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dc.contributor.author
Benabbou, Nawal
dc.contributor.author
Chakraborty, Mithun
dc.contributor.author
Ho, Xuan-Vinh
dc.contributor.author
Sliwinski, Jakub
dc.contributor.author
Zick, Yair
dc.date.accessioned
2020-10-30T06:40:06Z
dc.date.available
2020-10-30T03:56:48Z
dc.date.available
2020-10-30T06:40:06Z
dc.date.issued
2020-10
dc.identifier.issn
2167-8383
dc.identifier.issn
2167-8375
dc.identifier.other
10.1145/3411513
en_US
dc.identifier.uri
http://hdl.handle.net/20.500.11850/448694
dc.description.abstract
In this article, we introduce and analyze an extension to the matching problem on a weighted bipartite graph (i.e., the assignment problem): Assignment with Type Constraints. Here, the two parts of the graph are each partitioned into subsets, called types and blocks, respectively; we seek a matching with the largest sum of weights under the constraint that there is a pre-specified cap on the number of vertices matched in every type-block pair. Our primary motivation stems from the large-scale public housing program run by the state of Singapore, accounting for over 70% of its residential real estate. To promote ethnic diversity within its housing projects, Singapore imposes ethnicity quotas: The population is divided into ethnicity-based groups and each new housing development into blocks of flats such that each group must not own more than a certain percentage of flats in a block. However, other domains use similar hard capacity constraints to maintain diversity: These include matching prospective students to schools or medical residents to hospitals. Limiting agents’ choices for ensuring diversity in this manner naturally entails some welfare loss. One of our goals is to study the tradeoff between diversity and (utilitarian) social welfare in such settings. We first show that, while the classic assignment program is polynomial-time computable, adding diversity constraints makes the problem computationally intractable; however, we identify a ½-approximation algorithm, as well as reasonable assumptions on the structure of utilities (or weights) that permit poly-time algorithms. Next, we provide two upper bounds on the price of diversity—a measure of the loss in welfare incurred by imposing diversity constraints—as functions of natural problem parameters. We conclude the article with simulations based on publicly available data from two diversity-constrained allocation problems—Singapore Public Housing and Chicago School Choice—which shed light on how the constrained maximization as well as lottery-based variants perform in practice.(© 2020 ACM)
en_US
dc.language.iso
en
en_US
dc.publisher
ACM
en_US
dc.title
The Price of Quota-based Diversity in Assignment Problems
en_US
dc.type
Journal Article
ethz.journal.title
ACM Transactions on Economics and Computation
ethz.journal.volume
8
en_US
ethz.journal.issue
3
en_US
ethz.pages.start
14
en_US
ethz.size
32 p.
en_US
ethz.identifier.wos
ethz.identifier.scopus
ethz.publication.place
New York, NY
en_US
ethz.publication.status
published
en_US
ethz.relation.isNewVersionOf
20.500.11850/346592
ethz.date.deposited
2020-10-30T03:56:58Z
ethz.source
SCOPUS
ethz.eth
yes
en_US
ethz.availability
Metadata only
en_US
ethz.rosetta.installDate
2020-10-30T06:40:49Z
ethz.rosetta.lastUpdated
2020-10-30T06:40:49Z
ethz.rosetta.versionExported
true
ethz.COinS
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