# Ranking with Slot Constraints

arXiv: https://arxiv.org/abs/2310.17870 · HTML: https://mlsanity.com/paper/2310.17870/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 45 references that are in the map.
- First posted on arXiv 27 Oct 2023.

## Builds on (most cited first, 13 of 13)

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Fairness-Aware Ranking in Search & Recommendation Systems with Application to LinkedIn Talent Search](https://mlsanity.com/paper/1905.01989/) (2019)
- [Lazier Than Lazy Greedy](https://mlsanity.com/paper/1409.7938/) (2014)
- [Selection Problems in the Presence of Implicit Bias](https://mlsanity.com/paper/1801.03533/) (2018)
- [Fairness in Ranking under Uncertainty](https://mlsanity.com/paper/2107.06720/) (2021)
- [A scikit-based Python environment for performing multi-label classification](https://mlsanity.com/paper/1702.01460/) (2017)
- [Improving Screening Processes via Calibrated Subset Selection](https://mlsanity.com/paper/2202.01147/) (2022)
- [Multiwinner Elections with Diversity Constraints](https://mlsanity.com/paper/1711.06527/) (2017)
- [Balancing Relevance and Diversity in Online Bipartite Matching via Submodularity](https://mlsanity.com/paper/1811.05100/) (2018)
- [Diverse Weighted Bipartite b-Matching](https://mlsanity.com/paper/1702.07134/) (2017)
- [Improved approximation for 3-dimensional matching via bounded pathwidth local search](https://mlsanity.com/paper/1304.1424/) (2013)
- [Dropping Standardized Testing for Admissions Trades Off Information and Access](https://mlsanity.com/paper/2010.04396/) (2020)
- [Improved Approximation Algorithms for Stochastic-Matching Problems](https://mlsanity.com/paper/2010.08142/) (2020)

## Abstract (arXiv)

We introduce the problem of ranking with slot constraints, which can be used to model a wide range of application problems -- from college admission with limited slots for different majors, to composing a stratified cohort of eligible participants in a medical trial. We show that the conventional Probability Ranking Principle (PRP) can be highly sub-optimal for slot-constrained ranking problems, and we devise a new ranking algorithm, called MatchRank. The goal of MatchRank is to produce rankings that maximize the number of filled slots if candidates are evaluated by a human decision maker in the order of the ranking. In this way, MatchRank generalizes the PRP, and it subsumes the PRP as a special case when there are no slot constraints. Our theoretical analysis shows that MatchRank has a strong approximation guarantee without any independence assumptions between slots or candidates. Furthermore, we show how MatchRank can be implemented efficiently. Beyond the theoretical guarantees, empirical evaluations show that MatchRank can provide substantial improvements over a range of synthetic and real-world tasks.