College of Science and Health Theses and Dissertations

Date of Award

Spring 6-10-2022

Degree Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics

First Advisor

Ilie Ugarcovici, PhD

Abstract

An opinion profile can describe a set of individuals, groups or entities that form an opinion over a topic. Given a number of agents, a time evolving opinion denoted by a vector can be described over time using the linear mode where is a time variable and the matrix (which might depend on time and the current profile) contains the weights that affect the dynamics of profile . With varying conditions over time, these profiles can form groups, polarize, fragment, or reach consensus. In this work, we investigate the uniform bounded confidence model: an agent adjusts their opinion over time by averaging the opinions of those agents which are -close to that agent. By performing Monte Carlo simulations, we observed the phenomenon that consensus is very unlikely for and becomes prevalent as . To better understand this behavior, we conduct an in-depth analysis of evenly spaced profiles. We prove that guarantees consensus of all evenly spaced profiles for an odd number of agents . Numerical simulations also suggest that a smaller threshold value of guarantees consensus for these same profiles if . Also, for an even number of agents, numerical simulations show that seems to guarantee consensus if . Most importantly, our research indicates that the formation of separate groups created after 8-time steps is enough to determine whether consensus or fragmentation occurs. This mitigates a significant increase in processing time for certain values of within this bounded confidence algorithm.

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