💻 computer science

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

This paper develops a dynamic model of "budgeting discretion," demonstrating that street-level bureaucrats optimally ration their ability to override rigid policies by using a threshold rule that depends on both remaining resources and the statistical distribution of potential gains.

Original authors: Gaurab Pokharel, Sanmay Das, Patrick J. Fowler

Published 2026-02-11

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CC BY 4.0

Original authors: Gaurab Pokharel, Sanmay Das, Patrick J. Fowler

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The "Budget of Judgment": How Professionals Decide When to Break the Rules

Imagine you are a teacher in a massive school district. The school board has issued a strict, one-size-fits-all rule: "Every student who scores below 60% must attend summer school."

Most of the time, you follow this rule. It’s fair, it’s consistent, and it keeps you out of trouble with the principal. But every once in a while, you meet a student who scored a 59%, but they are actually a brilliant kid who just had a terrible week because their dog died. You know that if you "break the rule" and waive the summer school requirement, you’ll change their entire life.

But here is the catch: You only have a limited amount of "discretionary energy." If you spend all your time making special exceptions for every student, you’ll be too exhausted to handle the truly catastrophic cases later in the year. You have to ration your judgment like a precious resource.

This paper, Budgeting Discretion, explores exactly how professionals (like social workers, nurses, or border guards) manage this invisible "budget of judgment."

1. The Core Idea: Discretion is a Finite Resource

The researchers argue that "breaking the rules" isn't just a random act of kindness or rebellion. Instead, it is a strategic math problem.

In many high-stakes jobs, there is a Default Policy (the rulebook) and Discretion (the ability to say, "Wait, this case is special"). The paper treats discretion like a bank account. Every time you use your professional judgment to override a rule, you "spend" one unit of your budget. If you spend it all on small, mediocre improvements, you won't have anything left when a "Black Swan" event—a massive, life-altering emergency—comes along.

2. The "Shape" of the Opportunity (The Jackpot vs. The Steady Stream)

The most brilliant part of the paper is a mathematical discovery about the "shape" of the problems we face. They found that how a professional behaves depends on whether the "wins" they can achieve are steady or "jackpot-style."

The Steady Stream (Thin-Tailed): Imagine you are a gardener. Every time you pull a weed, you get a roughly equal amount of benefit. There are no "mega-weeds." In this world, you don't need to be patient. You should pull weeds as soon as you see them because waiting doesn't promise a bigger reward. Behavior: Routine and aggressive.
The Jackpot (Fat-Tailed): Imagine you are a fisherman. Most days you catch small fish, but once in a blue moon, you might hook a legendary giant marlin. If you use all your bait on the small fish, you’ll miss the marlin. In this world, you become a "wait-and-see" person. You ignore the small stuff to save your energy for the outlier. Behavior: Patient and selective.

The researchers proved that even if you change the units (measuring success in dollars vs. points), the behavioral pattern stays the same—it is determined entirely by whether the "jackpots" exist.

3. Real-World Proof: The Homelessness Case Study

To see if this math works in real life, the authors looked at data from homeless services in St. Louis. They watched how caseworkers decided who got "Transitional Housing" (the scarce, high-value resource) versus "Emergency Shelter" (the standard, default resource).

They found that caseworkers acted exactly like the "Strategic Budgeter" model:

The Monday Rush: Discretion spiked on Mondays. It’s like the workers were "batching" their decisions at the start of the week.
The Weekend Freeze: On weekends, discretion plummeted. Because the system's "intake" was effectively closed, the workers stopped trying to override the rules—they were essentially "saving" their budget for when the office reopened.
The Scarcity Reflex: When housing became scarce, caseworkers became much more "stingy" with their judgment. They stopped making "upgrades" and started "rationing" more strictly. They were effectively raising their "threshold" for what counted as a "special case."

The Big Picture

This paper tells us that when we design AI or automated systems to help humans make decisions, we shouldn't just focus on the rules. We need to realize that humans are strategic.

If we give a professional a rigid algorithm, they won't just follow it blindly; they will treat their ability to override that algorithm as a limited resource. If we want to build better systems, we need to design them to support that "budget of judgment," helping professionals save their best energy for the cases that truly matter.

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

1. Problem Statement

Street-level bureaucrats (e.g., caseworkers, nurses, judges) face a fundamental tension between following rigid, standardized policies and exercising professional discretion to address unique contextual nuances. While discretion can improve welfare, it is rarely an infinite resource. It is often constrained by downstream capacity (e.g., available housing slots or ICU beds), managerial oversight, or administrative bandwidth.

Existing literature often treats discretion as a static tradeoff between personal cost and public benefit. However, this paper identifies a dynamic rationing problem: using discretion today (e.g., overriding a policy to grant a scarce resource) reduces the ability to use that discretion for potentially higher-impact cases tomorrow. The authors seek to model how agents should optimally ration a finite "budget" of overrides over a finite time horizon.

2. Methodology

The paper employs a dual approach, combining formal mathematical modeling with empirical analysis of administrative data.

A. Theoretical Framework (Dynamic Programming)
The authors formalize discretion as a finite-horizon stochastic control problem.

The Model: An agent has a budget of $K$ overrides to be used over $T$ periods. In each period, the agent observes a "gain from discretion" ( $\Delta_t$ ), which is the incremental welfare improvement realized by overriding the default policy.
The Decision Rule: Using Dynamic Programming (DP), the authors derive that the optimal policy is a state-dependent threshold rule. An agent should only exercise discretion if the realized gain $\Delta_t$ exceeds a threshold $T_{\tau,k}$ , which represents the "shadow price" or opportunity cost of consuming one unit of the budget given the remaining time ( $\tau$ ) and remaining budget ( $k$ ).
Invariance Theorem: A major theoretical contribution is the proof that for "location-scale" families of improvement distributions, the rate at which an agent exercises discretion is invariant to the scale (units) of the gains and depends solely on the shape (specifically the tail heaviness) of the distribution.

B. Empirical Validation
The authors test their theory using administrative data from the St. Louis Homeless Management Information System (HMIS) (2008–2014).

Baseline Recovery: Since no formal "policy" existed in the historical data, they used a Short Explainable Rules Decision Tree (SER-DT) to recover the dominant heuristic policy from historical assignments.
Operationalization: Discretion is defined as deviations from this recovered baseline. They categorize overrides into "Upgrading" (assigning a more intensive resource, like Transitional Housing, than the policy suggests) and "Rationing" (assigning a less intensive resource, like Emergency Shelter, than the policy suggests).
Statistical Model: They use Generalized Linear Models (GLM) with a binomial-logit link to estimate how the probability of these overrides correlates with operational constraints (capacity, workload, and timing).

3. Key Contributions

Formalization of Budgeted Discretion: They move the study of street-level bureaucracy from static tradeoffs to a dynamic allocation problem, treating discretion as a finite, managed resource.
Behavioral Invariance Theorem: They provide a mathematical proof that an agent's "policy personality" (how often they act) is determined by the tail thickness of potential gains.
- Thin-tailed gains: Agents act routinely and early.
- Fat-tailed gains: Agents are patient, "hoarding" discretion for rare, high-impact outliers (the "black swan" events).
Empirical Linkage: They provide real-world evidence that caseworker discretion is not random but tracks operational scarcity and administrative cycles, validating the "rationing" mechanism.

4. Results

Theoretical Results:

Scale Invariance: Changing the units of welfare (e.g., from dollars to thousands of dollars) changes the numerical threshold but does not change the frequency of overrides.
Shape Dependence: In simulations, distributions with heavier tails (like Pareto or Lognormal) lead to much higher "patience" (higher probability of saving the budget for later periods) compared to thin-tailed distributions (like the Normal distribution).

Empirical Results:

Temporal Cycles: Discretion is significantly higher on Mondays (start-of-week batching) and significantly lower on weekends (consistent with reduced intake capacity and administrative constraints).
Capacity-Driven Rationing: The probability of "rationing" (downgrading a client to a less intensive resource) is higher when there is high slack in the default resource (Emergency Shelter) and lower when the scarce resource (Transitional Housing) becomes more available. This confirms that caseworkers dynamically adjust their rationing standards based on inventory.
Seasonality: Discretion patterns shift over the federal fiscal year, suggesting institutional/budgetary cycles influence how judgment is applied.

5. Significance

This paper has profound implications for Public Administration and AI/Algorithmic Governance:

For Policy Design: It suggests that "one-size-fits-all" algorithmic policies may fail because they don't account for the fact that humans will naturally ration their overrides.
For Auditing: It provides a framework for auditors to distinguish between "biased" discretion and "optimal" discretion. If an agent's override pattern matches the predicted "shape-dependent" behavior, it may indicate strategic, welfare-maximizing management of scarce resources rather than procedural error.
For Decision Support Systems (DSS): Instead of just telling a human what to do, future DSS should help manage when to use discretion, helping professionals balance immediate needs against the long-term value of their limited authority.