How to count thumb-ups and thumb-downs: user-rating based ranking of items from an axiomatic perspective

It is a common practice among Web 2.0 services to allow users to rate items on their sites. In this paper, we first point out the flaws of the popular methods for user-rating based ranking of items, and then argue that two well-known Information Retrieval (IR) techniques, namely the Probability Ranking Principle and Statistical Language Modelling, provide simple but effective solutions to this problem. Furthermore, we examine the existing and proposed methods in an axiomatic framework, and prove that only the score functions given by the Dirichlet Prior smoothing method as well as its special cases can satisfy both of the two axioms borrowed from economics.