Analysis of a nonlinear opinion dynamics model with biased assimilation
Embargo Lift Date
MetadataShow full item record
© 2020 Elsevier Ltd This paper analyzes a nonlinear opinion dynamics model which generalizes the DeGroot model by introducing a bias parameter for each individual. The original DeGroot model is recovered when the bias parameter is equal to zero. The magnitude of this parameter reflects an individual's degree of bias when assimilating new opinions, and depending on the magnitude, an individual is said to have weak, intermediate, and strong bias. The opinions of the individuals lie between 0 and 1. It is shown that for strongly connected networks, the equilibria with all elements equal identically to the extreme value 0 or 1 is locally exponentially stable, while the equilibrium with all elements equal to the neutral consensus value of 1/2 is unstable. Regions of attraction for the extreme consensus equilibria are given. For the equilibrium consisting of both extreme values 0 and 1, which corresponds to opinion polarization according to the model, it is shown that the equilibrium is unstable for all strongly connected networks if individuals all have weak bias, becomes locally exponentially stable for complete and two-island networks if individuals all have strong bias, and its stability heavily depends on the network topology when individuals have intermediate bias. Analysis on star graphs and simulations show that additional equilibria may exist where individuals form clusters.
Showing items related by title, author, creator and subject.
Nie, Katherine Su (2007)Numerous popular business publications and academic literature have highlighted that the Chinese cultural phenomenon of guanxi has made noticeable impacts on the economic efficiency in China’s economic transition. Despite ...
On the Effects of Heterogeneous Logical Interdependencies in a Multi-Dimensional Opinion Dynamics ModelYe, Mengbin ; Liu, J.; Anderson, B.D.O. (2018)In this paper, we investigate a recently proposed opinion dynamics model which considers a network of individuals simultaneously discussing a set of logically interdependent topics. The logical interdependence between the ...
Ye, Mengbin ; Qin, Y.; Govaert, A.; Anderson, B.D.O.; Cao, M. (2019)In many social situations, a discrepancy arises between an individual's private and expressed opinions on a given topic. Motivated by Solomon Asch's seminal experiments on social conformity and other related socio-psychological ...