Finding a fair classifier within a large feasible set

Develop a practical method that, given evidence of a large set of feasible models satisfying epsilon-relaxed parity constraints across multiple fairness metrics (specifically False Positive Rate, False Negative Rate, and Positive Predictive Value) and multiple groups, constructs or identifies a classifier that achieves these constraints in practice.

Background

The paper demonstrates, both analytically and empirically, that many models can satisfy relaxed parity across several fairness metrics simultaneously. While this challenges the strict practical implications of the impossibility theorem, it raises a key next-step problem: operationalizing the selection or construction of such a model.

The authors explicitly frame this as an open question and note related but nascent efforts, underscoring the need for algorithmic procedures that can reliably find fair classifiers within the identified fairness region.

References

"Our work leaves open an important next step in ensuring fairness across multiple metrics and for multiple groups: Once we know there is a large set of feasible models, how do we find such a model? ... Unfortunately, these questions are beyond our scope."

— The Possibility of Fairness: Revisiting the Impossibility Theorem in Practice  (2302.06347 - Bell et al., 2023) in Section 6, Conclusions and social impact

Corridor regularization controls specified trait coordinates; large or unknown trait sets, probe misspecification, adaptive evasion, and longer-training escape beyond the fixed coordinate remain open, although probe-wording and two-trait tests broaden coverage.

— Subliminal Learning as Trait-Direction Drift: A Mechanism and Targeted Control under SFT Distillation  (2609.01091 - Liu et al., 1 Sep 2026) in Section 5, Limitations