An Extended Mallows Model for Ranked Data Aggregation

Abstract

In this article, we study the rank aggregation problem, which aims to find a consensus ranking by aggregating multiple ranking lists. To address the problem probabilistically, we formulate an elaborate ranking model for full and partial rankings by generalizing the Mallows model. Our model assumes that the ranked data are generated through a multistage ranking process that is explicitly governed by parameters that measure the overall quality and stability of the process. The new model is quite flexible and has a closed form expression. Under mild conditions, we can derive a few useful theoretical properties of the model. Furthermore, we propose an efficient statistic called rank coefficient to detect over-correlated rankings and a hierarchical ranking model to fit the data. Through extensive simulation studies and real applications, we evaluate the merits of our models and demonstrate that they outperform the state-of-the-art methods in diverse scenarios. Supplementary materials for this article are available online.

Keywords:

• Consensus ranking
• Kendall tau distance
• Rank aggregation
• Rank coefficient

Acknowledgments

We thank Professor Persi Diaconis for his helpful comments and suggestions in investigating rank aggregation problem.

Funding

The research is supported in part by a grant from the Research Grants Council of the Hong Kong SAR (No. CUHK14203915) and a Mathematical Tianyuan Fund of the National Natural Science Foundation of China (No. 11626160).