{"type":"ScholarlyArticle","title":"Concentration of Distortion: The Value of Extra Voters in Randomized Social Choice","authors":[{"name":"Brandon Fain","slug":"brandon-fain","given":"Brandon","family":"Fain","affiliation":"Department of Computer Science , Duke University , USA"},{"name":"William Fan","slug":"william-fan","given":"William","family":"Fan","affiliation":"North Carolina School of Science and Mathematics , USA"},{"name":"Kamesh Munagala","slug":"kamesh-munagala","given":"Kamesh","family":"Munagala","affiliation":"Department of Computer Science , Duke University , USA"}],"abstract":"We study higher statistical moments of Distortion for randomized social choice in a metric implicit utilitarian model. The Distortion of a social choice mechanism is the expected approximation factor with respect to the optimal utilitarian social cost (OPT). The k'th moment of Distortion is the expected approximation factor with respect to the k'th power of OPT. We consider mechanisms that elicit alternatives by randomly sampling voters for their favorite alternative. We design two families of mechanisms that provide constant (with respect to the number of voters and alternatives) k'th moment of Distortion using just k samples if all voters can then participate in a vote among the proposed alternatives, or 2k-1 samples if only the sampled voters can participate. We also show that these numbers of samples are tight. Such mechanisms deviate from a constant approximation to OPT with probability that drops exponentially in the number of samples, independent of the total number of voters and alternatives. We conclude with simulations on real-world  Participatory Budgeting data to qualitatively complement our theoretical insights.","doi":"10.24963/ijcai.2020/16","url":"https://ijcai.org/proceedings/2020/16","pdf":"https://ijcai.org/proceedings/2020/0016.pdf","markdown":"https://ijcai.org/proceedings/2020/16.md","bibtex":"https://ijcai.org/proceedings/2020/bibtex/16","volume":{"slug":"2020","title":"Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2020","url":"https://ijcai.org/proceedings/2020/","year":2020,"location":"Yokohama","dates":"January 2021 (postponed from 11-17 July 2020)","editors":"Christian Bessiere","isbn":"978-0-9992411-6-5","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2020"},"section":"Agent-based and Multi-agent Systems","track":"Main track","number":16,"pages":{"first":110,"last":116},"keywords":["Agent-based and Multi-agent Systems: Computational Social Choice","Agent-based and Multi-agent Systems: Voting"],"videos":[{"label":"Video","url":"https://videos.ijcai20.org/25193/file_25193.m3u8","length_sec":272,"provider":"hls"}],"references":[{"position":1,"raw":"[Anshelevich and Postl, 2017] Elliot Anshelevich and John Postl. 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