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On a Modified DeGroot-Friedkin Model of Opinion Dynamics
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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