Continuous-time opinion dynamics on multiple interdependent topics
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In this paper, and inspired by the recent discrete-time model in Parsegov et al. (2017) and Friedkin et al. (2016), we study two continuous-time opinion dynamics models (Model 1 and Model 2) where the individuals discuss opinions on multiple logically interdependent topics. The logical interdependence between the different topics is captured by a “logic” matrix, which is distinct from the Laplacian matrix capturing interactions between individuals. For each of Model 1 and Model 2, we obtain a necessary and sufficient condition for the network to reach to a consensus on each separate topic. The condition on Model 1 involves a combination of the eigenvalues of the logic matrix and Laplacian matrix, whereas the condition on Model 2 requires only separate conditions on the logic matrix and Laplacian matrix. Further investigation of Model 1 yields two sufficient conditions for consensus, and allows us to conclude that one way to guarantee a consensus is to reduce the rate of interaction between individuals exchanging opinions. By placing further restrictions on the logic matrix, we also establish a set of Laplacian matrices which guarantee consensus for Model 1. The two models are also expanded to include stubborn individuals, who remain attached to their initial opinions. Sufficient conditions are obtained for guaranteeing convergence of the opinion dynamics system, with the final opinions generally being at a persistent disagreement. Simulations are provided to illustrate the results.
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Ye, Mengbin ; Liu, J.; Wang, L.; Anderson, B.D.O.; Cao, M. (2020)Recently, an opinion dynamics model has been proposed to describe a network of individuals discussing a set of logically interdependent topics. For each individual, the set of topics and the logical interdependencies ...
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Anderson, B.D.O.; Ye, Mengbin (2019)A fundamental aspect of society is the exchange and discussion of opinions between individuals, occurring in situations as varied as company boardrooms, elementary school classrooms and online social media. After a very ...