Best of Both Worlds: Ex-Ante and Ex-Post Fairness in Resource Allocation

Freeman, Rupert; Shah, Nisarg; Vaish, Rohit

doi:10.1145/3391403.3399537

Cited by 32 publications

(59 citation statements)

References 3 publications

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“…The state of the art BoBW results for additive valuations are presented in the two recent papers of Freeman et al [2020], Aziz [2020]. Both of these works are based on the well known paradigm that we call here "faithful implementation of a fractional allocation": a distribution over deterministic allocations is a faithful implementation of the fractional allocation if the ex-ante (expected) value of every agent under the distribution is the same as it is in the fractional allocation, and ex-post (for any realization) it is the same as the expectation, up to the value of one item.…”

Section: Previous Bobw Results For Additive Valuationsmentioning

confidence: 99%

Best-of-Both-Worlds Fair-Share Allocations

Babaioff¹,

Ezra²,

Feige³

2021

Preprint

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We consider the problem of fair allocation of indivisible items among n agents with additive valuations, when agents have equal entitlements to the goods, and there are no transfers. Best-of-Both-Worlds (BoBW) fairness mechanisms aim to give all agents both an ex-ante guarantee (such as getting the proportional share in expectation) and an ex-post guarantee. Prior BoBW results have focused on expost guarantees that are based on the "up to one item" paradigm, such as envy-free up to one item (EF1). In this work we attempt to give every agent a high value ex-post, and specifically, a constant fraction of her maximin share (MMS). The up to one item paradigm fails to give such a guarantee, and it is not difficult to present examples in which previous BoBW mechanisms give some agent only a 1 n fraction of her MMS.Our main result is a deterministic polynomial-time algorithm that computes a distribution over allocations that is ex-ante proportional, and ex-post, every allocation gives every agent at least her proportional share up to one item, and more importantly, at least half of her MMS. Moreover, this last ex-post guarantee holds even with respect to a more demanding notion of a share, introduced in this paper, that we refer to as the truncated proportional share (TPS). Our guarantees are nearly best possible, in the sense that one cannot guarantee agents more than their proportional share ex-ante, and one cannot guarantee agents more than a n 2n−1 fraction of their TPS ex-post.

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Section: Previous Bobw Results For Additive Valuationsmentioning

confidence: 99%

Best-of-Both-Worlds Fair-Share Allocations

Babaioff¹,

Ezra²,

Feige³

2021

Preprint

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“…We note that there is already a substantial stream of work aimed at measuring fairness in this setting. Concepts such as envy-freeness up to one object (Lipton et al, 2004), envy-freeness up to any object (Caragiannis et al, 2019), and proportionality up to one object (Conitzer, Freeman, and Shah, 2017) have been widely studied, and prior work has considered ex post fairness in conjunction with ex ante guarantees in more general multiobject assignment settings (Budish et al, 2013;Akbarpour and Nikzad, 2020;Freeman, Shah, and Vaish, 2020;Aziz, 2020;Babaioff, Ezra, and Feige, 2021). None of this work is relevant to the house allocation setting that we consider in this work, since the fairness guarantees are too permissive when each agent receives only a single object.…”

Section: Discussionmentioning

confidence: 99%

Order Symmetry: A New Fairness Criterion for Assignment Mechanisms

Freeman¹,

Pritchard²

2021

Preprint

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We introduce a new fairness criterion, order symmetry, for assignment mechanisms that match n objects to n agents with ordinal preferences over the objects. An assignment mechanism is order symmetric with respect to some probability measure over preference profiles if every agent is equally likely to receive their favorite object, every agent is equally likely to receive their second favorite, and so on. When associated with a sufficiently symmetric probability measure, order symmetry is a relaxation of anonymity that, crucially, can be satisfied by discrete assignment mechanisms. Furthermore, it can be achieved without sacrificing other desirable axiomatic properties satisfied by existing mechanisms. In particular, we show that it can be achieved in conjunction with strategyproofness and ex post efficiency via the top trading cycles mechanism (but not serial dictatorship). We additionally design a novel mechanism that is both order symmetric and ordinally efficient. The practical utility of order symmetry is substantiated by simulations on Impartial Culture and Mallows-distributed preferences for four common assignment mechanisms.

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“…It is easy to observe that this is equivalent to satisfying the following stronger guarantee which uses the stochastic dominance (SD) relation. This is akin to the SD-EF1 strengthening of EF1 [13,4].…”

Section: Preliminariesmentioning

confidence: 96%

Two-Sided Matching Meets Fair Division

Freeman¹,

Micha²,

Shah³

2021

Preprint

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We introduce a new model for two-sided matching which allows us to borrow popular fairness notions from the fair division literature such as envy-freeness up to one good and maximin share guarantee. In our model, each agent is matched to multiple agents on the other side over whom she has additive preferences. We demand fairness for each side separately, giving rise to notions such as double envy-freeness up to one match (DEF1) and double maximin share guarantee (DMMS). We show that (a slight strengthening of) DEF1 cannot always be achieved, but in the special case where both sides have identical preferences, the round-robin algorithm with a carefully designed agent ordering achieves it. In contrast, DMMS cannot be achieved even when both sides have identical preferences.* A preliminary version appeared in the proceedings of the 30th International Joint Conference on Artificial Intelligence (IJCAI-21). 1 Assigning students to courses has been studied before [8,20,7], but these papers typically only consider the preferences of the students. 2 http://csse.utoronto.ca/social-needs-marketplace

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Best of Both Worlds: Ex-Ante and Ex-Post Fairness in Resource Allocation

Cited by 32 publications

References 3 publications

Best-of-Both-Worlds Fair-Share Allocations

Best-of-Both-Worlds Fair-Share Allocations

Order Symmetry: A New Fairness Criterion for Assignment Mechanisms

Two-Sided Matching Meets Fair Division

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