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Rank-maximal allocation is a rule for fair division of indivisible items. Suppose we have to allocate some items among people. Each person can rank the items from best to worst. The RM rule says that we have to give as many people as possible their best item. Subject to that, we have to give as many people as possible their next-best item, and so on.
In the special case in which each person should receive a single item , the problem is called rank-maximal matching or greedy matching.
The idea is similar to that of utilitarian cake-cutting, where the goal is to maximize the sum of utilities of all participants. However, the utilitarian rule works with cardinal utility functions, while the RM rule works with ordinal utilities.
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