# Subset Selection Based On Multiple Rankings in the Presence of Bias: Effectiveness of Fairness Constraints for Multiwinner Voting Score Functions

arXiv: https://arxiv.org/abs/2306.09835 · HTML: https://mlsanity.com/paper/2306.09835/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 100 references that are in the map.
- First posted on arXiv 16 Jun 2023.

## Builds on (most cited first, 30 of 35)

- [Deep reinforcement learning from human preferences](https://mlsanity.com/paper/1706.03741/) (2017)
- [Mitigating Bias in Algorithmic Hiring: Evaluating Claims and Practices](https://mlsanity.com/paper/1906.09208/) (2019)
- [Identifying and Correcting Label Bias in Machine Learning](https://mlsanity.com/paper/1901.04966/) (2019)
- [Fairness in Rankings and Recommendations: An Overview](https://mlsanity.com/paper/2104.05994/) (2021)
- [Recovering from Biased Data: Can Fairness Constraints Improve Accuracy?](https://mlsanity.com/paper/1912.01094/) (2019)
- [Multi-Winner Voting with Approval Preferences](https://mlsanity.com/paper/2007.01795/) (2020)
- [Selection Problems in the Presence of Implicit Bias](https://mlsanity.com/paper/1801.03533/) (2018)
- [Your 2 is My 1, Your 3 is My 9: Handling Arbitrary Miscalibrations in Ratings](https://mlsanity.com/paper/1806.05085/) (2018)
- [Interventions for Ranking in the Presence of Implicit Bias](https://mlsanity.com/paper/2001.08767/) (2020)
- [Fair ranking: a critical review, challenges, and future directions](https://mlsanity.com/paper/2201.12662/) (2022)
- [Properties of Multiwinner Voting Rules](https://mlsanity.com/paper/1506.02891/) (2015)
- [Fair Ranking with Noisy Protected Attributes](https://mlsanity.com/paper/2211.17067/) (2022)
- [On Fair Selection in the Presence of Implicit Variance](https://mlsanity.com/paper/2006.13699/) (2020)
- [Finding a Collective Set of Items: From Proportional Multirepresentation to Group Recommendation](https://mlsanity.com/paper/1402.3044/) (2014)
- [Efficiently Learning Mixtures of Mallows Models](https://mlsanity.com/paper/1808.05731/) (2018)
- [Allocating Opportunities in a Dynamic Model of Intergenerational Mobility](https://mlsanity.com/paper/2101.08451/) (2021)
- [Computational Aspects of Multi-Winner Approval Voting](https://mlsanity.com/paper/1407.3247/) (2014)
- [Equality of Voice: Towards Fair Representation in Crowdsourced Top-K Recommendations](https://mlsanity.com/paper/1811.08690/) (2018)
- [Multiwinner Elections with Diversity Constraints](https://mlsanity.com/paper/1711.06527/) (2017)
- [What Do Multiwinner Voting Rules Do? An Experiment Over the Two-Dimensional Euclidean Domain](https://mlsanity.com/paper/1901.09217/) (2019)
- [On Fair Selection in the Presence of Implicit and Differential Variance](https://mlsanity.com/paper/2112.05630/) (2021)
- [Concentric mixtures of Mallows models for top-k rankings: sampling and identifiability](https://mlsanity.com/paper/2010.14260/) (2020)
- [Achieving Fully Proportional Representation: Approximability Results](https://mlsanity.com/paper/1312.4026/) (2013)
- [The Effect of the Rooney Rule on Implicit Bias in the Long Term](https://mlsanity.com/paper/2010.10992/) (2020)
- [Selection in the Presence of Implicit Bias: The Advantage of Intersectional Constraints](https://mlsanity.com/paper/2202.01661/) (2022)
- [Maximizing Submodular Functions for Recommendation in the Presence of Biases](https://mlsanity.com/paper/2305.02806/) (2023)
- [Evaluating approval-based multiwinner voting in terms of robustness to noise](https://mlsanity.com/paper/2002.01776/) (2020)
- [Two-Sided Fairness in Non-Personalised Recommendations](https://mlsanity.com/paper/2011.05287/) (2020)
- [Diverse Representation via Computational Participatory Elections -- Lessons from a Case Study](https://mlsanity.com/paper/2205.15394/) (2022)
- [Multi-winner Approval Voting Goes Epistemic](https://mlsanity.com/paper/2201.06655/) (2022)

## Built on by (most cited first, 2 of 2)

- [Centralized Selection with Preferences in the Presence of Biases](https://mlsanity.com/paper/2409.04897/) (2024)
- [Generalized Top-k Mallows Model for Ranked Choices](https://mlsanity.com/paper/2510.22040/) (2025)

## Abstract (arXiv)

We consider the problem of subset selection where one is given multiple rankings of items and the goal is to select the highest ``quality'' subset. Score functions from the multiwinner voting literature have been used to aggregate rankings into quality scores for subsets. We study this setting of subset selection problems when, in addition, rankings may contain systemic or unconscious biases toward a group of items. For a general model of input rankings and biases, we show that requiring the selected subset to satisfy group fairness constraints can improve the quality of the selection with respect to unbiased rankings. Importantly, we show that for fairness constraints to be effective, different multiwinner score functions may require a drastically different number of rankings: While for some functions, fairness constraints need an exponential number of rankings to recover a close-to-optimal solution, for others, this dependency is only polynomial. This result relies on a novel notion of ``smoothness'' of submodular functions in this setting that quantifies how well a function can ``correctly'' assess the quality of items in the presence of bias. The results in this paper can be used to guide the choice of multiwinner score functions for the subset selection setting considered here; we additionally provide a tool to empirically enable this.