The mathematics of ranking

August 16 to August 20, 2010

at the

American Institute of Mathematics, San Jose, California

organized by

Shivani Agarwal and Lek-Heng Lim

Original Announcement

This workshop will bring together researchers from a broad spectrum of both fundamental and applied areas to share their perspectives on ranking problems, with a focus on the underlying mathematics.

Ranking problems arise in a multitude of domains, ranging from elections to web search and from management science to drug discovery. Consequently, ranking problems have been studied under different guises in many different fields, and each field has developed its own mathematical tools for studying ranking. This workshop will bring together for the first time researchers from mathematics, statistics, computer science, operations research, economics and game theory, and from both academic and industry backgrounds, to share their perspectives on ranking problems and on the mathematical tools used to study them.

Some of the topics we plan to discuss at the workshop are

  1. Classical statistical approaches to ranking
  2. Algebraic and geometric approaches to ranking
  3. Markov chain and other graph-based approaches to ranking
  4. Machine learning approaches to ranking
  5. Connections with other approaches to ranking, such as those studied in social choice theory, economics, and game theory
At the end of the workshop, we hope that all participants will have learned about many different views of ranking; we also hope that the interactions themselves will lead to new and potentially more useful views of ranking than those currently understood. We expect that the focused nature of the interactions will lead to reformulations and solutions of some open questions related to ranking. More importantly, the bridges built during this workshop will play an important role in facilitating future dialogue and collaboration between different disciplines related to ranking; this will be of tremendous value not only to researchers investigating mathematical aspects of ranking, but also to the increasing number of practitioners using ranking techniques in their applications.

Material from the workshop

A list of participants.

The workshop schedule.

A report on the workshop activities.

Papers arising from the workshop:

Pairwise ranking: choice of method can produce arbitrarily different rank order
by  Ngoc Mai Tran
A new way to analyze paired comparison rules
by  Donald G. Saari