Can a Few Decide for Many? The Metric Distortion of Sortition

Ioannis Caragiannis, Evi Micha, Jannik Peters
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:5660-5679, 2024.

Abstract

Recent works have studied the design of algorithms for selecting representative sortition panels. However, the most central question remains unaddressed: Do these panels reflect the entire population’s opinion? We present a positive answer by adopting the concept of metric distortion from computational social choice, which aims to quantify how much a panel’s decision aligns with the ideal decision of the population when preferences and agents lie on a metric space. We show that uniform selection needs only logarithmically many agents in terms of the number of alternatives to achieve almost optimal distortion. We also show that Fair Greedy Capture, a selection algorithm introduced recently by Ebadian and Micha (2024), matches uniform selection’s guarantees of almost optimal distortion and also achieves constant ex-post distortion, ensuring a “best of both worlds” performance.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-caragiannis24a, title = {Can a Few Decide for Many? {T}he Metric Distortion of Sortition}, author = {Caragiannis, Ioannis and Micha, Evi and Peters, Jannik}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {5660--5679}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/caragiannis24a/caragiannis24a.pdf}, url = {https://proceedings.mlr.press/v235/caragiannis24a.html}, abstract = {Recent works have studied the design of algorithms for selecting representative sortition panels. However, the most central question remains unaddressed: Do these panels reflect the entire population’s opinion? We present a positive answer by adopting the concept of metric distortion from computational social choice, which aims to quantify how much a panel’s decision aligns with the ideal decision of the population when preferences and agents lie on a metric space. We show that uniform selection needs only logarithmically many agents in terms of the number of alternatives to achieve almost optimal distortion. We also show that Fair Greedy Capture, a selection algorithm introduced recently by Ebadian and Micha (2024), matches uniform selection’s guarantees of almost optimal distortion and also achieves constant ex-post distortion, ensuring a “best of both worlds” performance.} }
Endnote
%0 Conference Paper %T Can a Few Decide for Many? The Metric Distortion of Sortition %A Ioannis Caragiannis %A Evi Micha %A Jannik Peters %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-caragiannis24a %I PMLR %P 5660--5679 %U https://proceedings.mlr.press/v235/caragiannis24a.html %V 235 %X Recent works have studied the design of algorithms for selecting representative sortition panels. However, the most central question remains unaddressed: Do these panels reflect the entire population’s opinion? We present a positive answer by adopting the concept of metric distortion from computational social choice, which aims to quantify how much a panel’s decision aligns with the ideal decision of the population when preferences and agents lie on a metric space. We show that uniform selection needs only logarithmically many agents in terms of the number of alternatives to achieve almost optimal distortion. We also show that Fair Greedy Capture, a selection algorithm introduced recently by Ebadian and Micha (2024), matches uniform selection’s guarantees of almost optimal distortion and also achieves constant ex-post distortion, ensuring a “best of both worlds” performance.
APA
Caragiannis, I., Micha, E. & Peters, J.. (2024). Can a Few Decide for Many? The Metric Distortion of Sortition. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:5660-5679 Available from https://proceedings.mlr.press/v235/caragiannis24a.html.

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