In the procedures used in Germany so far, the nursery schools send out their offers individually and uncoordinated. “This leads to problems when, on the one hand, parents feel forced to accept an early offer that is actually unattractive to them just to have a secure place, or, on the other hand, when they temporarily hold back several places in the hope of a better offer and thus block them for other families,” says Thilo Klein, professor at Pforzheim University and project head at ZEW Mannheim. The former leads to an unfair allocation, which causes “justified envy” of other applicants, e.g. because a child does not get a place in its sibling’s nursery school, although it would have priority there due to its sibling status. The latter slows down the admission process and leads to uncertainty among parents and employers.
Why have previous approaches to solving the problem failed?
A possible blanket solution to the problem is the introduction of a central clearing house. One example of this is the German Hochschulstart platform for the allocation of university places, which compiles rankings of applicants and universities and ensures that university places are allocated in a well thought-out manner. “Nursery schools, however, are often not able to transmit complete ranking lists about applicants to a central clearing house,” says Tobias Riehm, a researcher in the ZEW “Market Design” Department. “Here it is also necessary to take into account so-called complementarities, such as the desired gender and age mix in the care groups. It is not so easy to translate these into rankings.”
Mechanism takes complementarities into account
The mechanism implemented in the authors’ software application deviates from the literature on the “theory of stable allocations” by still allowing nursery schools to make decentralised offers. In the iterative procedure, the nursery school managers receive a list of the applicants that are still interested in each round via a software platform and enter the places they have to offer. This takes complementarities into account, as nursery schools can make their offers dependent on confirmed places from previous rounds. At the same time, a quick and fair allocation is achieved by the platform automating the parents’ decisions and only retaining the best offer for them in each round. All other offers are rejected immediately. “The mechanism thus combines the advantages of centralised allocation with those of decentralised allocation,” says Sven Giegerich, one of the authors of the study.
Procedure scales well and reduces number of applicants with justified envy
In terms of speed, the study shows that the allocation procedure takes about an hour and goes through some 6 to 10 rounds. The procedure is just as fast in big cities as in small towns. This can be explained by the preference of parents to get a place in a nearby nursery school. It can thus be said that big cities also consist of many local nursery school markets. In terms of fairness, the study paints a differentiated picture: In the pilot cities, the new procedure reduces the number of applicants with justified envy by only half compared to the previously applied procedure. This is the price for maintaining the autonomy of the nursery schools. With a centralised procedure, justified envy could be completely avoided. However, the nursery schools’ freedom of choice would be so severely restricted that it would no longer be attractive for 20 per cent of the nursery schools to participate voluntarily in the centralised procedure.
The new method builds on the “theory of stable allocations and the practice of market design”, for which Alvin E. Roth and Lloyd S. Shapley were awarded the Nobel Prize in Economics in 2012. It was developed in consultation with parents, nursery schools and municipalities, analysed in terms of its game theoretic properties, implemented in open-source software and successfully introduced in five small, medium-sized and large German cities so far. The software solution developed as part of the project complements existing nursery school management platforms and can be easily accessed via application programming interfaces.