Data-driven rank breaking for efficient rank aggregation

Rank aggregation systems collect ordinal preferences from individuals to produce a global ranking that represents the social preference. To reduce the computational complexity of learning the global ranking, a common practice is to use rank-breaking. Individuals' preferences are broken into pairwise comparisons and then applied to efficient algorithms tailored for independent pairwise comparisons. However, due to the ignored dependencies, naive rank-breaking approaches can result in inconsistent estimates. The key idea to produce unbiased and accurate estimates is to treat the paired comparisons outcomes 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 in some canonical scenarios. Further, we identify how the accuracy depends on the spectral gap of a corresponding comparison graph.