# On Fair Selection in the Presence of Implicit and Differential Variance

arXiv: https://arxiv.org/abs/2112.05630 · HTML: https://mlsanity.com/paper/2112.05630/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 34 references that are in the map.
- First posted on arXiv 10 Dec 2021.

## Builds on (most cited first, 11 of 11)

- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [Fair prediction with disparate impact: A study of bias in recidivism prediction instruments](https://mlsanity.com/paper/1610.07524/) (2016)
- [Algorithmic decision making and the cost of fairness](https://mlsanity.com/paper/1701.08230/) (2017)
- [Fairness Beyond Disparate Treatment & Disparate Impact: Learning Classification without Disparate Mistreatment](https://mlsanity.com/paper/1610.08452/) (2016)
- [Mitigating Bias in Algorithmic Hiring: Evaluating Claims and Practices](https://mlsanity.com/paper/1906.09208/) (2019)
- [On the Fairness of Disentangled Representations](https://mlsanity.com/paper/1905.13662/) (2019)
- [Recovering from Biased Data: Can Fairness Constraints Improve Accuracy?](https://mlsanity.com/paper/1912.01094/) (2019)
- [Selection Problems in the Presence of Implicit Bias](https://mlsanity.com/paper/1801.03533/) (2018)
- [Interventions for Ranking in the Presence of Implicit Bias](https://mlsanity.com/paper/2001.08767/) (2020)
- [On Fair Selection in the Presence of Implicit Variance](https://mlsanity.com/paper/2006.13699/) (2020)
- [Affirmative Action Policies for Top-k Candidates Selection, With an Application to the Design of Policies for University Admissions](https://mlsanity.com/paper/1905.09947/) (2019)

## Built on by (most cited first, 9 of 9)

- [Toward Operationalizing Pipeline-aware ML Fairness: A Research Agenda for Developing Practical Guidelines and Tools](https://mlsanity.com/paper/2309.17337/) (2023)
- [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)
- [Fairness in Ranking under Disparate Uncertainty](https://mlsanity.com/paper/2309.01610/) (2023)
- [MAFT: Efficient Model-Agnostic Fairness Testing for Deep Neural Networks via Zero-Order Gradient Search](https://mlsanity.com/paper/2412.20086/) (2024)
- [Balancing Utility and Fairness in Submodular Maximization (Technical Report)](https://mlsanity.com/paper/2211.00980/) (2022)
- [Subset Selection Based On Multiple Rankings in the Presence of Bias: Effectiveness of Fairness Constraints for Multiwinner Voting Score Functions](https://mlsanity.com/paper/2306.09835/) (2023)
- [Coresets for Clustering Under Stochastic Noise](https://mlsanity.com/paper/2510.23438/) (2025)
- [LSHFed: Robust and Communication-Efficient Federated Learning with Locally-Sensitive Hashing Gradient Mapping](https://mlsanity.com/paper/2511.01296/) (2025)

## Abstract (arXiv)

Discrimination in selection problems such as hiring or college admission is often explained by implicit bias from the decision maker against disadvantaged demographic groups. In this paper, we consider a model where the decision maker receives a noisy estimate of each candidate's quality, whose variance depends on the candidate's group -- we argue that such differential variance is a key feature of many selection problems. We analyze two notable settings: in the first, the noise variances are unknown to the decision maker who simply picks the candidates with the highest estimated quality independently of their group; in the second, the variances are known and the decision maker picks candidates having the highest expected quality given the noisy estimate. We show that both baseline decision makers yield discrimination, although in opposite directions: the first leads to underrepresentation of the low-variance group while the second leads to underrepresentation of the high-variance group. We study the effect on the selection utility of imposing a fairness mechanism that we term the γ-rule (it is an extension of the classical four-fifths rule and it also includes demographic parity). In the first setting (with unknown variances), we prove that under mild conditions, imposing the γ-rule increases the selection utility -- here there is no trade-off between fairness and utility. In the second setting (with known variances), imposing the γ-rule decreases the utility but we prove a bound on the utility loss due to the fairness mechanism.