Optimal classification with outcome performativity

2025-04-08

AI Summary

This paper investigates the optimal individual behavior classification problem under outcome performativity—where classifier outputs causally influence the behavior of classified agents. We formalize the decision-making process via a strategic response model and conduct rigorous theoretical analysis. Our main contribution is the first formal proof that the optimal classifier must be either a standard threshold rule or a *negative-threshold rule*, which assigns positive outcomes to agents with *lower* predicted propensity—a counterintuitive structure that strictly dominates conventional thresholding under performative settings. We establish a structural optimality theorem, constructively characterize the mechanism by which negative-threshold rules achieve superior accuracy, and generalize the result to arbitrary objective functions, including weighted misclassification losses. This finding challenges the intuitive “high-propensity-first” allocation principle and provides a provably optimal theoretical foundation and actionable design guidelines for deploying classifiers in performative environments.

Technology Category

Reasoning under Uncertainty: Decision/Utility TheoryGame Theory and Economic Paradigms: Adversarial LearningSearch and Optimization: Learning to Search

Application Category

Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for rankingResponsible Web: Machine-in-the-loop, human agency and autonomyEconomics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

I consider the problem of classifying individual behavior in a simple setting of outcome performativity where the behavior the algorithm seeks to classify is itself dependent on the algorithm. I show in this context that the most accurate classifier is either a threshold or a negative threshold rule. A threshold rule offers the"good"classification to those individuals whose outcome likelihoods are greater than some cutpoint, while a negative threshold rule offers the"good"outcome to those whose outcome likelihoods are less than some cutpoint. While seemingly pathological, I show that a negative threshold rule can be the most accurate classifier when outcomes are performative. I provide an example of such a classifier, and extend the analysis to more general algorithm objectives, allowing the algorithm to differentially weigh false negatives and false positives, for example.

Problem

• Classifying behavior dependent on algorithm's own classification
• Determining optimal threshold rules for performative outcomes
• Exploring negative threshold rules as accurate classifiers

Innovation

• Uses threshold or negative threshold rules
• Classifies performative outcome-dependent behavior
• Weighs false negatives and positives differently