Anonymous social influence |
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| Institution: | 1. Université Paris 1 Panthéon-Sorbonne, France;2. Paris School of Economics – Université Paris 1 Panthéon-Sorbonne, France;3. Paris School of Economics – CNRS, Centre d?Économie de la Sorbonne, 106-112 Bd de l?Hôpital, 75647 Paris Cedex 13, France;4. Université catholique de Louvain – CORE, Belgium;1. Department of Neurology, Second Xiangya Hospital of Central South University, Changsha, P.R. China;2. Department of General Surgery, Xiangya Hospital of Central South University, Changsha, P.R. China;3. Department of Hemotology, Second Xiangya Hospital of Central South University, Changsha, P.R. China;4. Department of Anesthesiology, Xiangya Hospital of Central South University, Changsha, P.R. China;1. GREYC UMR CNRS 6072, Caen, France;2. LCMT UMR CNRS 6507, Caen, France;1. College of Business, Korea Advanced Institute of Science and Technology, 291 Daehak-ro, Yuseong-gu, Daejeon 34141, Republic of Korea;2. Department of Economics, Yale University, 28 Hillhouse Avenue, New Haven CT 06511, USA;1. Université Paris 1, 106-112, Bd de l’Hôpital, 75013 Paris, France;2. Université de Lyon, Lyon, F-69007, France;3. CNRS, GATE Lyon Saint-Etienne, Ecully, F-69130, France;4. University Jean Monnet, Saint-Etienne, F-42000, France;5. Paris School of Economics, Université Paris 1, 106-112, Bd de l’Hôpital, 75013 Paris, France;1. Institut Néel, CNRS et Université Joseph Fourier BP 166, F 38042 Grenoble Cedex 9, France;2. Faculté des Sciences et Techniques de Tanger, BP 416 Tanger, Université Abdelmalek Essaâdi, Morocco;3. Institute of Physics and National Laboratory for Condensed Matter Physics, Chinese Academy of Sciences, P.O. Box 603, Beijing 100190, China;4. National Laboratory for Solid State Microstuctures, Department of Physics, Nanjing University, 210093 Nanjing, China |
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| Abstract: | We study a stochastic model of influence where agents have “yes” or “no” inclinations on some issue, and opinions may change due to mutual influence among the agents. Each agent independently aggregates the opinions of the other agents and possibly herself. We study influence processes modeled by ordered weighted averaging operators, which are anonymous: they only depend on how many agents share an opinion. For instance, this allows to study situations where the influence process is based on majorities, which are not covered by the classical approach of weighted averaging aggregation. We find a necessary and sufficient condition for convergence to consensus and characterize outcomes where the society ends up polarized. Our results can also be used to understand more general situations, where ordered weighted averages are only used to some extent. Furthermore, we apply our results to fuzzy linguistic quantifiers, i.e., expressions like “most” or “at least a few”. |
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| Keywords: | Influence Anonymity Ordered weighted averaging operator Convergence Consensus Fuzzy linguistic quantifier |
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