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.

翻译：本文研究一种择校场景，其中学生无法确切知晓哪所大学更适合自己。尽管学生难以获得精确的偏好排序，但通常能够比较大学的具体特征，例如声誉、地理位置和校园设施。受此启发，我们提出一种基于特征的择校不确定性模型：学生的偏好建立在其对不同特征效用线性组合的基础上，而组合系数被视为随机变量。我们的主要目标是使学生获得更高的稳定性概率与激励相容性。遗憾的是，这两个目标在一般情况下不可兼得。研究表明，采用期望排名优先的高校排序策略的学生主导递延接受算法，可在稳定性概率上达到$(1/n)^n$的最坏情况近似比；而通过精确定义的迭代比较向量实施的递延接受算法，则可保证可达的最强激励相容性形式。最后，我们针对模型的若干特定约束给出了补充结论。