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Constrained School Choice: An Experimental StudyPresentation by Jonathan Hohl
Constrained School Choice: An Experimental Study
by Caterina Calsamigla, GuillameHaeringer, Flip Klijn
Constrained School Choice: An Experimental StudyPresentation by Jonathan Hohl
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?
Constrained School Choice: An Experimental StudyPresentation by Jonathan Hohl
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.
Constrained School Choice: An Experimental StudyPresentation by Jonathan Hohl
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
Constrained School Choice: An Experimental StudyPresentation by Jonathan Hohl
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
Constrained School Choice: An Experimental StudyPresentation by Jonathan Hohl
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
Constrained School Choice: An Experimental StudyPresentation by Jonathan Hohl
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
Constrained School Choice: An Experimental StudyPresentation by Jonathan Hohl
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)
Constrained School Choice: An Experimental StudyPresentation by Jonathan Hohl
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
Constrained School Choice: An Experimental StudyPresentation by Jonathan Hohl
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 €
Constrained School Choice: An Experimental StudyPresentation by Jonathan Hohl
Segregation● Segregation increases significantly for all mechanism when
constraint is imposed.
Constrained School Choice: An Experimental StudyPresentation by Jonathan Hohl
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
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