Informational Size in School Choice

TL;DR

This paper introduces a new measure of informational size in school choice mechanisms, revealing that strategy-proof mechanisms are less informative than non-strategy-proof ones and that TTC demands less information than DA in larger markets.

Contribution

It proposes a novel informational size metric for matching mechanisms, providing insights into their information demands and comparative advantages in different market sizes.

Findings

IA mechanism requires more information than DA, explaining its popularity.

TTC demands less information than DA when at least four students are involved.

Informational size helps understand mechanisms' auditability, manipulation vulnerability, and privacy features.

Abstract

This paper introduces a novel measurement of informational size to school choice problems, which inherits its ideas from Mount and Reiter (1974). This concept measures a matching mechanism's information size by counting the maximal relevant preference and priority rankings to secure a certain pairwise assignment of a student to a school across all possible matching problems. Our analysis uncovers two key insights. First, the three prominent strategy-proof matching mechanisms, the deferred acceptance (DA) mechanism, the top trading cycles (TTC) mechanism, and the serial dictatorship (SD) mechanism, is (strictly) less informative than the non-strategy-proof immediate acceptance (IA) mechanism. This result highlights a previously omitted advantage of IA in term of its information demand, which partially explain the its popularity in real-world matching problems especially when acquiring information is both pecuniarily and cognitively costly. Second, when the matching problem contains at least four students, the TTC demands less information compared to the DA to implement a desired allocation. The issue of comparison between TTC and DA has puzzled researchers both in theory (Gonczarowski and Thomas, 2023) and in experiment (Hakimov and Kubler, 2021). Our result responds to this issue from an informational perspective: in experiments with relatively fewer students, agents tend to prefer DA over TTC as DA requires fewer information to secure one's allocation in all problems (Guillen and Veszteg, 2021), while the opposite is true when the market size increases (Pais et al., 2011). Among others, our informational size concept offers a new perspective to understand the differences in auditability (Grigoryan and Moller, 2024), manipulation vulnerability (Pathak and Sonmez, 2013), and privacy protection (Haupt and Hitzig, 2022), among some commonly used matching mechanisms.