Weighted Maxmin Fair Share Allocation of Indivisible Chores

Aziz, Haris; Chan, Hau; Li, Bo

doi:10.24963/ijcai.2019/7

Cited by 57 publications

(100 citation statements)

References 9 publications

(17 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…There are also further solution concepts that we have not considered, most notably the maximum Nash welfare solution [see Caragiannis et al, 2016], which could be studied in this context both from the axiomatic and the computational points of view. Another promising direction would be to extend the work to other preference representations, including ordinal preferences [Aziz et al, 2015], or to chores instead of goods [e.g., Aziz et al, 2017]. Also, it would be interesting to obtain analogues of procedures such as sequential allocation and round-robin that respect the connectivity constraints and still produce desirable allocations.…”

Section: Discussionmentioning

confidence: 99%

Fair Division of a Graph

Bouveret¹,

Cechlárová

Elkind

et al. 2017

Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence

129

View full text Add to dashboard Cite

We consider fair allocation of indivisible items under an additional constraint: there is an undirected graph describing the relationship between the items, and each agent's share must form a connected subgraph of this graph. This framework captures, e.g., fair allocation of land plots, where the graph describes the accessibility relation among the plots. We focus on agents that have additive utilities for the items, and consider several common fair division solution concepts, such as proportionality, envy-freeness and maximin share guarantee. While finding good allocations according to these solution concepts is computationally hard in general, we design efficient algorithms for special cases where the underlying graph has simple structure, and/or the number of agents-or, less restrictively, the number of agent types-is small. In particular, despite non-existence results in the general case, we prove that for acyclic graphs a maximin share allocation always exists and can be found efficiently.

show abstract

Section: Discussionmentioning

confidence: 99%

Fair Division of a Graph

Bouveret¹,

Cechlárová

Elkind

et al. 2017

Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence

129

View full text Add to dashboard Cite

show abstract

“…In the context of item assignment, weak concavity is equivalent to increasing differences -agents care more about not getting the worst item than about getting the best item. Increasing differences make sense in fair division of chores [8] and we relate to it in Section 9.…”

Section: Related Workmentioning

confidence: 99%

Fair Allocation with Diminishing Differences

Segal-Halevi¹,

Hassidim

Aziz

2020

jair

Self Cite

View full text Add to dashboard Cite

Ranking alternatives is a natural way for humans to explain their preferences. It is being used in many settings, such as school choice, course allocations and residency matches. In some cases, several "items" are given to each participant. Without having any information on the underlying cardinal utilities, arguing about fairness of allocation requires extending the ordinal item ranking to ordinal bundle ranking. The most commonly used such extension is stochastic dominance (SD), where a bundle X is preferred over a bundle Y if its score is better according to all additive score functions. SD is a very conservative extension, by which few allocations are necessarily fair while many allocations are possibly fair. We propose to make a natural assumption on the underlying cardinal utilities of the players, namely that the difference between two items at the top is larger than the difference between two items at the bottom. This assumption implies a preference extension which we call diminishing differences (DD), where X is preferred over Y if its score is better according to all additive score functions satisfying the DD assumption. We give a full characterization of allocations that are necessarily-proportional or possibly-proportional according to this assumption. Based on this characterization, we present a polynomial-time algorithm for finding a necessarily-DD-proportional allocation if it exists. Using simulations, we show that with high probability, a necessarily-proportional allocation does not exist but a necessarily-DD-proportional allocation exists, and moreover, that allocation is proportional according to the underlying cardinal utilities. We also consider chore allocation under the analogous conditionincreasing-differences. (Avinatan Hassidim), UNSW Sydney and Data61 CSIRO, Australia. haris.aziz@unsw.edu.au (Haris Aziz)A preliminary version of this paper was published in the proceedings of IJCAI 2017 [42]. In the present version, the proofs are substantially revised and simplified, omitted proofs are included, and there are two new sections: one on division of chores (section 9) and one on binary utilities (section 10).

show abstract

“…Theorem 6.1 For the public ranking model, RounRobi is SP and has an approximation ratio of 2 − 1 n . Proof: Aziz et al [2017] proved that RounRobi gives an approximation bound of 2 − 1 n if at each round every agent is allocated the item with smallest cost. Note that the algorithm is ordinal hence no agent can change the outcome by misreporting her cardinal utilities.…”

Section: Strategyproof Algorithmsmentioning

confidence: 99%

“…This work is partially supported by NSF CAREER Award No. 1553385. 2014; Amanatidis et al, 2015;Barman and Murthy, 2017;Ghodsi et al, 2018;Aziz et al, 2017]. None of these works took a mechanism design perspective to the problem of computing approximately MMS allocation.…”

Section: Introductionmentioning

confidence: 99%

Strategyproof and Approximately Maxmin Fair Share Allocation of Chores

Aziz

2019

Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence

Self Cite

View full text Add to dashboard Cite

We initiate the work on fair and strategyproof allocation of indivisible chores. The fairness concept we consider in this paper is maxmin share (MMS) fairness. We consider three previously studied models of information elicited from the agents: the ordinal model, the cardinal model, and the public ranking model in which the ordinal preferences are publicly known. We present both positive and negative results on the level of MMS approximation that can be guaranteed if we require the algorithm to be strategyproof. Our results uncover some interesting contrasts between the approximation ratios achieved for chores versus goods.

show abstract

Weighted Maxmin Fair Share Allocation of Indivisible Chores

Cited by 57 publications

References 9 publications

Fair Division of a Graph

Fair Division of a Graph

Fair Allocation with Diminishing Differences

Strategyproof and Approximately Maxmin Fair Share Allocation of Chores

Contact Info

Product

Resources

About