Who’s Shaping Who’s Opinions? Estimating the Degree of Influence Exerted by Each Contact in a Social Network

It is important in domains such as organizational behavior, politics, marketing, sociology, psychology, engineering, and economics to study how people that belong to a network form their opinions on a specific topic, how these opinions evolve, and how a consensus is reached. Researchers have mainly focused on estimating hidden opinions, identifying opinion trends, opinion leaders, consensus points, and the impact of the structure of the network on consensus. This dissertation proposes a model that (a) enables the tracking of the opinions of every member of a network, and (b) helps identifying who is influencing who’s opinions and to what degree when the opinions and connections of only a small subset of the people in the network is observed. This dissertation has three phases. Phase I provides the theoretical background of opinion dynamics and the philosophical concepts that surround individuals and opinions. Phase II develops the infrastructure and mathematical framework required to model opinions, opinion dynamics, and consensus over large networks. Phase III uses the mathematical constructs of the previous phase to present a statistical framework for the estimation of the influence that each person has on the opinions of others (influence network). The estimation problem is solved for the scenarios of complete information (when we know who is connected to whom and we have opinion measurements for all the agents); and when we have incomplete information (only part of the network and measurements are observed)