Fairness in Aggregation: Optimal Top-$k$ and Improved Full Ranking

Diptarka Chakraborty, Arya Mazumdar, Barna Saha, Alvin Hong Yao Yan
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:12460-12474, 2026.

Abstract

Ensuring fairness in algorithmic ranking systems is a critical challenge with significant societal implications for hiring, recommendations, web search, and data management. Standard methods for aggregating multiple preference orders into a consensus ranking may perpetuate and even amplify the lack of representation of underrepresented groups. To address this, recent research has focused on incorporating fairness constraints to ensure the presence of different groups in the top-$k$ positions of the final aggregate ranking. We study two fairness-aware variants under the well-known Spearman footrule, which corresponds to the $L_1$ distance between rankings. First, we address the practically salient task of computing a fair aggregate top-$k$ ranking – crucial in settings like recommendations and hiring where selection is primarily based on the top-$k$ results – and present the first optimal algorithm for this problem. Second, we consider fair (full) rank aggregation over all candidates (not specifically on top-$k$). We already know of a $3$-approximation for this fair rank aggregation variant (Wei et al., SIGMOD’22; Chakraborty et al., NeurIPS’22), whereas an exact algorithm exists for the corresponding unconstrained (unfair) version (Dwork et al., WWW’01). Closing the computational gap between fair and unconstrained rank aggregation has remained a tantalizing open problem. We make significant progress by giving a $2$-approximation algorithm for fair (full) rank aggregation, improving substantially over the previous $3$-approximation. Further, we complement our theoretical contributions with experiments on different real-world datasets, which corroborate our theoretical results and demonstrate strong empirical performance relative to state-of-the-art baselines.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-chakraborty26b, title = {Fairness in Aggregation: Optimal Top-$k$ and Improved Full Ranking}, author = {Chakraborty, Diptarka and Mazumdar, Arya and Saha, Barna and Yan, Alvin Hong Yao}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {12460--12474}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/chakraborty26b/chakraborty26b.pdf}, url = {https://proceedings.mlr.press/v306/chakraborty26b.html}, abstract = {Ensuring fairness in algorithmic ranking systems is a critical challenge with significant societal implications for hiring, recommendations, web search, and data management. Standard methods for aggregating multiple preference orders into a consensus ranking may perpetuate and even amplify the lack of representation of underrepresented groups. To address this, recent research has focused on incorporating fairness constraints to ensure the presence of different groups in the top-$k$ positions of the final aggregate ranking. We study two fairness-aware variants under the well-known Spearman footrule, which corresponds to the $L_1$ distance between rankings. First, we address the practically salient task of computing a fair aggregate top-$k$ ranking – crucial in settings like recommendations and hiring where selection is primarily based on the top-$k$ results – and present the first optimal algorithm for this problem. Second, we consider fair (full) rank aggregation over all candidates (not specifically on top-$k$). We already know of a $3$-approximation for this fair rank aggregation variant (Wei et al., SIGMOD’22; Chakraborty et al., NeurIPS’22), whereas an exact algorithm exists for the corresponding unconstrained (unfair) version (Dwork et al., WWW’01). Closing the computational gap between fair and unconstrained rank aggregation has remained a tantalizing open problem. We make significant progress by giving a $2$-approximation algorithm for fair (full) rank aggregation, improving substantially over the previous $3$-approximation. Further, we complement our theoretical contributions with experiments on different real-world datasets, which corroborate our theoretical results and demonstrate strong empirical performance relative to state-of-the-art baselines.} }
Endnote
%0 Conference Paper %T Fairness in Aggregation: Optimal Top-$k$ and Improved Full Ranking %A Diptarka Chakraborty %A Arya Mazumdar %A Barna Saha %A Alvin Hong Yao Yan %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-chakraborty26b %I PMLR %P 12460--12474 %U https://proceedings.mlr.press/v306/chakraborty26b.html %V 306 %X Ensuring fairness in algorithmic ranking systems is a critical challenge with significant societal implications for hiring, recommendations, web search, and data management. Standard methods for aggregating multiple preference orders into a consensus ranking may perpetuate and even amplify the lack of representation of underrepresented groups. To address this, recent research has focused on incorporating fairness constraints to ensure the presence of different groups in the top-$k$ positions of the final aggregate ranking. We study two fairness-aware variants under the well-known Spearman footrule, which corresponds to the $L_1$ distance between rankings. First, we address the practically salient task of computing a fair aggregate top-$k$ ranking – crucial in settings like recommendations and hiring where selection is primarily based on the top-$k$ results – and present the first optimal algorithm for this problem. Second, we consider fair (full) rank aggregation over all candidates (not specifically on top-$k$). We already know of a $3$-approximation for this fair rank aggregation variant (Wei et al., SIGMOD’22; Chakraborty et al., NeurIPS’22), whereas an exact algorithm exists for the corresponding unconstrained (unfair) version (Dwork et al., WWW’01). Closing the computational gap between fair and unconstrained rank aggregation has remained a tantalizing open problem. We make significant progress by giving a $2$-approximation algorithm for fair (full) rank aggregation, improving substantially over the previous $3$-approximation. Further, we complement our theoretical contributions with experiments on different real-world datasets, which corroborate our theoretical results and demonstrate strong empirical performance relative to state-of-the-art baselines.
APA
Chakraborty, D., Mazumdar, A., Saha, B. & Yan, A.H.Y.. (2026). Fairness in Aggregation: Optimal Top-$k$ and Improved Full Ranking. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:12460-12474 Available from https://proceedings.mlr.press/v306/chakraborty26b.html.

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