Researcher ORCID Identifier
0000-0003-2324-9450
Graduation Year
2023
Document Type
Open Access Senior Thesis
Degree Name
Bachelor of Science
Department
Mathematics
Reader 1
Jamie Haddock
Reader 2
Michael E. Orrison
Terms of Use & License Information
Rights Information
2023 Claire S Chang
Abstract
Ranking from pairwise comparisons is a particularly rich subset of ranking problems. In this work, we focus on a family of ranking methods for pairwise comparisons which encompasses the well-known Massey, Colley, and Markov methods. We will accomplish two objectives to deepen our understanding of this family. First, we will consider its network diffusion interpretation. Second, we will analyze its sensitivity by studying the "maximal upset" where the direction of an arc between the highest and lowest ranked alternatives is flipped. Through these analyses, we will build intuition to answer the question "What are the characteristics of robust ranking methods?" to ensure fair rankings in a variety of applications, ranging from choosing political candidates to ranking web pages to comparing sports teams.
Recommended Citation
Chang, Claire S., "The Sensitivity of a Laplacian Family of Ranking Methods" (2023). HMC Senior Theses. 270.
https://scholarship.claremont.edu/hmc_theses/270
