Multitasking, Multi-Armed Bandits, and the Italian Judiciary

We model how a judge schedules cases as a multi-armed bandit problem. The model indicates that a first-in-first-out (FIFO) scheduling policy is optimal when the case completion hazard rate function is monotonic. But there are two ways to implement FIFO in this context: at the hearing level or at the case level. Our model indicates that the former policy, prioritizing the oldest hearing, is optimal when the case completion hazard rate function decreases, and the latter policy, prioritizing the oldest case, is optimal when the case completion hazard rate function increases. This result convinced six judges of the Roman Labor Court of Appeals -- a court that exhibits increasing hazard rates -- to switch from hearing-level FIFO to case-level FIFO. Tracking these judges for eight years, we estimate that our intervention decreased the average case duration by 12% and the probability of a decision being appealed to the Italian supreme court by 3.8%, relative to a 44-judge control sample.