A market design solution to a multi-category housing allocation problem

We study multi-category housing allocation problems: A set of objects, which is
sorted into categories of equal size, has to be allocated to a 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 fair as possible.

Caspari, Gian (2023), A market design solution to a multi-category housing allocation problem, Journal of Mechanism and Institution Design 8(1) , 75-96