  We consider data in the form of pairwise comparisons of n items, with the
goal of precisely identifying the top k items for some value of k < n, or
alternatively, recovering a ranking of all the items. We analyze the Copeland
counting algorithm that ranks the items in order of the number of pairwise
comparisons won, and show it has three attractive features: (a) its
computational efficiency leads to speed-ups of several orders of magnitude in
computation time as compared to prior work; (b) it is robust in that
theoretical guarantees impose no conditions on the underlying matrix of
pairwise-comparison probabilities, in contrast to some prior work that applies
only to the BTL parametric model; and (c) it is an optimal method up to
constant factors, meaning that it achieves the information-theoretic limits for
recovering the top k-subset. We extend our results to obtain sharp guarantees
for approximate recovery under the Hamming distortion metric, and more
generally, to any arbitrary error requirement that satisfies a simple and
natural monotonicity condition.
