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We study the problem of fairly allocating a set of indivisible goods amongagents with matroid rank valuations -- every good provides a marginal value of$0$ or $1$ when added to a bundle and valuations are submodular. We generalizethe Yankee Swap algorithm to create a simple framework, called General YankeeSwap, that can efficiently compute allocations that maximize any justicecriterion (or fairness objective) satisfying some mild assumptions. Along withmaximizing a justice criterion, General Yankee Swap is guaranteed to maximizeutilitarian social welfare, ensure strategyproofness and use at most aquadratic number of valuation queries. We show how General Yankee Swap can beused to compute allocations for five different well-studied justice criteria:(a) Prioritized Lorenz dominance, (b) Maximin fairness, (c) Weighted leximin,(d) Max weighted Nash welfare, and (e) Max weighted $p$-mean welfare. Inparticular, our framework provides the first polynomial time algorithms tocompute weighted leximin, max weighted Nash welfare and max weighted $p$-meanwelfare allocations for agents with matroid rank valuations.

A General Framework for Fair Allocation under Matroid Rank Valuations