Optimal classification with outcome performativity

Elizabeth Maggie Penn

Papers from arXiv.org

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.

Date: 2025-04
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