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Title: Fairly Allocating Goods and (Terrible) Chores
We study the fair allocation of mixture of indivisible goods and chores under lexicographic preferences---a subdomain of additive preferences. A prominent fairness notion for allocating indivisible items is envy-freeness up to any item (EFX). Yet, its existence and computation has remained a notable open problem. By identifying a class of instances with terrible chores, we show that determining the existence of an EFX allocation is NP-complete. This result immediately implies the intractability of EFX under additive preferences. Nonetheless, we propose a natural subclass of lexicographic preferences for which an EFX and Pareto optimal (PO) allocation is guaranteed to exist and can be computed efficiently for any mixed instance. Focusing on two weaker fairness notions, we investigate finding EF1 and Pareto optimal allocations for special instances with terrible chores, and show that MMS and PO allocations can be computed efficiently for any mixed instance with lexicographic preferences.  more » « less
Award ID(s):
2144413 2052488 2107173 1850076
PAR ID:
10443108
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
Proceedings of the Thirty-Second International Joint Conference on Artificial Intelligence
Page Range / eLocation ID:
2738 to 2746
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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