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We present a simple algorithmic framework, called\n            <jats:italic toggle=\"yes\">General Yankee Swap<\/jats:italic>\n            , 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 weighted\n            <jats:italic toggle=\"yes\">p<\/jats:italic>\n            -mean welfare. In particular, this framework provides the first polynomial time algorithms to compute weighted leximin, max weighted Nash welfare, and max weighted\n            <jats:italic toggle=\"yes\">p<\/jats:italic>\n            -mean welfare allocations for agents with matroid rank valuations. We also extend this framework to the setting of binary chores\u2014items with marginal values -1 or 0\u2014and similarly show that it can be used to maximize any justice criteria satisfying some mild assumptions.\n          <\/jats:p>","DOI":"10.1145\/3728367","type":"journal-article","created":{"date-parts":[[2025,4,4]],"date-time":"2025-04-04T07:12:00Z","timestamp":1743750720000},"page":"1-32","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["A General Framework for Fair Allocation under Matroid Rank Valuations"],"prefix":"10.1145","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6261-6228","authenticated-orcid":false,"given":"Vignesh","family":"Viswanathan","sequence":"first","affiliation":[{"name":"Manning College of Information and Computer Sciences, University of Massachusetts Amherst","place":["Amherst, United States"]}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0635-6230","authenticated-orcid":false,"given":"Yair","family":"Zick","sequence":"additional","affiliation":[{"name":"Manning College of Information and Computer Sciences, University of Massachusetts Amherst","place":["Amherst, United States"]}]}],"member":"320","published-online":{"date-parts":[[2025,9,11]]},"reference":[{"key":"e_1_3_4_2_1","first-page":"46","volume-title":"Proceedings of the 28th International Joint Conference on Artificial Intelligence (IJCAI\u201919)","author":"Aziz Haris","year":"2019","unstructured":"Haris Aziz, Hau Chan, and Bo Li. 2019. 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