constrained school choice- an experimental study presentation · constrained school choice: an...

Constrained School Choice: An Experimental StudyPresentation by Jonathan Hohl

Constrained School Choice: An Experimental Study

by Caterina Calsamigla, GuillameHaeringer, Flip Klijn


School Choice Problem

Abdulkadiroglu, Sönmez (2003): ● set of schools & set of students ● students:

- strict preferences over schools,- option of remaining unassigned

- prefers being unassigned to being assigned to given school: unacceptable / otherwise acceptable

● schools:- fixed capacity- strict priority order

→ Matching

How can students be assigned to a given number ofvacant seats in school programs the best possible way?


3 School Choice mechanismsBoston (BOS): Each school assigns seats one at a time to the students that apply to it following itspriority order. If the school capacity is or was attained, the school rejects anyremaining future applicants. Terminates when all students have been assigned.

Student Optimal Stable Matching (SOSM):Each school tentatively assigns seats one at a time to the students that apply to it orthat were tentatively assigned a seat in a previous round, following its priority order.When the school capacity is attained the school rejects any remaining students thatapply to it. Terminates then no student is rejected. Then the tentative matching becomes final.

Top Trading Cycles (TTC):Each school with vacant seats „points“ to the student with hightest priority among thestudents that have not been assigned a seat yet. This procedure, together with theabove described procedure for the students, induces a cycle or cycles of studentsand schools. If a student is in a cycle he is assigned a seat at the school he appliesto. If a school is in a cycle then its number of vacant seats is decreased by one. If aschool has no more vacant seats then it is no longer availabe and students thatapplied to it are rejected.Terminates when all students have been assigned.


Implementation of a constraintTheoretical assumption: unlimited number of acceptable schools

BUT in practice → Constrained list of preferences

Consequence of a constraint:● fear of rejection → true preferences are not revealed

Suboptimal Matching


Experimental Design I● 36 students, 36 school seats

● 7 schools:

● To each student corresponds a district school.Each school is the district school of as many students as itscapacity.

1 2 3 2 3 41 6

2x 5x

5A, B C, D, E,

F, G


Experimental Design II

● for each school:

● for each student (2 different environments):1. Random

Or2. Designed: preferences depend on quality, proximity and a random factor

→ competitive (smaller capacity) schools and districtschools more likely to be amongst the most preferredschools

List of priorities

1

...

X

…

36

Students livingin the district ofthat school

Random orderof leftoverstudents

X = Number of seats


Experimental Design III

3 x 2 x 2 Design● 3 mechanisms● designed / undesigned● constrained / unconstrained

● → overall 12 different treatments

● Payoffs dependent on the school students are assigned to

→ Observation of 4 different aspects


Suboptimal Play● For SOSM and TTC in the constrained case the number of

participants revealing their true preferences significantlyreduced. (For BOS truth-telling no dominant strategy)


Misrepresentations● 2 Biases:

● Small School Bias (SSB):lowering the position of a more competitive (smaller)school in the ranking

● District School Bias (DSB):ranking the district school higher in list than in preferences

→ significant differences for both biases between constrainedand unconstrained case

DSB SSB


Efficiency and Stability●

● stability: guarantees that the schools an individual prefers tothe one he has been assigned to are filled with higherpriority students

→ low for all mechanisms.

mean payoffs in €


Segregation● Segregation increases significantly for all mechanism when

constraint is imposed.


Conclusion● Constraint has an overall negative impact:

➢ less truth telling➢ reduced efficiency and stability➢ increased segregation

● much of the use of dominated strategies derives fromaspects that are not part of the mechanisms themselves→ capacities in schools

● Pointing out the importance to consider small and seeminglyunimportant details in matching mechanisms

constrained school choice- an experimental study presentation · constrained school choice: an...

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