Consensus ranking by quantum annealing

TL;DR

This paper introduces an improved quantum annealing method for Kemeny consensus ranking that enhances performance and scalability, enabling better handling of larger datasets in preference aggregation tasks.

Contribution

It proposes a novel hybrid quantum-classical approach with enhancements that significantly improve quantum annealing's efficiency for ranking aggregation.

Findings

Outperforms existing quantum annealing methods in ranking accuracy.

Handles larger candidate sets more efficiently.

Compared favorably with KwikSort in execution time.

Abstract

Consensus ranking is a technique used to derive a single ranking that best represents the preferences of multiple individuals or systems. It aims to aggregate different rankings into one that minimizes overall disagreement or distance from each of the individual rankings. Kemeny ranking aggregation, in particular, is a widely used method in decision-making and social choice, with applications ranging from search engines to music recommendation systems. It seeks to determine a consensus ranking of a set of candidates based on the preferences of a group of individuals. However, existing quantum annealing algorithms face challenges in efficiently processing large datasets with many candidates. In this paper, we propose a method to improve the performance of quantum annealing for Kemeny rank aggregation. Our approach identifies the pairwise preference matrix that represents the solution list and subsequently reconstructs the ranking using classical methods. This method already yields better results than existing approaches. Furthermore, we present a range of enhancements that significantly improve the proposed method's performance, thereby increasing the number of candidates that can be effectively handled. Finally, we evaluate the efficiency of our approach by comparing its performance and execution time with that of KwikSort, a well-known approximate algorithm.