# Revisiting Fairness Impossibility with Endogenous Behavior

arXiv: https://arxiv.org/abs/2604.06378 · HTML: https://mlsanity.com/paper/2604.06378/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 29 references that are in the map.
- First posted on arXiv 7 Apr 2026.

## Builds on (most cited first, 21 of 21)

- [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)
- [Inherent Trade-Offs in the Fair Determination of Risk Scores](https://mlsanity.com/paper/1609.05807/) (2016)
- [Algorithmic decision making and the cost of fairness](https://mlsanity.com/paper/1701.08230/) (2017)
- [Performative Prediction](https://mlsanity.com/paper/2002.06673/) (2020)
- [Strategic Classification](https://mlsanity.com/paper/1506.06980/) (2015)
- [Fairness in Machine Learning: Lessons from Political Philosophy](https://mlsanity.com/paper/1712.03586/) (2017)
- [Strategic Classification from Revealed Preferences](https://mlsanity.com/paper/1710.07887/) (2017)
- [The Social Cost of Strategic Classification](https://mlsanity.com/paper/1808.08460/) (2018)
- [The Disparate Effects of Strategic Manipulation](https://mlsanity.com/paper/1808.08646/) (2018)
- [Causal Strategic Linear Regression](https://mlsanity.com/paper/2002.10066/) (2020)
- [Performative Prediction: Past and Future](https://mlsanity.com/paper/2310.16608/) (2023)
- [Making Decisions under Outcome Performativity](https://mlsanity.com/paper/2210.01745/) (2022)
- [Long-Term Fairness with Unknown Dynamics](https://mlsanity.com/paper/2304.09362/) (2023)
- [Pushing the limits of fairness impossibility: Who's the fairest of them all?](https://mlsanity.com/paper/2208.12606/) (2022)
- [Fair Prediction with Endogenous Behavior](https://mlsanity.com/paper/2002.07147/) (2020)
- [A Possibility in Algorithmic Fairness: Can Calibration and Equal Error Rates Be Reconciled?](https://mlsanity.com/paper/2002.07676/) (2020)
- [Addressing Strategic Manipulation Disparities in Fair Classification](https://mlsanity.com/paper/2205.10842/) (2022)
- [Algorithmic Fairness in Performative Policy Learning: Escaping the Impossibility of Group Fairness](https://mlsanity.com/paper/2405.20447/) (2024)
- [Incentive-Aware Machine Learning; Robustness, Fairness, Improvement & Causality](https://mlsanity.com/paper/2505.05211/) (2025)
- [Classification in Equilibrium: Structure of Optimal Decision Rules](https://mlsanity.com/paper/2511.08347/) (2025)

## Abstract (arXiv)

In many real-world settings, institutions can and do adjust the consequences attached to algorithmic classification decisions, such as the size of fines, sentence lengths, or benefit levels. We refer to these consequences as the stakes associated with classification. These stakes can give rise to behavioral responses to classification, as people adjust their actions in anticipation of how they will be classified. Much of the algorithmic fairness literature evaluates classification outcomes while holding behavior fixed, treating behavioral differences across groups as exogenous features of the environment. Under this assumption, the stakes of classification play no role in shaping outcomes. We revisit classic impossibility results in algorithmic fairness in a setting where people respond strategically to classification. We show that, in this environment, the well-known incompatibility between error-rate balance and predictive parity disappears, but only by potentially introducing a qualitatively different form of unequal treatment. Concretely, we construct a two-stage design in which a classifier first standardizes its statistical performance across groups, and then adjusts stakes so as to induce comparable patterns of behavior. This requires treating groups differently in the consequences attached to identical classification decisions. Our results demonstrate that fairness in strategic settings cannot be assessed solely by how algorithms map data into decisions. Rather, our analysis treats the human consequences of classification as primary design variables, introduces normative criteria governing their use, and shows that their interaction with statistical fairness criteria generates qualitatively new tradeoffs. Our aim is to make these tradeoffs precise and explicit.