horizon 2020 Program under the scheme \u201cINFRAIA-01-2018-2019\u2013Integrating Activities for Advanced Communities\u201d","award":["I 5205"],"award-info":[{"award-number":["I 5205"]}]},{"name":"CHIST-ERA grant \u201cSAI\u201d: CHIST-ERA-19-XAI-010, FWF","award":["952026"],"award-info":[{"award-number":["952026"]}]},{"name":"CHIST-ERA grant \u201cSAI\u201d: CHIST-ERA-19-XAI-010, FWF","award":["871042"],"award-info":[{"award-number":["871042"]}]},{"name":"CHIST-ERA grant \u201cSAI\u201d: CHIST-ERA-19-XAI-010, FWF","award":["I 5205"],"award-info":[{"award-number":["I 5205"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Two of the main factors shaping an individual\u2019s opinion are social coordination and personal preferences, or personal biases. To understand the role of those and that of the topology of the network of interactions, we study an extension of the voter model proposed by Masuda and Redner (2011), where the agents are divided into two populations with opposite preferences. We consider a modular graph with two communities that reflect the bias assignment, modeling the phenomenon of epistemic bubbles. We analyze the models by approximate analytical methods and by simulations. Depending on the network and the biases\u2019 strengths, the system can either reach a consensus or a polarized state, in which the two populations stabilize to different average opinions. The modular structure generally has the effect of increasing both the degree of polarization and its range in the space of parameters. When the difference in the bias strengths between the populations is large, the success of the very committed group in imposing its preferred opinion onto the other one depends largely on the level of segregation of the latter population, while the dependency on the topological structure of the former is negligible. We compare the simple mean-field approach with the pair approximation and test the goodness of the mean-field predictions on a real network.<\/jats:p>","DOI":"10.3390\/e25060838","type":"journal-article","created":{"date-parts":[[2023,5,25]],"date-time":"2023-05-25T02:58:48Z","timestamp":1684983528000},"page":"838","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Voter-like Dynamics with Conflicting Preferences on Modular Networks"],"prefix":"10.3390","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0009-0009-8674-9904","authenticated-orcid":false,"given":"Filippo","family":"Zimmaro","sequence":"first","affiliation":[{"name":"Department of Computer Science, University of Pisa, 56126 Pisa, Italy"},{"name":"Department of Mathematics, University of Bologna, 40126 Bologna, Italy"},{"name":"Department of Network and Data Science, Central European University, 1100 Vienna, Austria"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3577-6189","authenticated-orcid":false,"given":"Pierluigi","family":"Contucci","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Bologna, 40126 Bologna, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4957-5406","authenticated-orcid":false,"given":"J\u00e1nos","family":"Kert\u00e9sz","sequence":"additional","affiliation":[{"name":"Department of Network and Data Science, Central European University, 1100 Vienna, Austria"}]}],"member":"1968","published-online":{"date-parts":[[2023,5,24]]},"reference":[{"key":"ref_1","unstructured":"Weber, M. 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