The Landau Legacy: From Chess to Pagerank

Abstract

Social sciences routinely use pairwise comparisons to rank or classify multidimensional items. A century ago, German mathematician Edmund Landau contributed the ranking rule underlying Google’s celebrated PageRank algorithm. We show how this method flows naturally from the most intuitive classification that arose with chess tournaments. Next, we introduce the concept of handicapping as a novel and intuitive way of characterizing normalizations of the Landau method. We then recast a number of ranking theories within Landau’s framework, thereby showing similarities and the ease with which each may be deduced from the previous one. The fields covered are sports, sociology, social choice, bibliometrics, internet ranking, learning, network economics and management. We show that the Landau method is close to the Leontief input-output model and how the former is a limit of the latter. Lastly, we give self-contained proofs of the Perron and Frobenius theorems whose use in the social sciences Landau pioneered.