We revisit the setting of fairly allocating indivisible items when agents have different weights representing their entitlements. First, we propose a parameterized family of relaxations for weighted envy-freeness and the same for weighted proportionality; the parameters indicate whether smaller-weight or larger-weight agents should be given a higher priority. We show that each notion in these families can always be satisfied, but any two cannot necessarily be fulfilled simultaneously. We then introduce an intuitive weighted generalization of maximin share fairness and establish the optimal approximation of it that can be guaranteed. Furthermore, we characterize the implication relations between the various weighted fairness notions introduced in this and prior work, and relate them to the lower and upper quota axioms from apportionment.
|Title of host publication
|AAAI-22 Technical Tracks 5
|Association for the Advancement of Artificial Intelligence
|Number of pages
|Published - 30 Jun 2022
|36th AAAI Conference on Artificial Intelligence, AAAI 2022 - Virtual, Online
Duration: 22 Feb 2022 → 1 Mar 2022
|Proceedings of the 36th AAAI Conference on Artificial Intelligence, AAAI 2022
|36th AAAI Conference on Artificial Intelligence, AAAI 2022
|22/02/22 → 1/03/22
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