Revisiting Fairness Impossibility with Endogenous Behavior

In a groundbreaking arXiv paper, researchers Elizabeth Maggie Penn and John W. Patty challenge a foundational assumption in algorithmic fairness. Their work, "Revisiting Fairness Impossibility with Endogenous Behavior," moves beyond the static models that dominate fairness literature. They introduce the critical concept of "stakes"—the real-world consequences like fines or benefits attached to AI classifications—and demonstrate that people strategically adapt their behavior in anticipation of these outcomes. This endogenous behavior fundamentally changes the fairness calculus.

The paper's core finding is that the famous impossibility theorem, which states that error-rate balance (equal false positive/negative rates across groups) and predictive parity (equal precision) are incompatible, breaks down in strategic settings. The authors construct a novel two-stage design: first, a classifier standardizes its statistical performance, then it adjusts the stakes to induce comparable behavioral responses. This technically resolves the impossibility but creates a new, profound ethical tradeoff: it requires applying different consequences to identical classification decisions for different groups. The analysis forces a paradigm shift, treating human consequences as primary design variables rather than just evaluating algorithmic mappings.