Georgia Institute of Technology College of Sciences

Ranking items from comparisons is a ubiquitous task in many real-world applications. For example, sports teams can be ranked based on outcomes of matches; students' homework solutions can be ranked based on peer grading. In this lecture, I will discuss: (1) how we can design mathematical models for the problem of ranking or rating a set of items from pairwise comparisons between them; (2) how to do statistical inference based on the models. The model we focus on is the Bradley-Terry model proposed in 1952, which is also related to the Elo rating system implemented for the US Chess Federation in 1960.