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PreprintCC BY-NC-ND 4.0arXiv

Pairwise comparisons meet optimal transport theory

  • Matteo Brunelli
  • Silvia Lorenzini
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Abstract

In this paper, we reinterpret pairwise comparison theory through the lens of optimal transport. The main contribution is the connection established between pairwise comparison matrices, doubly stochastic scaling, and entropy-regularized transport problems. Using Sinkhorn scaling, we show how consistency, priority derivation, and inconsistency assessment can be studied within a common optimal-transport framework. As methodological consequences of this connection, we obtain a new characterization of consistency, a Sinkhorn-based prioritization method, and an entropy-based inconsistency index. We study these proposals both analytically and numerically and compare them with established methods from the literature

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Cite

BibTeXRIS
BibTeX
@misc{brunelli2026pairwise,
  title = {{Pairwise comparisons meet optimal transport theory}},
  author = {Matteo Brunelli and Silvia Lorenzini},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.19841},
  eprint = {2609.19841},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.19841},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Pairwise comparisons meet optimal transport theory
AU  - Matteo Brunelli
AU  - Silvia Lorenzini
PY  - 2026
DA  - 2026/09/17
PB  - arXiv
DO  - 10.48550/arxiv.2609.19841
UR  - https://arxiv.org/abs/2609.19841
AB  - In this paper, we reinterpret pairwise comparison theory through the lens of optimal transport. The main contribution is the connection established between pairwise comparison matrices, doubly stochastic scaling, and entropy-regularized transport problems. Using Sinkhorn scaling, we show how consistency, priority derivation, and inconsistency assessment can be studied within a common optimal-transport framework. As methodological consequences of this connection, we obtain a new characterization of consistency, a Sinkhorn-based prioritization method, and an entropy-based inconsistency index. We study these proposals both analytically and numerically and compare them with established methods from the literature
ER  -