[Paper Review] Predictive Enforcement

Yeon‐Koo Che, Jinwoo Kim+1 more|arXiv (Cornell University)|May 8, 2024

Regulation and Compliance Studies5 citations

TL;DR

The paper develops a dynamic, data-informed enforcement model where enforcement decisions influence crime data collection, and analyzes optimal predictive enforcement under exogenous and endogenous crime with a changing-world bandit framework.

ABSTRACT

We study law enforcement guided by data-informed predictions of "hot spots" for likely criminal offenses. Such "predictive" enforcement could lead to data being selectively and disproportionately collected from neighborhoods targeted for enforcement by the prediction. Predictive enforcement that fails to account for this endogenous "datafication" may lead to the over-policing of traditionally high-crime neighborhoods and performs poorly, in particular, in some cases as poorly as if no data were used. Endogenizing the incentives for criminal offenses identifies additional deterrence benefits from the informationally efficient use of data.

Motivation & Objective

• Motivate and formalize how data-informed predictions influence enforcement and data collection in policing contexts.
• Develop a continuous-time bandit framework with a changing world to model enforcement and datafication.
• Derive an optimal predictive enforcement policy (OP) and compare it to non-predictive (NP) and greedy predictive (GP) benchmarks.
• Endogenize crime incentives to study how enforcement affects criminal behavior and data collection.
• Characterize when predictive enforcement improves welfare and when it can underperform due to data feedback loops.

Proposed method

• Model a policymaker (PM) choosing enforcement y_t in [0,1] at cost c per unit to prevent crimes arriving as a Poisson process with rate lambda when the state is high (H).
• State dynamics follow a continuous-time Markov chain with switching rates rho_L and rho_H and stationary probability pi_0.
• Prediction updates the PM’s belief p_t about the state being H via Bayes’ rule, with belief dynamics defined by a differential equation dot{p}=f(p,y) that includes natural state transitions and learning from detections.
• Formulate three enforcement regimes: non-predictive (NP), greedy predictive (GP), and optimal predictive (OP), each with distinct decision rules y(p).
• Solve a dynamic programming problem leading to a Hamilton–Jacobi–Bellman (HJB) equation for the value function under OP, yielding a cutoff policy y(p)=1 if p>hat{p} and 0 otherwise.
• Show that OP’s cutoff hat{p} lies relative to pi_0 and pi_1 depending on the exogenous crime rate x lambda, and that OP can dominate GP or NP under intermediate crime rates.

Experimental results

Research questions

• RQ1 How does endogenous datafication (data collection driven by enforcement) affect the welfare and effectiveness of predictive enforcement?
• RQ2 Under exogenous crime, when is predictive enforcement (OP) better than non-predictive (NP) or greedy predictive (GP) policies?
• RQ3 How does changing-world dynamics (state that evolves over time) alter the value of learning and the structure of optimal enforcement?
• RQ4 What happens to enforcement and crime when crime incentives respond to enforcement (endogenous crime) and data are observable by criminals?
• RQ5 When do predictive policies fail due to feedback loops and when do they yield superior deterrence?

Key findings

• Under exogenous crime, GP does not outperform NP in the long run unless there is external learning; OP can outperform GP by exploring more (lower cutoff than the myopic one) at intermediate costs.
• The optimal cutoff hat{p} lies in three cases depending on x lambda and c, yielding Case 1 (low crime rate) with hat{p} > pi_0, Case 2 (high crime rate) with hat{p}=hat{p}_M and hat{p}≤pi_1, and Case 3 (intermediate) with hat{p} in (pi_1, pi_0) and hat{p}<hat{p}_M.
• Endogenizing crime incentives (criminals’ response to anticipated enforcement) yields stronger deterrence under OP than GP, since OP accounts for information value and strategic responses.
• With sufficiently small c, GP and OP coincide in policy, but OP still yields lower crime in equilibrium when incentives are endogenous.
• As the predictive advantage erodes (e.g., criminals gain access to data), the three regimes converge to a common outcome, highlighting the conditional value of prediction.