Evolution of Social Power for Opinion Dynamics Networks

This article studies the evolution of opinions and interpersonal influence structures in a group of agents as they discuss a sequence of issues, each of which follows an opinion dynamics model. In this work, we propose a general opinion dynamics model and an evolution of interpersonal influence structures based on the model of reflected appraisals proposed by Friedkin. Our contributions can be summarized as follows: (i) we introduce a model of opinion dynamics and evolution of interpersonal influence structures between issues viewed as a best response cost minimization to the neighbor's actions, (ii) we show that DeGroot's and Friedkin-Johnsen's models of opinion dynamics and their evolution of interpersonal influence structures are particular cases of our proposed model, and (iii) we prove the existence of an equilibrium. This work is a step towards providing a solid formulation of the evolution of opinions and interpersonal influence structures over a sequence of issues

Large population and long-term behavior of a stochastic binary opinion model

We propose and study a stochastic binary opinion model where agents in a group are considered to hold an opinion of 0 or 1 at each moment. An agent in the group updates his/her opinion based on the group's opinion configuration and his/her \emph{personality}. Considering the number of agents with opinion 1 as a continuous time Markov process, we analyze the long-term probabilities for large population size in relation to the personalities of the group. In particular, we focus on the question of "balance" where both opinions are present in nearly equal numbers as opposed to "dominance" where one opinion is dominant

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

The normalized Friedkin-Johnsen model (a work-in-progress report)

The formation of opinions in a social context has long been studied by sociologists. A well-known model is due to Friedkin and Johnsen (further referenced as the FJ model), which assumes that individuals hold an immutable internal opinion while they express an opinion that may differ from it but is more in agreement with the expressed opinions of their friends. Formally, the expressed opinion is modeled as the weighted average of the individual's internal opinion and the expressed opinions of their neighbors. This model has been used in recent research originating from the computer science community, studying the origination and reduction of conflict on social networks, how echo chambers arise and can be burst, and more. Yet, we argue that the FJ model in its elementary form is not suitable for some of these purposes. Indeed, the FJ model entails that the more friends one has, the less one's internal opinion matters in the formation of one's expressed opinion. Arguing that this may not be realistic, we propose a modification of the FJ model that normalizes the influence of one's friends and keeps the influence of one's internal opinion constant. This normalization was in fact suggested by Friedkin and Johnsen, but it has been ignored in much of the recent computer science literature. In this work-in-progress report, we present the details of the normalized model, and investigate the consequences of this normalization, both theoretically and empirically