Modeling Opinion Dynamics Using the Affine Boomerang Model
Social network analysis is the study of interpersonal behavior that represents group members as nodes and using edges to characterize the relationship between members. The aim of this study is to analyze a recently proposed opinion dynamics model, which isstructured under the assumption that if two people have a positive relationship, then their opinions will come closer to agreement, and if they have a negative relationship, their opinions will diverge. We will study the model by simulating it for star graphs, where individual interact with one mutual person and not each other, and cycle graphs, where each individual interacts with two people, to observe how the structure of positive and negative relationships drives the opinions of the members of the network.In the case of a star graph with two opposing factions, we should observe that within each faction, members will agree, but the opinions of the factions will polarize. Simulations show that in the case where there are more than two factions, the opinions of some of the factions may oscillate, unless all edges are negative. Furthermore, in cycle graphs with two factions, it is apparent that there is a direct relationship to increasing an individual’s attachment to their opinion and the time it takes forit to reach a polarizing steady state. Understanding how social network structures impact the ability for a group to come to agreement gives us further insight about human interaction, which can be applied toward information dissemination, political science, and economics.