We present several results related to ranking. We give a general margin-based bound for ranking based on the L covering number of the hypothesis space. Our bound suggests that algorithms that maximize the ranking margin generalize well. We then describe a new algorithm, Smooth Margin Ranking, that precisely converges to a maximum ranking-margin solution. The algorithm is a modification of RankBoost, analogous to Approximate Coordinate Ascent Boosting. We also prove a remarkable property of AdaBoost: under very natural conditions, AdaBoost maximizes the exponentiated loss associated with the AUC and achieves the same AUC as RankBoost. This explains the empirical observations made by Cortes and Mohri, and Caruana and Niculescu-Mizil, about the excellent performance of AdaBoost as a ranking algorithm, as measured by the AUC. © Springer-Verlag Berlin Heidelberg 2005. ∞