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arXiv · 1503.04179

On a Modified DeGroot-Friedkin Model of Opinion Dynamics

Zhi Xu·Ji Liu·Tamer Basar
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Abstract

This paper studies the opinion dynamics that result when individuals consecutively discuss a sequence of issues. Specifically, we study how individuals' self-confidence levels evolve via a reflected appraisal mechanism. Motivated by the DeGroot-Friedkin model, we propose a Modified DeGroot-Friedkin model which allows individuals to update their self-confidence levels by only interacting with their neighbors and in particular, the modified model allows the update of self-confidence levels to take place in finite time without waiting for the opinion process to reach a consensus on any particular issue. We study properties of this Modified DeGroot-Friedkin model and compare the associated equilibria and stability with those of the original DeGroot-Friedkin model. Specifically, for the case when the interaction matrix is doubly stochastic, we show that for the modified model, the vector of individuals' self-confidence levels asymptotically converges to a unique nontrivial equilibrium which for each individual is equal to 1/n, where n is the number of individuals. This implies that eventually, individuals reach a democratic state.

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Zhi Xu, Ji Liu, Tamer Basar. 2015-03-13. On a Modified DeGroot-Friedkin Model of Opinion Dynamics. https://arxiv.org/abs/1503.04179

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