Given a set of items, the ranking problem is to determine an arrangement of items in order of importance. Example items include web pages, sports teams, stocks, political candidates, colleges, job applicants, works of art, and grant applications. A related problem is the rating problem, where each item is given a numerical rating. Sorting a list of ratings gives a ranking for those items. At the heart of many ranking methods is pair-wise comparison, either explicit or implicit. However, pair-wise rankings can give rise to incomplete or inconsistent outcomes due to Arrows Impossibility Theorem. The main work of this proposal is to learn the theory of ratings and rankings in consultation with Mike Jones, an expert in this area. I will implement and test about 10 ranking methods. In the future, beyond the scope of this project, I anticipate applying these ranking techniques to an image comparison problem using human and computer observers.