The Role of Precedence Order in Matching with Multi-Criteria Admissions

2026-07-31

AI Summary

This study investigates how priority ordering among multiple criteria affects matching outcomes and the preferences of individual criteria in school choice settings, particularly when rankings across criteria are misaligned and arbitrary. Integrating mechanism design theory, comparative statics, and large-market asymptotics, it derives the first criterion-level comparative static results under general responsive preferences. The core finding is that, holding the applicant pool fixed, swapping the last two criteria in the priority order typically makes all parties prefer arrangements in which their own criterion appears later. This effect holds universally under the Boston mechanism but may reverse under the Deferred Acceptance mechanism due to rejection chains; however, such reversals vanish asymptotically in sufficiently thick large markets. Rejection chains are identified as the sole source of reversals in priority-ordering effects.

Abstract

Admission systems often fill seats by applying criterion-specific rankings sequentially. We derive criterion-wise comparative statics with respect to precedence order when rankings may be arbitrarily nonaligned, and each criterion evaluates the entire admitted set through a responsive preference. For a fixed applicant set, reversing the final two blocks makes each criterion weakly prefer the outcome in which its block is later. This comparison can reverse if two blocks are followed by another criterion, even under reserve-type rankings. Under student-proposing deferred acceptance, it can also reverse with two criteria because rejection chains change the focal college's applicant set; such feedback is the only possible source of failure. In regular large markets, failures vanish for almost all colleges and, under sufficient thickness, uniformly across colleges. Under the Boston mechanism, final acceptance prevents feedback; thus the comparison holds in every finite market for fixed submitted rank-order lists and criterion-independent acceptability.

Problem

• precedence order
• multi-criteria admissions
• matching
• comparative statics
• responsive preferences

Innovation

• precedence order
• multi-criteria matching
• deferred acceptance
• comparative statics
• responsive preferences