Who's #1? The science of rating and ranking, by Amy N. Langville and Carl D. Meyer, Princeton, Princeton University Press, 2012, xvi+247 pp., £19.95 or US$29.95 (hardback), ISBN 978-0-691-15422-0
The authors describe this book as arising from the fact that they could not find a single convenient source containing the multitude of methods and applications of rating and ranking. Since the domain is indeed vast, with a huge number of applications, this is not surprising. Applications include rating and ranking sports teams, chess players, films, university departments, university graduates, surgeons, election candidates, and, of course, the modern classic of websites. The book emphasises sports teams and adopts a simple running example using American football data. This is, perhaps, a pity, since it means that much relevant material is omitted – such as a discussion of league tables in social policy contexts.
Partly because of the huge number of applications, with slightly different constraints and requirements, but also partly because researchers with different kinds of quantitative backgrounds have addressed the issues, a great many different approaches have been proposed (and indeed re-invented) in the literature.
The authors carefully distinguish ranking (yielding a rank-ordered list) from rating (yielding a list of numerical scores). Other authors use the term (unidimensional) ‘scaling’ for the latter – so that other methods, not covered in this book, can be found in books on scaling Citation1–3.
The coverage of the book is indicated by the mathematical prerequisites, which are an elementary knowledge of linear algebra and some knowledge of optimisation. As someone with a particular interest in the subject matter of the book, and appreciating the importance and ubiquity of the ideas and methods described within, I liked their comment on what to do if you have not had classes on these prerequisites: you should read the book anyway. However, readers of this review will have spotted the gaping omission from those prerequisites: they do not mention statistics. The penultimate paragraph of the book comments on the authors’ decision not to include statistical methods, adding ‘this is probably a disappointment to hard core statisticians’. It is indeed a disappointment to this hard-core statistician – because I believe they have missed a number of opportunities. On the one hand, statistics provides a nice integrating and unifying theory for many methods of rating and ranking, and on the other it leads to methods not included in this book.
Having said that, I have not previously seen such a nice discussion of so many diverse optimisation rating and ranking methods. These include the methods of Massey, Colley, Keener, Elo, and many others. There is even a discussion of point spreads and spread betting.
In summary, while, perhaps inevitably given the size of the domain, the book misses quite a large amount of relevant material, it does provide an excellent, accessible, and stimulating discussion of the material it does cover. Overall, the book makes a valuable addition to the canon of rating and ranking.
References
- Kempf-Leonard , K. 2005 . Encyclopedia of Social Measurement , Edited by: Kempf-Leonard , K. Amsterdam : Elsevier .
- Runn-Rankin , P. , Knezek , G. A. , Wallace , S. and Zhang , S. 2004 . Scaling Methods , Mahwah : Lawrence Eerlbaum Associates .
- van der Ven , A. H.G.S. 1980 . Introduction to Scaling , Chichester : Wiley .