Dividing connected chores fairly

Heydrich, Sandy; Stee, Rob van

doi:10.1016/j.tcs.2015.05.041

Cited by 23 publications

(11 citation statements)

References 12 publications

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“…The loss in social welfare by enforcing allocations to be fair is quantitatively measured by the price of fairness. Bounding the price of fairness for goods and chores are widely concerned in the literature [15,19,28,13,11,29]. In this paper, we study the price of fairness for indivisible chores under (weighted) PROPX requirement, and show that our algorithm achieves the optimal ratio.…”

Section: Other Related Workmentioning

confidence: 97%

Almost (Weighted) Proportional Allocations for Indivisible Chores

Li¹,

Li²,

Wu³

2021

Preprint

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In this paper, we consider how to fairly allocate m indivisible chores to a set of n (asymmetric) agents. As exact fairness cannot be guaranteed, motivated by the extensive study of EF1, EFX and PROP1 allocations, we propose and study proportionality up to any item (PROPX), and show that a PROPX allocation always exists. We argue that PROPX might be a more reliable relaxation for proportionality in practice than the commonly studied maximin share fairness (MMS) by the facts that (1) MMS allocations may not exist even with three agents, but PROPX allocations always exist even for the weighted case when agents have unequal obligation shares; (2) any PROPX allocation ensures 2-approximation for MMS, but an MMS allocation can be as bad as Θ(n)-approximation to PROPX.We propose two algorithms to compute PROPX allocations and each of them has its own merits. Our first algorithm is based on a recent refinement for the well-known procedure -envy-cycle elimination, where the returned allocation is simultaneously PROPX and 4/3-approximate MMS. A by-product result is that an exact EFX allocation for indivisible chores exists if all agents have the same ordinal preference over the chores, which might be of independent interest. The second algorithm is called bidand-take, which applies to the weighted case. Furthermore, we study the price of fairness for (weighted) PROPX allocations, and show that the algorithm computes allocations with the optimal guarantee on the approximation ratio to the optimal social welfare without fairness constraints.* The authors thank Haris Aziz and Warut Suksompong for their valuable comments and suggested related works.

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Section: Other Related Workmentioning

confidence: 97%

Almost (Weighted) Proportional Allocations for Indivisible Chores

Li¹,

Li²,

Wu³

2021

Preprint

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“…These protocols were improved by [DFHY18], who obtained a bounded envyfree chore division method for any number of agents. [HvS15] consider the fair division of chores with connected pieces and bound the loss in social welfare due to fairness. [SH18] studies the envyfree division of a cake when some parts have been burned in the oven (i.e., the value densities can be positive, negative, or zero anywhere) and showed the existence of connected envy-free allocations for three players using a topological approach based on an analog of Sperner's lemma.…”

Section: Non-convex Economies and Disconnected Sets Of Equilibriamentioning

confidence: 99%

Algorithms for Competitive Division of Chores

Brânzei¹,

Sandomirskiy²

2019

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We study the problem of allocating divisible bads (chores) among multiple agents with additive utilities, when money transfers are not allowed. The competitive rule is known to be the best mechanism for goods under additive utilities and was recently extended to chores by Bogomolnaia et al. [BMSY17]. For both goods and chores, the rule produces Pareto optimal and envy-free allocations. In the case of goods, the outcome of the competitive rule can be easily computed. Competitive allocations solve the Eisenberg-Gale convex program; hence the outcome is unique and can be approximately found by standard gradient methods. An exact algorithm that runs in polynomial time in the number of agents and goods was given by Orlin [Orl10].In the case of chores, the competitive rule does not solve any convex optimization problem; instead, competitive allocations correspond to local minima, local maxima, and saddle points of the Nash Social Welfare on the Pareto frontier of the set of feasible utilities. The rule becomes multivalued and none of the standard methods can be applied to compute its outcome.In this paper, we show that all the outcomes of the competitive rule for chores can be computed in strongly polynomial time if either the number of agents or the number of chores is fixed. The approach is based on a combination of three ideas: all consumption graphs of Pareto optimal allocations can be listed in polynomial time; for a given consumption graph, a candidate for a competitive allocation can be constructed via explicit formula; and a given allocation can be checked for being competitive using a maximum flow computation as in Devanur et al. [DPSV02]. Our algorithm immediately gives an approximately-fair allocation of indivisible chores by the rounding technique of Barman and Krishnamurthy [BK19].

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“…Additionally, the trade-off of (general forms of) fairness with efficiency for allocation problems (in different domains, ranging from online advertisement portals (Bateni et al 2016) to manufacturing and retail (Haitao Cui et al 2007)) has been widely studied in the literature, and recently conceptualized and studied as the "price of fairness" (Bertsimas et al 2011, Dickerson et al 2014, Heydrich and van Stee 2015. We hope that the concepts of individual rationality and fairness that our work introduces would inspire similar studies (theoretical and empirical) on their trade-offs with different notions of efficiency such as social welfare maximization and profit optimization.…”

Section: Related Workmentioning

confidence: 99%

The Costs and Benefits of Sharing: Sequential Individual Rationality and Sequential Fairness

Gopalakrishnan¹,

Mukherjee²,

Tulabandhula³

2016

Preprint

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Authors are encouraged to submit new papers to INFORMS journals by means of a style file template, which includes the journal title. However, use of a template does not certify that the paper has been accepted for publication in the named journal. INFORMS journal templates are for the exclusive purpose of submitting to an INFORMS journal and should not be used to distribute the papers in print or online or to submit the papers to another publication.

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Dividing connected chores fairly

Cited by 23 publications

References 12 publications

Almost (Weighted) Proportional Allocations for Indivisible Chores

Almost (Weighted) Proportional Allocations for Indivisible Chores

Algorithms for Competitive Division of Chores

The Costs and Benefits of Sharing: Sequential Individual Rationality and Sequential Fairness

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