The paper establishes a near-complete implication hierarchy among 22 fairness notions for additive and non-additive valuations over goods, chores, and mixed manna, with an automated inference engine.
EF1 for Mixed Manna with Unequal Entitlements
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abstract
We study fair division of indivisible mixed manna when agents have unequal entitlements, with weighted envy-freeness up to one item (WEF1) as our primary notion of fairness. We identify several shortcomings of existing techniques to achieve WEF1. Hence, we relax WEF1 to weighted envy-freeness up to 1 transfer (WEF1T), and give a polynomial-time algorithm for achieving it. We also generalize Fisher markets to the mixed manna setting, and use them to get a polynomial-time algorithm for two agents that outputs a WEF1 allocation.
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Exploring Relations among Fairness Notions in Discrete Fair Division
The paper establishes a near-complete implication hierarchy among 22 fairness notions for additive and non-additive valuations over goods, chores, and mixed manna, with an automated inference engine.