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

Street-level bureaucrats, such as caseworkers, triage nurses, and school administration, operate under a fundamental tension. The official policy on who to prioritize for services may conflict with bureaucrats estimation of who would benefit most from those services. The social theory of street-level bureaucracy argues that frontline agents use discretionary authority to bridge this gap, overriding policy recommendations when professional judgment identifies cases where doing so would meaningfully improve outcomes. As algorithmic recommendations become embedded in allocation settings, understanding the structure of this discretionary behavior is fundamental to designing tools that account for, rather than suppress, this value of professional judgment. We formalize discretion as a finite-horizon dynamic allocation problem. An agent implements a default policy but holds a limited budget of K overrides across T periods. Each period, the agent observes whether deviating from the default would yield a welfare gain and must decide whether to spend a scarce override now or conserve it for future opportunities. We show that the optimal policy is a state-dependent threshold rule and prove a behavioral invariance: for location-scale families of improvement distributions, the rate at which an optimal agent exercises discretion is independent of the amount of welfare gains and depends only on the distribution's shape. Fat-tailed gains induce patience (conserving overrides for rare, high-stakes cases); thin-tailed gains induce routine, front-loaded spending. We also compare the conceptual implications of our model with operational data from a homelessness service system. Override rates shift with short-run capacity openings in scarce housing, rising when recent exits free slots, and falling when interventions are congested. This could be the result of a perceived increase in the discretionary budget. Further, the temporal pattern of spending is front-loaded: override rates peak on Mondays and early in the fiscal year, consistent with the routine, early-spending behavior our model predicts under thin-tailed improvement distributions. These findings identify a systematic structure in both human and theoretically optimal decision-making, with direct implications for the design of human-AI allocation systems that are both more efficient and equitable.