Uneven playing fields in school choice: the consequences of manipulability

 Here's a study of a school choice system using the manipulable (not strategy proof) immediate acceptance ("Boston") algorithm for school choice, in the Wake County Public School System in North Carolina, the 15th largest in the U.S. (The authors are all market design economists at North Carolina State University.)

Identifying the Harm of Manipulable School-Choice Mechanisms
By Umut Dur, Robert G. Hammond, and Thayer Morrill
American Economic Journal: Economic Policy , February 2018, 10(1): 187–213
https://doi.org/10.1257/pol.20160132

Abstract: An important but under-explored issue in student assignment procedures is heterogeneity in the level of strategic sophistication among students. Our work provides the first direct measure of which students rank schools following their true preference order (sincere students) and which rank schools by manipulating their true preferences (sophisticated students). We present evidence that our proxy for sophistication captures systematic differences among students. Our results demonstrate that sophisticated students are 9.6 percentage points more likely to be assigned to one of their preferred schools. Further, we show that this large difference in assignment probability occurs because sophisticated students systematically avoid over-demanded schools.

Here's the operational definition of a sophisticated student:
" In their application procedure, students have a two-week window during which they must log into a website and submit their preferences. A student is free to change her ranking as many times as she wishes. Moreover, upon each visit, a student learns how many students have ranked each school first. Therefore, a sophisticated student benefits from logging into the website multiple times or logging in closer to the deadline. On the other hand, a student submitting her true preferences needs only to log into the website once.
"Following this logic, our classification of sincere and sophisticated students is drawn from the number of logins to the application website. Specifically, we classify students who log in once as sincere and those who log in more than once as sophisticated. We then show a series of results to demonstrate that our login proxy for sophistication is capturing important, systematic differences across students. For instance, some students who visit the application website multiple times change their rankings near the end of the selection period by removing popular (i.e., over-demanded) schools from the top of their rankings. More generally, we demonstrate that sophisticated students avoid over-demanded schools by not ranking them as their first choice. As a result, sophisticated students are more likely to receive an assignment but, conditional on receiving an assignment, are less likely to be assigned to a highly over-demanded school."