{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T21:41:08Z","timestamp":1780522868114,"version":"3.54.1"},"reference-count":66,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2026,4,14]],"date-time":"2026-04-14T00:00:00Z","timestamp":1776124800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>I study the impact of mixed contrarians on the opinion dynamics of a heterogenous population with conformists using the Galam Majority Model. Activation of contrarians is a function of the majority\/minority ratio in the local groups of discussion. Restricting the group size to 3, two types of contrarians are included in respective proportions c3,0 for configurations with ratio 3 to 0 and c2,1 for ratio 2 to 1. I then derive the explicit update equation and analytically obtain the fixed points, their stability, and the resulting full two-dimensional landscape of the dynamics of opinion. Setting c3,0=c2,1=c recovers the original results obtained with uniform contrarians. The findings allow for considering a wide spectrum of new disruptive strategies to secure either a majority\/minority ending ensuring the opinion having the larger initial support to win, or a single attractor dynamics at fifty\/fifty, which implies a random winner regardless of initial supports.<\/jats:p>","DOI":"10.3390\/e28040443","type":"journal-article","created":{"date-parts":[[2026,4,14]],"date-time":"2026-04-14T10:29:08Z","timestamp":1776162548000},"page":"443","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Ratio-Dependent Contrarian Activation in Opinion Dynamics"],"prefix":"10.3390","volume":"28","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9003-5420","authenticated-orcid":false,"given":"Serge","family":"Galam","sequence":"first","affiliation":[{"name":"CEVIPOF\u2014Centre for Political Research, Sciences Po and CNRS, 1, Place Saint Thomas d\u2019Aquin, 75007 Paris, France"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,4,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"206","DOI":"10.1140\/epjb\/s10051-025-01053-7","article-title":"Sociophysics models inspired by the Ising model","volume":"98","author":"Mullick","year":"2025","journal-title":"Eur. 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