Budgeting Discretion: Theory and Evidence on Street-Level Decision-Making

TL;DR

This paper develops Budgeted Discretion, a finite-horizon dynamic model in which frontline agents manage a limited override budget $K$ over $T$ periods to improve outcomes relative to a default policy. The optimal rule is a state-dependent threshold that governs when to exercise discretion, and a central result shows an invariance: for location-scale improvement distributions, the override rate is determined only by the distribution’s shape, not payoff units; fat-tailed gains induce patience, while thin-tailed gains promote more routine spending. The authors validate the theory with homelessness services data (HMIS), showing discretion rises with short-run capacity openings and exhibits start-of-week batching and weekend intake constraints, consistent with capacity-driven opportunity costs. The findings provide a unit-free lens to compare discretionary patterns across settings and offer guidance for auditing override patterns and designing decision-support systems that explicitly budget discretion. Overall, the framework connects abstract dynamic programming to observable street-level behavior under scarcity, with practical implications for policy design and evaluation in public services.

Abstract

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.

Figures (2)

• Figure 1: Scale Invariance and Shape Dependence ($T=20, K=5$): We verify that the optimal spending probability is invariant to the scale of rewards (a) and is instead driven by the tail weight of the gain distribution (b).
• Figure 2: The Opportunity Cost Map: Heatmap of optimal thresholds $\mathcal{T}_{\tau,k}$ for a Pareto distribution ($T=20, K=5$). Darker regions indicate states where the agent requires a very high gain to justify spending. The thresholds naturally decay as time runs out ($\tau \to 0$) or budget becomes abundant relative to time ($k \to \tau$).

Theorems & Definitions (16)

• proposition 1
• proof : Sketch of proof
• theorem 1: Shape dependence of optimal policy
• proof : Sketch of proof
• Lemma 1: DP vs. Oracle Benchmark
• proof : Sketch of proof
• Lemma 2: Internal DP Behavior
• proof : Sketch of proof
• Corollary 1: Tail thickness and patience
• proposition 1