Contrarian Majority Rule Model with External Oscillating Propaganda and Individual Inertias
We study the Galam majority rule dynamics with contrarian behavior and an oscillating external propaganda in a population of agents that can adopt one of two possible opinions. In an iteration step, a random agent interacts with three other random agents and takes the majority opinion among the agen...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-09-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/25/10/1402 |
| _version_ | 1797573915351973888 |
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| author | Maria Cecilia Gimenez Luis Reinaudi Serge Galam Federico Vazquez |
| author_facet | Maria Cecilia Gimenez Luis Reinaudi Serge Galam Federico Vazquez |
| author_sort | Maria Cecilia Gimenez |
| collection | DOAJ |
| description | We study the Galam majority rule dynamics with contrarian behavior and an oscillating external propaganda in a population of agents that can adopt one of two possible opinions. In an iteration step, a random agent interacts with three other random agents and takes the majority opinion among the agents with probability <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>p</mi><mo>(</mo><mi>t</mi><mo>)</mo></mrow></semantics></math></inline-formula> (majority behavior) or the opposite opinion with probability <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo>−</mo><mi>p</mi><mo>(</mo><mi>t</mi><mo>)</mo></mrow></semantics></math></inline-formula> (contrarian behavior). The probability of following the majority rule <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>p</mi><mo>(</mo><mi>t</mi><mo>)</mo></mrow></semantics></math></inline-formula> varies with the temperature <i>T</i> and is coupled to a time-dependent oscillating field that mimics a mass media propaganda, in a way that agents are more likely to adopt the majority opinion when it is aligned with the sign of the field. We investigate the dynamics of this model on a complete graph and find various regimes as <i>T</i> is varied. A transition temperature <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>T</mi><mi>c</mi></msub></semantics></math></inline-formula> separates a bimodal oscillatory regime for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>T</mi><mo><</mo><msub><mi>T</mi><mi>c</mi></msub></mrow></semantics></math></inline-formula>, where the population’s mean opinion <i>m</i> oscillates around a positive or a negative value from a unimodal oscillatory regime for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>T</mi><mo>></mo><msub><mi>T</mi><mi>c</mi></msub></mrow></semantics></math></inline-formula> in which <i>m</i> oscillates around zero. These regimes are characterized by the distribution of residence times that exhibit a unique peak for a resonance temperature <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>T</mi><mo>*</mo></msup></semantics></math></inline-formula>, where the response of the system is maximum. An insight into these results is given by a mean-field approach, which also shows that <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>T</mi><mo>*</mo></msup></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>T</mi><mi>c</mi></msub></semantics></math></inline-formula> are closely related. |
| first_indexed | 2024-03-10T21:16:44Z |
| format | Article |
| id | doaj.art-8aa63010fe954c4ca5a010d17699bbd5 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-10T21:16:44Z |
| publishDate | 2023-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-8aa63010fe954c4ca5a010d17699bbd52023-11-19T16:24:23ZengMDPI AGEntropy1099-43002023-09-012510140210.3390/e25101402Contrarian Majority Rule Model with External Oscillating Propaganda and Individual InertiasMaria Cecilia Gimenez0Luis Reinaudi1Serge Galam2Federico Vazquez3Instituto de Física Enrique Gaviola (IFEG-Conicet), Facultad de Matemática, Astronomía, Fśica y Computación (FaMAF, Universidad Nacional de Córdoba), Córdoba X5000HUA, ArgentinaInstituto de Investigaciones en Físico-Química de Córdoba (INFIQC, Conicet), Facultad de Ciencias Químicas (Universidad Nacional de Córdoba), Córdoba X5000HUA, ArgentinaCEVIPOF—Centre for Political Research, Sciences Po and CNRS, 1, Place Saint Thomas d’Aquin, 75007 Paris, FranceInstituto de Cálculo, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires and Conicet, Intendente Guiraldes 2160, Cero + Infinito, Buenos Aires C1428EGA, ArgentinaWe study the Galam majority rule dynamics with contrarian behavior and an oscillating external propaganda in a population of agents that can adopt one of two possible opinions. In an iteration step, a random agent interacts with three other random agents and takes the majority opinion among the agents with probability <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>p</mi><mo>(</mo><mi>t</mi><mo>)</mo></mrow></semantics></math></inline-formula> (majority behavior) or the opposite opinion with probability <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo>−</mo><mi>p</mi><mo>(</mo><mi>t</mi><mo>)</mo></mrow></semantics></math></inline-formula> (contrarian behavior). The probability of following the majority rule <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>p</mi><mo>(</mo><mi>t</mi><mo>)</mo></mrow></semantics></math></inline-formula> varies with the temperature <i>T</i> and is coupled to a time-dependent oscillating field that mimics a mass media propaganda, in a way that agents are more likely to adopt the majority opinion when it is aligned with the sign of the field. We investigate the dynamics of this model on a complete graph and find various regimes as <i>T</i> is varied. A transition temperature <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>T</mi><mi>c</mi></msub></semantics></math></inline-formula> separates a bimodal oscillatory regime for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>T</mi><mo><</mo><msub><mi>T</mi><mi>c</mi></msub></mrow></semantics></math></inline-formula>, where the population’s mean opinion <i>m</i> oscillates around a positive or a negative value from a unimodal oscillatory regime for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>T</mi><mo>></mo><msub><mi>T</mi><mi>c</mi></msub></mrow></semantics></math></inline-formula> in which <i>m</i> oscillates around zero. These regimes are characterized by the distribution of residence times that exhibit a unique peak for a resonance temperature <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>T</mi><mo>*</mo></msup></semantics></math></inline-formula>, where the response of the system is maximum. An insight into these results is given by a mean-field approach, which also shows that <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>T</mi><mo>*</mo></msup></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>T</mi><mi>c</mi></msub></semantics></math></inline-formula> are closely related.https://www.mdpi.com/1099-4300/25/10/1402opinion dynamicsmajority rule modelnoiseperiodic fieldstochastic resonance |
| spellingShingle | Maria Cecilia Gimenez Luis Reinaudi Serge Galam Federico Vazquez Contrarian Majority Rule Model with External Oscillating Propaganda and Individual Inertias Entropy opinion dynamics majority rule model noise periodic field stochastic resonance |
| title | Contrarian Majority Rule Model with External Oscillating Propaganda and Individual Inertias |
| title_full | Contrarian Majority Rule Model with External Oscillating Propaganda and Individual Inertias |
| title_fullStr | Contrarian Majority Rule Model with External Oscillating Propaganda and Individual Inertias |
| title_full_unstemmed | Contrarian Majority Rule Model with External Oscillating Propaganda and Individual Inertias |
| title_short | Contrarian Majority Rule Model with External Oscillating Propaganda and Individual Inertias |
| title_sort | contrarian majority rule model with external oscillating propaganda and individual inertias |
| topic | opinion dynamics majority rule model noise periodic field stochastic resonance |
| url | https://www.mdpi.com/1099-4300/25/10/1402 |
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