Street-level bureaucrats, such as caseworkers and border guards routinely face the dilemma of whether to follow rigid policy or exercise discretion based on professional judgement. However, frequent overrides threaten consistency and introduce bias, explaining why bureaucracies often ration discretion as a finite resource. While prior work models discretion as a static cost-benefit tradeoff, we lack a principled model of how discretion should be rationed over time under real operational constraints. We formalize discretion as a dynamic allocation problem in which an agent receives stochastic opportunities to improve upon a default policy and must spend a limited override budget K over a finite horizon T. We show that overrides follow a dynamic threshold rule: use discretion only when the opportunity exceeds a time and budget-dependent cutoff. Our main theoretical contribution identifies a behavioral invariance: for location-scale families of improvement distributions, the rate at which an optimal agent exercises discretion is independent of the scale of potential gains and depends only on the distribution's shape (e.g., tail heaviness). This result implies systematic differences in discretionary "policy personality." When gains are fat-tailed, optimal agents are patient, conserving discretion for outliers. When gains are thin-tailed, agents spend more routinely. We illustrate these implications using data from a homelessness services system. Discretionary overrides track operational constraints: they are higher at the start of the workweek, suppressed on weekends when intake is offline, and shift with short-run housing capacity. These results suggest that discretion can be both procedurally constrained and welfare-improving when treated as an explicitly budgeted resource, providing a foundation for auditing override patterns and designing decision-support systems.

翻译：街头官僚（如个案工作者和边境警卫）在日常工作中常面临遵循僵化政策还是依据专业判断行使裁量权的两难困境。然而，频繁的政策推翻会威胁决策一致性并引入偏见，这解释了为何官僚机构常将裁量权作为有限资源进行配给。现有研究多将裁量权建模为静态的成本效益权衡，但缺乏在真实运作约束下裁量权应如何随时间进行理性配给的原则性模型。我们将裁量权形式化为动态分配问题：代理人随机获得改进默认政策的机会，并必须在有限时间范围T内使用有限的推翻预算K。研究表明，政策推翻遵循动态阈值规则：仅当机会收益超过随时间与预算变化的临界值时方可行使裁量权。我们的核心理论贡献在于发现行为不变性：对于改进分布的位移-尺度族，最优代理人行使裁量权的速率独立于潜在收益的尺度，仅取决于分布形态（如尾部厚度）。这一结果意味着裁量权“政策个性”存在系统性差异：当收益呈厚尾分布时，最优代理人表现耐心，为异常值保留裁量权；当收益呈薄尾分布时，代理人更频繁地行使裁量权。我们通过无家可归者服务系统的数据验证这些推论。裁量性推翻行为与实际运作约束相符：在工作周初期较高，在周末因服务系统关闭而受抑制，并随短期住房容量变化而调整。这些结果表明，当裁量权被明确视为预算化资源时，既能受到程序性约束又能提升社会福利，为审计推翻行为模式与设计决策支持系统提供了理论基础。