Data-driven Rank Breaking for Efficient Rank Aggregation

TL;DR

This paper introduces an optimal rank-breaking estimator for rank aggregation that accounts for data dependencies, ensuring consistency and minimizing error, while analyzing the tradeoff between accuracy and computational complexity.

Contribution

It proposes a novel, data topology-aware rank-breaking method that guarantees consistent, accurate ranking estimates with optimal error bounds.

Findings

The estimator achieves the best possible error bounds.

Accuracy depends on the spectral gap of the comparison graph.

The method balances accuracy and computational complexity effectively.

Abstract

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.