  Rank aggregation systems collect ordinal preferences from individuals to
produce a global ranking that represents the social preference. Rank-breaking
is a common practice to reduce the computational complexity of learning the
global ranking. The individual preferences are broken into pairwise comparisons
and applied to efficient algorithms tailored for independent paired
comparisons. However, due to the ignored dependencies in the data, naive
rank-breaking approaches can result in inconsistent estimates. The key idea to
produce accurate and consistent estimates is to treat the pairwise comparisons
unequally, depending on the topology of the collected data. In this paper, we
provide the optimal rank-breaking estimator, which not only achieves
consistency but also achieves the best error bound. This allows us to
characterize the fundamental tradeoff between accuracy and complexity. Further,
the analysis identifies how the accuracy depends on the spectral gap of a
corresponding comparison graph.
