The threshold model with anticonformity under random sequential updating

Bartłomiej Nowak, Michel Grabisch and Katarzyna Sznajd-Weron
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Bartłomiej Nowak: Wroclaw University of Science and Technology

Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) from HAL

Abstract: We study an asymmetric version of the threshold model with anticonformity under asynchronous update mode that mimics continuous time. We study this model on a complete graph using three different approaches: mean-field approximation, Monte Carlo simulation, and the Markov chain approach. The latter approach yields analytical results for arbitrarily small systems, in contrast to the mean-field approach, which is strictly correct only for an infinite system. We show that for sufficiently large systems, all three approaches produce the same results, as expected. We consider two cases: (1) homogeneous, in which all agents have the same tolerance threshold, and (2) heterogeneous, in which the thresholds are given by a beta distribution parametrized by two positive shape parameters α and β. The heterogeneous case can be treated as a generalized model that reduces to a homogeneous model in special cases. We show that particularly interesting behaviors, including social hysteresis and critical mass, arise only for values of α and β that yield the shape of the distribution observed in real social systems.

Keywords: opinion dynamics; threshold model; anticonformity; mean-field approximation; Markov chain; dynamique d'opinion; modèle à seuil; anti-conformisme; approximation à champ moyen; chaîne de Markov (search for similar items in EconPapers)
Date: 2022-01
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-03573376v1
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Published in 2022

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Related works:
Working Paper: Threshold model with anticonformity under random sequential updating (2022)
Working Paper: The threshold model with anticonformity under random sequential updating (2022)
Working Paper: Threshold model with anticonformity under random sequential updating (2022)
Working Paper: Threshold model with anticonformity under random sequential updating (2022)
Working Paper: The threshold model with anticonformity under random sequential updating (2022)
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