TY - GEN
T1 - On a Modified DeGroot-Friedkin model of opinion dynamics
AU - Xu, Zhi
AU - Liu, Ji
AU - Başar, Tamer
N1 - Publisher Copyright:
© 2015 American Automatic Control Council.
PY - 2015/7/28
Y1 - 2015/7/28
N2 - 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 converges to a unique nontrivial equilibrium which for each individual is equal to 1 over n, where n is the number of individuals. This implies that eventually individuals reach a democratic state.
AB - 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 converges to a unique nontrivial equilibrium which for each individual is equal to 1 over n, where n is the number of individuals. This implies that eventually individuals reach a democratic state.
UR - http://www.scopus.com/inward/record.url?scp=84940936219&partnerID=8YFLogxK
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U2 - 10.1109/ACC.2015.7170871
DO - 10.1109/ACC.2015.7170871
M3 - Conference contribution
AN - SCOPUS:84940936219
T3 - Proceedings of the American Control Conference
SP - 1047
EP - 1052
BT - ACC 2015 - 2015 American Control Conference
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2015 American Control Conference, ACC 2015
Y2 - 1 July 2015 through 3 July 2015
ER -