# Achievability and Impossibility of Exact Pairwise Ranking

arXiv: https://arxiv.org/abs/2111.10021 · HTML: https://mlsanity.com/paper/2111.10021/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 13 references that are in the map.
- First posted on arXiv 19 Nov 2021.

## Builds on (most cited first, 5 of 5)

- [Simple, Robust and Optimal Ranking from Pairwise Comparisons](https://mlsanity.com/paper/1512.08949/) (2015)
- [Estimation from Pairwise Comparisons: Sharp Minimax Bounds with Topology Dependence](https://mlsanity.com/paper/1505.01462/) (2015)
- [Spectral MLE: Top-K Rank Aggregation from Pairwise Comparisons](https://mlsanity.com/paper/1504.07218/) (2015)
- [Stochastically Transitive Models for Pairwise Comparisons: Statistical and Computational Issues](https://mlsanity.com/paper/1510.05610/) (2015)
- [Competitive analysis of the top-K ranking problem](https://mlsanity.com/paper/1605.03933/) (2016)

## Abstract (arXiv)

We consider the problem of recovering the rank of a set of n items based on noisy pairwise comparisons. We assume the SST class as the family of generative models. Our analysis gave sharp information theoretic upper and lower bound for the exact requirement, which matches exactly in the parametric limit. Our tight analysis on the algorithm induced by the moment method gave better constant in Minimax optimal rate than ~citetshah2017simple and contribute to their open problem. The strategy we used in this work to obtain information theoretic bounds is based on combinatorial arguments and is of independent interest.