Playing on a Level Field: Sincere and Sophisticated Players in the Boston Mechanism with a Coarse Priority Structure

TL;DR

This paper compares the outcomes of sincere and strategic students under the manipulable Boston Mechanism and the strategy-proof Deferred Acceptance in large markets, revealing complex preferences and market forces influencing mechanism choice.

Contribution

It provides robust theorems showing that many students prefer either mechanism, and that sincerity can sometimes be beneficial, reconciling theory with empirical observations.

Findings

Many students prefer Boston over Deferred Acceptance.

Some populations benefit from sincerity in the Boston Mechanism.

Market forces influence mechanism selection.

Abstract

Who gains and who loses from a manipulable school-choice mechanism? Studying the outcomes of sincere and sophisticated students under the manipulable Boston Mechanism as compared with the strategy-proof Deferred Acceptance, we provide robust "anything-goes" theorems for large random markets with coarse priority structures. I.e., there are many sincere and sophisticated students who prefer the Boston Mechanism to Deferred Acceptance, and vice versa. Some populations may even benefit from being sincere (if also perceived as such). Our findings reconcile qualitative differences between previous theory and known empirical results. We conclude by studying market forces that can influence the choice between these mechanisms.