# On Fair Selection in the Presence of Implicit Variance

arXiv: https://arxiv.org/abs/2006.13699 · HTML: https://mlsanity.com/paper/2006.13699/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jun 2020.

## Built on by (most cited first, 14 of 14)

- [Fair ranking: a critical review, challenges, and future directions](https://mlsanity.com/paper/2201.12662/) (2022)
- [Fairness for AUC via Feature Augmentation](https://mlsanity.com/paper/2111.12823/) (2021)
- [On Fair Selection in the Presence of Implicit and Differential Variance](https://mlsanity.com/paper/2112.05630/) (2021)
- [Proactive and Reactive Engagement of Artificial Intelligence Methods for Education: A Review](https://mlsanity.com/paper/2301.10231/) (2023)
- [Fairness in Matching under Uncertainty](https://mlsanity.com/paper/2302.03810/) (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)
- [On Meritocracy in Optimal Set Selection](https://mlsanity.com/paper/2102.11932/) (2021)
- [The Equity Framework: Fairness Beyond Equalized Predictive Outcomes](https://mlsanity.com/paper/2205.01072/) (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)
- [Sampling Individually-Fair Rankings that are Always Group Fair](https://mlsanity.com/paper/2306.11964/) (2023)
- [Trading-off price for data quality to achieve fair online allocation](https://mlsanity.com/paper/2306.13440/) (2023)
- [Affirmative Action vs. Affirmative Information](https://mlsanity.com/paper/2102.10019/) (2021)
- [Centralized Selection with Preferences in the Presence of Biases](https://mlsanity.com/paper/2409.04897/) (2024)

## Abstract (arXiv)

Quota-based fairness mechanisms like the so-called Rooney rule or four-fifths rule are used in selection problems such as hiring or college admission to reduce inequalities based on sensitive demographic attributes. These mechanisms are often viewed as introducing a trade-off between selection fairness and utility. In recent work, however, Kleinberg and Raghavan showed that, in the presence of implicit bias in estimating candidates' quality, the Rooney rule can increase the utility of the selection process. We argue that even in the absence of implicit bias, the estimates of candidates' quality from different groups may differ in another fundamental way, namely, in their variance. We term this phenomenon implicit variance and we ask: can fairness mechanisms be beneficial to the utility of a selection process in the presence of implicit variance (even in the absence of implicit bias)? To answer this question, we propose a simple model in which candidates have a true latent quality that is drawn from a group-independent normal distribution. To make the selection, a decision maker receives an unbiased estimate of the quality of each candidate, with normal noise, but whose variance depends on the candidate's group. We then compare the utility obtained by imposing a fairness mechanism that we term γ-rule (it includes demographic parity and the four-fifths rule as special cases), to that of a group-oblivious selection algorithm that picks the candidates with the highest estimated quality independently of their group. Our main result shows that the demographic parity mechanism always increases the selection utility, while any γ-rule weakly increases it. We extend our model to a two-stage selection process where the true quality is observed at the second stage. We discuss multiple extensions of our results, in particular to different distributions of the true latent quality.