A Bayesian Hierarchical Model for Ranking Aggregation

Abstract

Rankings—an ordering of items from best to worst—are a common way to summarize a group of items, often at an individual level. These ranks are ordinal data, and should not be acted on by standard mathematical operations such as averaging. Thus, combining these individual rankings to get a consensus can present a difficult challenge. In this paper we present a novel method of combining rankings via a Bayesian hierarchical model, using rankings and their corresponding ratings—an assessment of item quality—to create a data augmentation scheme similar to established literature. Simulations show that this method provides an accurate recovery of true rankings, particularly when the ranking system exhibits clustering within the structure. Additionally this method has the added benefit of being able to describe properties of the rankings, including how preferred one item is to another and the probability that an individual will rank one item higher than another.