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We investigate the fair allocation of indivisible goods to agents with possibly different entitlements represented by weights. Previous work has shown that guarantees for additive valuations with existing envy-based notions cannot be extended to the case where agents have matroid-rank (i.e., binary submodular) valuations. We propose two families of envy-based notions for matroid-rank and general submodular valuations, one based on the idea of transferability and the other on marginal values. We show that our notions can be satisfied via generalizations of rules such as picking sequences and maximum weighted Nash welfare. In addition, we introduce welfare measures based on harmonic numbers, and show that variants of maximum weighted harmonic welfare offer stronger fairness guarantees than maximum weighted Nash welfare under matroid-rank valuations.
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This content will become publicly available on April 4, 2026
A General Framework for Fair Allocation under Matroid Rank Valuations
We study the problem of fairly allocating a set of indivisible goods among agents with matroid rank valuations: every good provides a marginal value of 0 or 1 when added to a bundle and valuations are submodular.We present a simple algorithmic framework, calledGeneral Yankee Swap, that can efficiently compute allocations that maximize any justice criterion (or fairness objective) satisfying some mild assumptions. Along with maximizing a justice criterion, General Yankee Swap is guaranteed to maximize utilitarian social welfare, ensure strategyproofness and use at most a quadratic number of valuation queries. We show how General Yankee Swap can be used 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 weightedp-mean welfare.In particular, this framework provides the first polynomial time algorithms to compute weighted leximin, max weighted Nash welfare and max weightedp-mean welfare allocations for agents with matroid rank valuations. We also extend this framework to the setting of binary chores — items with marginal values -1 or 0 — and similarly show that it can be used to maximize any justice criteria satisfying some mild assumptions.
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- Award ID(s):
- 2327057
- PAR ID:
- 10628527
- Publisher / Repository:
- ACM
- Date Published:
- Journal Name:
- ACM Transactions on Economics and Computation
- ISSN:
- 2167-8375
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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