# Price of Fairness in Short-Term and Long-Term Algorithmic Selections

arXiv: https://arxiv.org/abs/2605.06227 · HTML: https://mlsanity.com/paper/2605.06227/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 44 of its 61 references that are in the map.
- First posted on arXiv 7 May 2026.

## Builds on (most cited first, 30 of 44)

- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [Constrained Policy Optimization](https://mlsanity.com/paper/1705.10528/) (2017)
- [Algorithmic decision making and the cost of fairness](https://mlsanity.com/paper/1701.08230/) (2017)
- [Preventing Fairness Gerrymandering: Auditing and Learning for Subgroup Fairness](https://mlsanity.com/paper/1711.05144/) (2017)
- [Fairness in Criminal Justice Risk Assessments: The State of the Art](https://mlsanity.com/paper/1703.09207/) (2017)
- [Strategic Classification](https://mlsanity.com/paper/1506.06980/) (2015)
- [Delayed Impact of Fair Machine Learning](https://mlsanity.com/paper/1803.04383/) (2018)
- [Fairness in Learning: Classic and Contextual Bandits](https://mlsanity.com/paper/1605.07139/) (2016)
- [Provably Efficient Safe Exploration via Primal-Dual Policy Optimization](https://mlsanity.com/paper/2003.00534/) (2020)
- [Strategic Classification from Revealed Preferences](https://mlsanity.com/paper/1710.07887/) (2017)
- [Fairness in Reinforcement Learning](https://mlsanity.com/paper/1611.03071/) (2016)
- [The Measure and Mismeasure of Fairness](https://mlsanity.com/paper/1808.00023/) (2018)
- [How Do Classifiers Induce Agents To Invest Effort Strategically?](https://mlsanity.com/paper/1807.05307/) (2018)
- [Learning Policies with Zero or Bounded Constraint Violation for Constrained MDPs](https://mlsanity.com/paper/2106.02684/) (2021)
- [How Do Fair Decisions Fare in Long-term Qualification?](https://mlsanity.com/paper/2010.11300/) (2020)
- [Algorithms for Fairness in Sequential Decision Making](https://mlsanity.com/paper/1901.08568/) (2019)
- [A Moral Framework for Understanding of Fair ML through Economic Models of Equality of Opportunity](https://mlsanity.com/paper/1809.03400/) (2018)
- [On the Long-term Impact of Algorithmic Decision Policies: Effort Unfairness and Feature Segregation through Social Learning](https://mlsanity.com/paper/1903.01209/) (2019)
- [Calibrated Fairness in Bandits](https://mlsanity.com/paper/1707.01875/) (2017)
- [State Augmented Constrained Reinforcement Learning: Overcoming the Limitations of Learning with Rewards](https://mlsanity.com/paper/2102.11941/) (2021)
- [From Fair Decision Making to Social Equality](https://mlsanity.com/paper/1812.02952/) (2018)
- [Fair Algorithms for Learning in Allocation Problems](https://mlsanity.com/paper/1808.10549/) (2018)
- [Long-Term Fairness with Unknown Dynamics](https://mlsanity.com/paper/2304.09362/) (2023)
- [Fair Classification with Adversarial Perturbations](https://mlsanity.com/paper/2106.05964/) (2021)
- [Truly No-Regret Learning in Constrained MDPs](https://mlsanity.com/paper/2402.15776/) (2024)
- [Group-Fairness in Influence Maximization](https://mlsanity.com/paper/1903.00967/) (2019)
- [Achieving Long-Term Fairness in Sequential Decision Making](https://mlsanity.com/paper/2204.01819/) (2022)
- [Fairness and Utilization in Allocating Resources with Uncertain Demand](https://mlsanity.com/paper/1906.09050/) (2019)
- [Enabling Long-term Fairness in Dynamic Resource Allocation](https://mlsanity.com/paper/2208.05898/) (2022)
- [Towards Return Parity in Markov Decision Processes](https://mlsanity.com/paper/2111.10476/) (2021)

## Abstract (arXiv)

Algorithmic decision-making in high-stakes settings can have profound impacts on individuals and populations. While much prior work studies fairness in static settings, recent results show that enforcing static fairness constraints may exacerbate long-run disparities. Motivated by this tension, we study a stylized sequential selection problem in which a decision-maker repeatedly selects individuals, affecting both immediate utility and the population distribution over time. We introduce notions of group fairness for both the short and long term and theoretically analyze the trade-off between fairness and utility via the Price of Fairness (PoF). We characterize optimal and fair policies in the short term and show that the PoF can be large even when group distributions are nearly identical. In contrast, we show that long-term disparities can vanish under simple investment policies that achieve a low PoF. We also empirically validate these theoretical observations using both synthetic and real datasets.