Multi-attribute proportional representation

Lang, Jérôme; Skowron, Piotr

doi:10.1016/j.artint.2018.07.005

Cited by 26 publications

(21 citation statements)

References 30 publications

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“…Our diversity concept comes close to that of Bredereck et al [2018] who also achieve diversity by imposing hard constraints on the maximization of a (submodular) objective that measures the quality of the solution; however, they work in a committee (subset) selection setting with variously structured agent labels while we solve a matching problem with both agents and items split into disjoint subsets. Lang and Skowron [2016] focus on multi-attribute proportional representation in committee selection where they essentially define diversity in terms of the divergence between the realized distribution of attribute values in the outcome and some target distribution, but admit no notion of solution quality in addition to diversity.…”

Section: Related Workmentioning

confidence: 99%

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The Price of Quota-based Diversity in Assignment Problems

Benabbou

Chakraborty

et al. 2020

ACM Trans. Econ. Comput.

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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.

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Section: Related Workmentioning

confidence: 99%

“…This is a challenge we wish to tackle in the future. For existing work on diversity requirements based on multiple overlapping attributes in a subset selection setting (not matching), please refer to Bredereck et al [2018]; Lang and Skowron [2016].…”

Section: Types Based On "Overlapping" Attributesmentioning

confidence: 99%

The Price of Quota-based Diversity in Assignment Problems

Benabbou

Chakraborty

et al. 2020

ACM Trans. Econ. Comput.

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“…However, there is no efficient algorithm since the input in CAP is exponentially large in the number of attributes. Lang and Skowron [31] also consider the problem of committee selection with multiple partitions; however, the goal is to produce a committee close to a given target composition of attributes as opposed to maximizing a score function.…”

Section: Other Related Workmentioning

confidence: 99%

Multiwinner Voting with Fairness Constraints

Celis

Huang

Vishnoi

2018

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

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Multiwinner voting rules are used to select a small representative subset of candidates or items from a larger set given the preferences of voters. However, if candidates have sensitive attributes such as gender or ethnicity (when selecting a committee), or specified types such as political leaning (when selecting a subset of news items), an algorithm that chooses a subset by optimizing a multiwinner voting rule may be unbalanced in its selection -it may under or over represent a particular gender or political orientation in the examples above. We introduce an algorithmic framework for multiwinner voting problems when there is an additional requirement that the selected subset should be "fair" with respect to a given set of attributes. Our framework provides the flexibility to (1) specify fairness with respect to multiple, non-disjoint attributes (e.g., ethnicity and gender) and (2) specify a score function. We study the computational complexity of this constrained multiwinner voting problem for monotone and submodular score functions and present several approximation algorithms and matching hardness of approximation results for various attribute group structure and types of score functions. We also present simulations that suggest that adding fairness constraints may not affect the scores significantly when compared to the unconstrained case.

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“…More recently, a wide literature about k-sccs which are representation-focused on some attributes of the alternatives (sex, age, profession, ethnicity) has been growing. See, for instance, Lang and Skowron (2016), Bredereck et al (2018), Celis et al (2018).…”

Section: Introductionmentioning

confidence: 99%

Breaking ties in collective decision-making

Bubboloni

Gori

2020

Decisions Econ Finan

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Many classic social preference (multiwinner social choice) correspondences are resolute only when two alternatives and an odd number of individuals are considered. Thus, they generally admit several resolute refinements, each of them naturally interpreted as a tie-breaking rule. A tie-breaking rule is compulsory every time a single final decision is needed. Unfortunately, using a tie-breaking rule on some social preference (multiwinner social choice) correspondence can dramatically compromise its properties. In particular, very often, the arithmetic relation between the number of alternatives and the number of voters does not allow to maintain both anonymity and neutrality. In those cases, the only possibility is to look at suitable different forms of symmetry that are coherent with the decision context. We find out conditions which make a social preference (multiwinner social choice) correspondence admit a resolute refinement fulfilling some weak versions of the anonymity and neutrality principles. We also clear when it is possible to obtain, for those resolute refinements, the reversal symmetry (immunity to the reversal bias). The theory we develop turns out to be useful in many common applicative contexts and allows to explicitly construct those refinements. Keywords Social preference correspondence • Multiwinner social choice correspondence • Resoluteness • Anonymity • Neutrality • Tie-breaking rule JEL Classification D71 Daniela Bubboloni was supported by GNSAGA of INdAM.

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Multi-attribute proportional representation

Cited by 26 publications

References 30 publications

The Price of Quota-based Diversity in Assignment Problems

The Price of Quota-based Diversity in Assignment Problems

Multiwinner Voting with Fairness Constraints

Breaking ties in collective decision-making

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