Engineering Commons^™

The Sensitivity Of A Laplacian Family Of Ranking Methods, Claire S. Chang

HMC Senior Theses

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?" …