  The process of rank aggregation is intimately intertwined with the structure
of skew-symmetric matrices. We apply recent advances in the theory and
algorithms of matrix completion to skew-symmetric matrices. This combination of
ideas produces a new method for ranking a set of items. The essence of our idea
is that a rank aggregation describes a partially filled skew-symmetric matrix.
We extend an algorithm for matrix completion to handle skew-symmetric data and
use that to extract ranks for each item. Our algorithm applies to both pairwise
comparison and rating data. Because it is based on matrix completion, it is
robust to both noise and incomplete data. We show a formal recovery result for
the noiseless case and present a detailed study of the algorithm on synthetic
data and Netflix ratings.
