Serial Dictatorship Mechanism with Grouping

Every year, the local governments in Japan assign children to nursery schools before a new school year starts. The assignment should be fair in social welfare as well as should be acceptable for the parents. We solve the matching problem of children and nursery schools based on a serial dictatorship mechanism. It is reasonable that a parent requests the siblings be assigned to the same nursery school. On the other hand, since two or more children of a parent are often dealt with independently based on the children's priority ordering, the siblings may be assigned to different nursery schools. To tackle this problem, we assume a group of agents who are children of a parent and a group of objects which belong to the same nursery school. We present a serial dictatorship mechanism under the conditions that there are groups of agents and objects. Using the given independent children's priority ordering, we reorder children from the viewpoint of parents' needs. The priority orderings of the siblings become equal, and they are assigned to the vacancies in the same group, a nursery school. The assignment is feasible, i.e., parents do not decline it. The proposed approach is practical in real situations, as well as easily explainable for fairness.