A paper on an effort to mathematically analyze three commonly-used ranking methods appears this month in the SIAM Journal on Scientific Computing.
Authors Timothy Chartier, Erich Kreutzer, Amy Langville, and Kathryn Pedings studied the sensitivity and stability of PageRank, which has been used by Google to rank Web pages, and the Colley and Massey methods, which have been used by the Bowl Championship Series to rank college football teams. The team applied the Colley and Massey ranking techniques and a modified version of PageRank, the Markov Web page rankings, to a sports season.
The researchers found the Colley and Massey ranking techniques to be insensitive to small changes in input data, while the Markov or PageRank method was highly sensitive to changes, which often resulted in anomalies in rankings. The Markov or PageRank method also showed increased sensitivity as the rank position increased.
The authors say that analyzing the algorithms and techniques that underlie ranking methods is important to ensure fairness, considering Web page authors and teams try to game or spam ranking systems to achieve a higher ranking.
From Society for Industrial and Applied Mathematics
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