Revisiting Fairness Impossibility with Endogenous Behavior

2026-04-07

AI Summary

This study addresses a critical limitation in traditional algorithmic fairness research, which treats group behavioral differences as exogenous and overlooks individuals’ strategic responses to classification decisions and their endogenous interaction with classification stakes. To remedy this, the paper proposes a two-stage mechanism: first standardizing statistical performance across groups, then differentially adjusting classification stakes to induce convergent behavior. By integrating game-theoretic reasoning with fairness theory, the work demonstrates that under strategic responses, error rate balance and predictive consistency can coexist—thereby circumventing classical impossibility results. However, this comes at the cost of a novel form of inequality: identical classifications may entail different consequences across groups. The study establishes classification stakes as a central design variable and delineates a new trade-off between statistical fairness and consequential equity.

Technology Category

Game Theory and Economic Paradigms: Fair DivisionPhilosophy and Ethics of AI: Bias, Fairness & EquityMachine Learning: Ethics, Bias, and Fairness

Application Category

Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environmentsUser Modeling, Personalization and Recommendation: Fairness-aware retrieval and rankingResponsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

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.

Problem

• algorithmic fairness
• strategic behavior
• endogenous response
• fairness impossibility
• classification stakes

Innovation

• endogenous behavior
• algorithmic fairness
• strategic response
• stakes adjustment
• fairness impossibility