The Efficiency of Fair Division

Kidney exchange provides a life-saving alternative to long waiting lists for patients in need of a new kidney. Fielded exchanges typically match under utilitarian or near-utilitarian rules; this approach marginalizes certain classes of patients. In this paper, we focus on improving access to kidneys for highly-sensitized, or hard-tomatch, patients. Toward this end, we formally adapt a recently introduced measure of the tradeoff between fairness and efficiencythe price of fairness-to the standard kidney exchange model. We show that the price of fairness in the standard theoretical model is small. We then introduce two natural definitions of fairness and empirically explore the tradeoff between matching more hard-tomatch patients and the overall utility of a utilitarian matching, on real data from the UNOS nationwide kidney exchange and simulated data from each of the standard kidney exchange distributions.

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“…Caragiannis et al defined an essentially identical concept in parallel [12]. We adopt that notion here.…”

Section: The Price Of Fairnessmentioning

confidence: 99%

Price of Fairness in Kidney Exchange.

2014

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“…For the upper bound on the utilitarian price of proportionality, we can cite the proof by Caragiannis et al [6], as it also applies to connected chores. Proof.…”

Section: The Price Of Proportionalitymentioning

confidence: 99%

Dividing connected chores fairly

Heydrich

Stee

2015

Theoretical Computer Science

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In this paper we consider the fair division of chores (tasks that need to be performed by agents, with negative utility for them), and study the loss in social welfare due to fairness. Previous work has been done on this so-called price of fairness, concerning fair division of cakes and chores with non-connected pieces and of cakes with connected pieces. In this paper, we consider situations where each player has to receive one connected piece of the chores. We provide tight or nearly tight bounds on the price of fairness with respect to the three main fairness criteria proportionality, envy-freeness and equitability and for utilitarian and egalitarian welfare. We also give the first proof of the existence of equitable divisions for chores with connected pieces.

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“…Let C* denote the most efficient allocation for I from the subset of allocations satisfying a fairness criterion ψ ∈ {proportionality, equitability, envy-freeness} (Note 6). Then (following Caragiannis et al, 2012) the price of ψ is defined by the ratio i∈M j∈N u i j z * i j i∈M j∈N u i j c * i j .…”

Section: Definitions Terminology and Notationsmentioning

confidence: 99%

“…Caragiannis et al (2012) define the prices of proportionality, envy-freeness, and equitability, and places bounds on this price. Aumann and Dombb (2011) extend this result to the case where distributions of the cake must be contiguous.…”

Section: Literature Reviewmentioning

confidence: 99%

“…A second difficulty in the cake-cutting problem thus arises: while an allocation may be, e.g., envy-free, it may also be inefficient; in other words, the total social welfare derived from the allocation may be lower than the maximum possible social welfare for the given instance. Caragiannis et al (2012) and Aumann and Dombb (2011) use the concept of price of fairness to quantify the decrease in efficiency when the optimal allocation, which maximizes total societal utility, is modified to meet a fairness criterion. (I provide a formal definition of the price of fairness in Section 1.2.…”

Section: Introductionmentioning

confidence: 99%

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Superadditivity and Subadditivity in Fair Division

Mirchandani¹

2013

JMR

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I examine the classic problem of fair division of a piecewise homogeneous good. Previous work developed algorithms satisfying various combinations of fairness notions (such as proportionality, envy-freeness, equitability, and Pareto-optimality). However, this previous work assumed that all utility functions are additive. Recognizing that additive functions accurately model utility only in certain situations, I investigate superadditive and subadditive utility functions. Next, I propose a new division protocol that utilizes nonlinear programming and test it on a sample instance. Finally, I prove theoretical results that address (a) relationships between fairness notions, and (b) the orthogonal issue of division efficiency (i.e., the price of satisfying particular fairness notions).

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The Efficiency of Fair Division

Cited by 133 publications

References 24 publications

Price of Fairness in Kidney Exchange.

Price of Fairness in Kidney Exchange.

Dividing connected chores fairly

Superadditivity and Subadditivity in Fair Division

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