# On Obtaining Stable Rankings

arXiv: https://arxiv.org/abs/1804.10990 · HTML: https://mlsanity.com/paper/1804.10990/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Apr 2018.

## Built on by (most cited first, 6 of 6)

- [Stability and Multigroup Fairness in Ranking with Uncertain Predictions](https://mlsanity.com/paper/2402.09326/) (2024)
- [Assumption-free stability for ranking problems](https://mlsanity.com/paper/2506.02257/) (2025)
- [Tracking Control for a Spherical Pendulum via Curriculum Reinforcement Learning](https://mlsanity.com/paper/2309.14096/) (2023)
- [Mining the Minoria: Unknown, Under-represented, and Under-performing Minority Groups](https://mlsanity.com/paper/2411.04761/) (2024)
- [A Tutorial On Intersectionality in Fair Rankings](https://mlsanity.com/paper/2502.05333/) (2025)
- [Generalizing Fair Top-k Selection: An Integrative Approach](https://mlsanity.com/paper/2603.04689/) (2026)

## Abstract (arXiv)

Decision making is challenging when there is more than one criterion to consider. In such cases, it is common to assign a goodness score to each item as a weighted sum of its attribute values and rank them accordingly. Clearly, the ranking obtained depends on the weights used for this summation. Ideally, one would want the ranked order not to change if the weights are changed slightly. We call this property em stability of the ranking. A consumer of a ranked list may trust the ranking more if it has high stability. A producer of a ranked list prefers to choose weights that result in a stable ranking, both to earn the trust of potential consumers and because a stable ranking is intrinsically likely to be more meaningful. In this paper, we develop a framework that can be used to assess the stability of a provided ranking and to obtain a stable ranking within an "acceptable" range of weight values (called "the region of interest"). We address the case where the user cares about the rank order of the entire set of items, and also the case where the user cares only about the top-k items. Using a geometric interpretation, we propose algorithms that produce stable rankings. In addition to theoretical analyses, we conduct extensive experiments on real datasets that validate our proposal.