Cs599: Structure and Dynamics of Networked Information (spring 2005) 02/23/2005: Rank Aggregation Scribes: Ranjit Raveendran and Animesh Pathak

In previous lectures, we had discussed the problem of searching for relevant results on the WWW by exploiting the link structure. Nowadays, there are already multiple search engines giving quite good results. However, given that there are so many search engines already, employing different techniques, we may be interested in combining their positive features, and constructing a meta-search engine that uses all of their results. This leads very naturally to the problem of rank aggregation: given several orders on items (such as search results), determine a consensus ordering, which somehow reflects all orderings together. This problem can be studied from different perspectives. We could treat it as a machine learning problem, by treating each search engine as an “expert”, and trying to learn which engine’s advice to trust, based on past performance. The goal would then be to perform no worse than the best expert, but without knowing ahead of time which one is actually the best expert. Another approach, which we will explore in future lectures, is to consider it as an optimization problem. By defining an appropriate notion of distance between rankings, we can then look for a ranking that is close to all given rankings in a certain sense. A third approach, to be pursued in this and the following lecture, exploits the close connection between rank aggregation and voting. In both settings, we have items (candidates or web pages), and orderings on them (voter preferences or search engine rankings). The goal is to find a ranking that is “agreeable” to all voters/search engines. By using this analogy, we can leverage several centuries of thought on the issue of voting and social choice.