Fair Rank Aggregation Article Swipe

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Diptarka Chakraborty , Syamantak Das , Arindam Khan , Aditya Subramanian ·

YOU? · · 2023 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2308.10499

Ranking algorithms find extensive usage in diverse areas such as web search, employment, college admission, voting, etc. The related rank aggregation problem deals with combining multiple rankings into a single aggregate ranking. However, algorithms for both these problems might be biased against some individuals or groups due to implicit prejudice or marginalization in the historical data. We study ranking and rank aggregation problems from a fairness or diversity perspective, where the candidates (to be ranked) may belong to different groups and each group should have a fair representation in the final ranking. We allow the designer to set the parameters that define fair representation. These parameters specify the allowed range of the number of candidates from a particular group in the top-$k$ positions of the ranking. Given any ranking, we provide a fast and exact algorithm for finding the closest fair ranking for the Kendall tau metric under block-fairness. We also provide an exact algorithm for finding the closest fair ranking for the Ulam metric under strict-fairness, when there are only $O(1)$ number of groups. Our algorithms are simple, fast, and might be extendable to other relevant metrics. We also give a novel meta-algorithm for the general rank aggregation problem under the fairness framework. Surprisingly, this meta-algorithm works for any generalized mean objective (including center and median problems) and any fairness criteria. As a byproduct, we obtain 3-approximation algorithms for both center and median problems, under both Kendall tau and Ulam metrics. Furthermore, using sophisticated techniques we obtain a $(3-\varepsilon)$-approximation algorithm, for a constant $\varepsilon>0$, for the Ulam metric under strong fairness.

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Ranking (information retrieval) Metric (unit) Rank (graph theory) Learning to rank Representation (politics) Voting Aggregate (composite) Ranking SVM Set (abstract data type) Computer science Mathematics Theoretical computer science Algorithm Machine learning Combinatorics Operations management Political science Law Economics Composite material Politics Programming language Materials science

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2308.10499
PDF: https://arxiv.org/pdf/2308.10499
OA Status: green
Related Works: 10
OpenAlex ID: https://openalex.org/W4386081452

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DOI: https://doi.org/10.48550/arxiv.2308.10499

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Title: Fair Rank Aggregation

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Type: preprint

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Language: en

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Publication year: 2023

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Publication date: 2023-08-21

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Authors: Diptarka Chakraborty, Syamantak Das, Arindam Khan, Aditya Subramanian

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Landing page: https://arxiv.org/abs/2308.10499

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PDF URL: https://arxiv.org/pdf/2308.10499

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Concepts: Ranking (information retrieval), Metric (unit), Rank (graph theory), Learning to rank, Representation (politics), Voting, Aggregate (composite), Ranking SVM, Set (abstract data type), Computer science, Mathematics, Theoretical computer science, Algorithm, Machine learning, Combinatorics, Operations management, Political science, Law, Economics, Composite material, Politics, Programming language, Materials science

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abstract_inverted_index.prejudice	49
abstract_inverted_index.problems)	217
abstract_inverted_index.problems,	234
abstract_inverted_index.(including	213
abstract_inverted_index.admission,	14
abstract_inverted_index.algorithm,	250
abstract_inverted_index.algorithms	1, 33, 176, 228
abstract_inverted_index.byproduct,	224
abstract_inverted_index.candidates	71, 114
abstract_inverted_index.extendable	183
abstract_inverted_index.framework.	203
abstract_inverted_index.historical	54
abstract_inverted_index.parameters	99, 105
abstract_inverted_index.particular	117
abstract_inverted_index.techniques	245
abstract_inverted_index.aggregation	20, 61, 198
abstract_inverted_index.employment,	12
abstract_inverted_index.generalized	210
abstract_inverted_index.individuals	43
abstract_inverted_index.Furthermore,	242
abstract_inverted_index.perspective,	68
abstract_inverted_index.Surprisingly,	204
abstract_inverted_index.sophisticated	244
abstract_inverted_index.meta-algorithm	193, 206
abstract_inverted_index.representation	87
abstract_inverted_index.3-approximation	227
abstract_inverted_index.block-fairness.	148
abstract_inverted_index.marginalization	51
abstract_inverted_index.representation.	103
abstract_inverted_index.strict-fairness,	166
abstract_inverted_index.$\varepsilon>0$,	254
abstract_inverted_index.$(3-\varepsilon)$-approximation	249
cited_by_percentile_year
countries_distinct_count	0
institutions_distinct_count	4
sustainable_development_goals[0].id	https://metadata.un.org/sdg/10
sustainable_development_goals[0].score	0.7099999785423279
sustainable_development_goals[0].display_name	Reduced inequalities
citation_normalized_percentile