Capacity Constraints Make Admissions Processes Less Predictable

TL;DR

Capacity constraints in admissions create complex dependencies that reduce the accuracy of machine learning predictions, especially when applicant pools differ from training data, raising concerns about prediction reliability.

Contribution

This paper introduces theoretical measures of instability and variability to analyze how capacity constraints affect ML prediction performance in admissions.

Findings

Prediction accuracy declines with applicant pool shifts.

Higher instability and variability lead to larger performance drops.

Empirical validation using NYC high school data supports the theory.

Abstract

Machine learning models are often used to make predictions about admissions process outcomes, such as for colleges or jobs. However, such decision processes differ substantially from the conventional machine learning paradigm. Because admissions decisions are capacity-constrained, whether a student is admitted depends on the other applicants who apply. We show how this dependence affects predictive performance even in otherwise ideal settings. Theoretically, we introduce two concepts that characterize the relationship between admission function properties, machine learning representation, and generalization to applicant pool distribution shifts: instability, which measures how many existing decisions can change when a single new applicant is introduced; and variability, which measures the number of unique students whose decisions can change. Empirically, we illustrate our theory on individual-level admissions data from the New York City high school matching system, showing that machine learning performance degrades as the applicant pool increasingly differs from the training data. Furthermore, there are larger performance drops for schools using decision rules that are more unstable and variable. Our work raises questions about the reliability of predicting individual admissions probabilities.