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, 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, the designer may deliberately reward those with lower likelihood ratios or concentrate rewards/penalties in a middle band to improve informational quality.

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而采取服从、欺骗或放弃等行为。在标准的单调似然比假设下，最优规则属于一个简洁且可解释的族类（单阈值与双截断规则），涵盖传统及反直觉的设计。我们的结果与先前认为最优分类器奖励更高信号的研究结论显著不同：在均衡中，设计者可能有意奖励具有较低似然比的个体，或将奖励/惩罚集中于中间区间，以提高信息质量。