Modelling heterogeneity and an open-mindedness social norm in opinion dynamics

Clinton Innes; Razvan C. Fetecau; Ralf W. Wittenberg; Clinton Innes; Razvan C. Fetecau; Ralf W. Wittenberg

doi:10.3934/nhm.2017003

Networks and Heterogeneous Media

2017, Volume 12, Issue 1: 59-92. doi: 10.3934/nhm.2017003

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Modelling heterogeneity and an open-mindedness social norm in opinion dynamics

Department of Mathematics, Simon Fraser University, 8888 University Dr., Burnaby, BC V5A 1S6, Canada

Received: 01 December 2015 Revised: 01 April 2016
Primary: 91D30, 37N99; Secondary: 70F99

We study heterogeneous interactions in a time-continuous bounded confidence model for opinion formation. The key new modelling aspects are to distinguish between open-minded and closed-minded behaviour and to include an open-mindedness social norm. The investigations focus on the equilibria supported by the proposed new model; particular attention is given to a novel class of equilibria consisting of multiple connected opinion clusters, which does not occur in the absence of heterogeneity. Various rigorous stability results concerning these equilibria are established. We also incorporate the effect of media in the model and study its implications for opinion formation.
- Opinion dynamics,
- bounded confidence,
- heterogeneous societies,
- group connectivity,
- opinion equilibria
Citation: Clinton Innes, Razvan C. Fetecau, Ralf W. Wittenberg. Modelling heterogeneity and an open-mindedness social norm in opinion dynamics[J]. Networks and Heterogeneous Media, 2017, 12(1): 59-92. doi: 10.3934/nhm.2017003

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Abstract

We study heterogeneous interactions in a time-continuous bounded confidence model for opinion formation. The key new modelling aspects are to distinguish between open-minded and closed-minded behaviour and to include an open-mindedness social norm. The investigations focus on the equilibria supported by the proposed new model; particular attention is given to a novel class of equilibria consisting of multiple connected opinion clusters, which does not occur in the absence of heterogeneity. Various rigorous stability results concerning these equilibria are established. We also incorporate the effect of media in the model and study its implications for opinion formation.

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