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We study multi-category housing allocation problems: A finite set of objects, which is sorted into categories of equal size, has to be allocated to a finite set of individuals, such that everyone obtains exactly one object from each category. We show that, in the large class of category-wise neutral and non-bossy mechanisms, any strategy-proof mechanism can be constructed by simply letting individuals choose an object from each category one after another following some priority order. We refer to these mechanisms as multi-category serial dictatorships and advocate for selecting priority orders across categories as fairly as possible.

We design and implement a program-proposing deferred acceptance mechanism with ties (DAT) and apply it to childcare assignment in two German cities. The mechanism can accommodate complementarities in providers' preferences, is fast to terminate even in larger cities, is difficult to manipulate in practice, and produces stable allocations. It can be further sped up by introducing two new features. First, allowing for an arbitrary share of facilities who participate in a centralized manner by submitting a rank-order-list over applicants. Second, by breaking ties in applicants' rank-order-lists on a first-come-first-serve basis, which sets incentives for programs to propose faster. We provide and evaluate simulation results.