Feature-based Uncertainty Model for School Choice

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.

Full version for the paper with the same title at AAMAS 2026