This paper characterizes optimal classification when individuals adjust their behavior in response to the classification rule. We model the interaction between a designer and a population as a Stackelberg game: the designer selects a classification rule anticipating how individuals will comply, cheat, or abstain in order to obtain a favorable classification. Under standard monotone likelihood ratio assumptions, and for a general set of classification objectives, optimal rules belong to a small and interpretable family--single-threshold and two-cut rules--that encompass both conventional and counterintuitive designs. Our results depart sharply from prior findings that optimal classifiers reward higher signals. In equilibrium, global accuracy can be maximized by rewarding those with lower likelihood ratios or by concentrating rewards or penalties in a middle band to improve informational quality. We further characterize classification objectives that rule out socially harmful equilibria that disincentivize compliance for some populations.

翻译：本文刻画了当个体根据分类规则调整其行为时的最优分类问题。我们将设计者与群体之间的互动建模为斯塔克尔伯格博弈：设计者选择一个分类规则，并预见到个体为获得有利分类将如何合规、作弊或放弃。在标准的单调似然比假设下，针对一般性的分类目标集合，最优规则属于一个简洁且可解释的族——单阈值与双截断规则——该族同时涵盖了传统设计与反直觉设计。我们的结果显著区别于先前关于最优分类器奖励更高信号的结论。在均衡状态下，全局准确率可以通过奖励那些具有较低似然比的个体来实现，或者通过将奖励或惩罚集中在中间区间以提高信息质量。我们进一步刻画了能够排除某些群体中抑制合规动机的社会有害均衡的分类目标。