Efficient Rank Aggregation via Lehmer Codes

TL;DR

This paper introduces a new rank aggregation method using Lehmer codes to transform permutations into vector form, enabling efficient, parallelizable aggregation with proven accuracy under Mallows models.

Contribution

It presents a novel Lehmer code-based approach for rank aggregation that is scalable, parallelizable, and backed by theoretical guarantees for correct centroid recovery.

Findings

Method is fully parallelizable and efficient.

Proven to recover the correct centroid with small sample sizes.

Applicable to partial rankings with similar guarantees.

Abstract

We propose a novel rank aggregation method based on converting permutations into their corresponding Lehmer codes or other subdiagonal images. Lehmer codes, also known as inversion vectors, are vector representations of permutations in which each coordinate can take values not restricted by the values of other coordinates. This transformation allows for decoupling of the coordinates and for performing aggregation via simple scalar median or mode computations. We present simulation results illustrating the performance of this completely parallelizable approach and analytically prove that both the mode and median aggregation procedure recover the correct centroid aggregate with small sample complexity when the permutations are drawn according to the well-known Mallows models. The proposed Lehmer code approach may also be used on partial rankings, with similar performance guarantees.