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Towards Foundation Models for Consensus Rank Aggregation

Yijun Jin, Simon Klüttermann, Chiara Balestra, Emmanuel Müller

Abstract

Aggregating a consensus ranking from multiple input rankings is a fundamental problem with applications in recommendation systems, search engines, job recruitment, and elections. Despite decades of research in consensus ranking aggregation, minimizing the Kemeny distance remains computationally intractable. Specifically, determining an optimal aggregation of rankings with respect to the Kemeny distance is an NP-hard problem, limiting its practical application to relatively small-scale instances. We propose the Kemeny Transformer, a novel Transformer-based algorithm trained via reinforcement learning to efficiently approximate the Kemeny optimal ranking. Experimental results demonstrate that our model outperforms classical majority-heuristic and Markov-chain approaches, achieving substantially faster inference than integer linear programming solvers. Our approach thus offers a practical, scalable alternative for real-world ranking-aggregation tasks.

Towards Foundation Models for Consensus Rank Aggregation

Abstract

Aggregating a consensus ranking from multiple input rankings is a fundamental problem with applications in recommendation systems, search engines, job recruitment, and elections. Despite decades of research in consensus ranking aggregation, minimizing the Kemeny distance remains computationally intractable. Specifically, determining an optimal aggregation of rankings with respect to the Kemeny distance is an NP-hard problem, limiting its practical application to relatively small-scale instances. We propose the Kemeny Transformer, a novel Transformer-based algorithm trained via reinforcement learning to efficiently approximate the Kemeny optimal ranking. Experimental results demonstrate that our model outperforms classical majority-heuristic and Markov-chain approaches, achieving substantially faster inference than integer linear programming solvers. Our approach thus offers a practical, scalable alternative for real-world ranking-aggregation tasks.
Paper Structure (24 sections, 11 equations, 3 figures, 2 tables, 1 algorithm)

This paper contains 24 sections, 11 equations, 3 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Rank Aggregator
  4. Transformers for Combinatorial Optimization
  5. Positioning Our Approach
  6. Methodology
  7. Problem Definition
  8. Kemeny Transformer
  9. Tokenization
  10. Encoder
  11. Decoder
  12. Training Method
  13. Experiments
  14. Hyperparameters
  15. Datasets
  16. ...and 9 more sections

Figures (3)

  • Figure 1: The Kemeny Transformer is organized as a classic encoder–decoder architecture. In this design, the encoder first processes the inputs to produce contextual representations, and the decoder then employs an auto-regressive procedure to sequentially generate a ranking that is close to Kemeny optimality.
  • Figure 2: Running time comparison between the Kemeny Transformer and the Gurobi solver as the length of the base rankings increases. The x-axis denotes the number of items in the base rankings; the y-axis shows the logarithm of the mean running time computed over multiple trials. Our model scales more efficiently to larger ranking problems.
  • Figure 3: Performance comparison across varying input dimensions (voters, items) for the Jiggling datatype. The remaining datatypes are shown in the supplementary material. To ensure a fair comparison across different scales, the y-axis shows the normalized Kemeny distance gap, with the best-performing method serving as the baseline ($0$). Settings within the gray region are included in our training scope, while the remaining settings are outside it. Both inside and outside of our training prior, the Kemeny Transformer achieves state-of-the-art performance.. A possible reason for this good generalization stems from the input normalization used.