战略分类缺失的一个杠杆：审计风险
Strategic Classification Has a Missing Lever: Audit Risk
- University of California, San Diego（加州大学圣地亚哥分校）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出战略分类中联合设计分类器与审计档案的模型，证明问题可分解，刻画最优审计分配，并指出特征可博弈性取决于验证政策。
AI中文摘要：
战略分类研究的是，当被分类的智能体可以针对分类器调整其特征时，决策者应如何选择分类器。在现有模型中，分类器是决策者唯一可用的工具，因此，一个具有预测性但易于伪造的特征只能被降权或丢弃。然而，在许多场景中，决策者还可以进行验证：贷款机构核实收入，招生办公室检查文件，税务机关审计申报。在本文中，我们提出一个战略分类模型，其中企业联合设计一个线性分类器和一个“审计档案”，该档案为每个可伪造特征分配一个被检测的概率和被抓住时的惩罚。我们证明，在线性成本下，分类器仅通过其引发的博弈租金分布来影响审计问题，因此联合设计问题可分解为选择评分规则和审计分配问题。我们利用这一分解来刻画最优审计分配，识别分配问题何时易于处理以及何时是NP难的（即，当智能体在检查上限下可以通过重叠特征进行博弈时），并界定一个必须通过审计学习租金的企业所遭受的遗憾。我们进一步表明，审计强度是一个需要调优而非最大化的量：福利关于它是单峰的，且企业和一个社会规划者在提供给定威慑水平的检测与惩罚组合上存在分歧。值得注意的是，两个具有相同成本和因果结构的人群可以在一个领域进行博弈而在另一个领域改善，这种差异是仅考虑成本的模型无法解释的。总之，我们的发现强调，一个特征是否“可博弈”取决于机构的验证政策，同样也取决于特征本身。
英文摘要：
Strategic classification studies how a decision maker should choose a classifier when the agents being classified can adjust their features in response to it. In existing models, the classifier is the only instrument available to the decision maker, and therefore a feature that is predictive but easy to fake can only be down-weighted or discarded. However, in many settings the decision maker can also verify: lenders verify income, admissions offices check documents, and tax authorities audit returns. In this paper, we propose a model of strategic classification in which the firm jointly designs a linear classifier and an \emph{audit profile}, which assigns to each fakeable feature a probability of detection and a penalty when caught. We show that under linear costs, the classifier affects the audit problem only through the distribution of gaming rents it induces, so that the joint design problem decomposes into the choice of a score rule and an audit allocation problem. We use this decomposition to characterize the optimal audit allocation, to identify when the allocation problem is tractable and when it is NP-hard (namely, when agents can game through overlapping features under an inspection cap), and to bound the regret of a firm that has to learn the rents by auditing. We further show that audit intensity is a quantity to be tuned rather than maximized: welfare is single-peaked in it, and a firm and a social planner disagree on the mix of detection and penalty that delivers a given level of deterrence. Notably, two populations with identical costs and causal structure can game in one domain and improve in the other, a difference that a cost-only model cannot account for. Together, our findings highlight that whether a feature is ``gameable'' depends on the institution's verification policy as much as on the feature itself.
