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MSc. by S. Selleck: Reducing Polarization in Opinion Networks in the Presence of Stubborn Leaders

Graph polarization before and after addition of a link.


From: 2022-01-27 10:30 to 11:00
Place: Dept. of Automatic Control Seminar Room KC 3N27 and Zoom
Contact: giacomocomo [at] gmail [dot] com
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A MSc. thesis in Automatic Control will be presented.

Presenter: Samuel Selleck
Title: Reducing Polarization in Opinion Networks in the Presence of Stubborn Leaders
Examiner: Emma Tegling
Supervisors: Giacomo Como


Abstract: We study the problem of reducing polarization (variance) of opinions at stationarity in a directed weighted graph with node set divided into two groups: stubborn, initialized with a fixed opinion and regular who repeatedly update their opinion to the average of their out-neighbors, known as the DeGroot model with stubborn nodes. We show how the polarization can be minimized for a number of simple constraints, but that the problem in general is not convex. Theory is developed for the change in opinions at stationarity and the polarization measure for a rank-1 update of the network (encompassing both addition of a directed and undirected link in the network). An algorithm for optimal infinitesimal link addition is proposed, achieving a two order of magnitude reduction in complexity with respect to the number of links in the network compared to a finite difference method. Lastly variations of the algorithm together with other trivial methods of recommending a link are compared for a number of random and real networks.