Feature-based Uncertainty Model for School Choice

2026-02-13

Technology Category

• Machine Learning: Learning Preferences or Rankings
• Knowledge Representation and Reasoning: Preferences
• Reasoning under Uncertainty: Decision/Utility Theory

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

In this work, we consider a school choice scenario where a student does not exactly know which college is better for her. Although it is hard for a student to obtain an exact preference, she can usually compare specific features of colleges, such as reputation, location, and campus facilities. Motivated by this, we propose a feature-based uncertainty model for school choice where a student's preference is based on a linear combination of her utilities over different features, and the coefficients of the combination are treated as random variables. Our main goal is to achieve a higher probability of stability (ProS) and incentive compatibility (IC) for students. Unfortunately, these two goals are incompatible in general. We show that a student-proposing deferred acceptance (DA) that prioritizes colleges with higher expected ranking can achieve a worst-case approximation ratio of $(1/n)^n$ on ProS, while a DA with a carefully defined iterated comparison vector can guarantee the strongest achievable form of IC. Finally, we provide additional results for some specific restrictions on the model.

Problem

• school choice
• feature-based uncertainty
• stability
• incentive compatibility
• preference modeling

Innovation

• feature-based uncertainty
• school choice
• deferred acceptance
• probability of stability
• incentive compatibility