On a Modified DeGroot-Friedkin Model of Opinion Dynamics

A social network typically consists of two components: a collection of social actors (individuals, groups of people or organizations) and a description of the connections among those actors. Within a social network, the interactions among actors are capable of spreading and influencing the opinions. Consequently, one's opinion is not merely formed by himself or herself, but is also affected by the opinions of others through interactions. How much one trusts his or her own opinion and how much one is willing to accept others' opinions both depend on the self-confidence level of the particular social actor. This thesis 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, which in simple words, describes the phenomenon that individuals' self-appraisals on some dimension (e.g., self-confidence, self-esteem) are influenced by the appraisals of other individuals on them. 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/n, where n is the number of individuals. This implies that eventually individuals reach a democratic state.Ope