{"type":"ScholarlyArticle","title":"Approval-Based Elections and Distortion of Voting Rules","authors":[{"name":"Grzegorz Pierczyński","slug":"grzegorz-pierczynski","given":"Grzegorz","family":"Pierczyński","affiliation":"University of Warsaw , Warsaw , Poland"},{"name":"Piotr Skowron","slug":"piotr-skowron","given":"Piotr","family":"Skowron","affiliation":"University of Warsaw , Warsaw , Poland"}],"abstract":"We consider elections where both voters and candidates can be associated with points in a metric space and voters prefer candidates that are closer to those that are farther away. It is often assumed that the optimal candidate is the one that minimizes the total distance to the voters. Yet, the voting rules often do not have access to the metric space M and only see preference rankings induced by M. Consequently, they often are incapable of selecting the optimal candidate. The distortion of a voting rule measures the worst-case loss of the quality being the result of having access only to preference rankings. We extend the idea of distortion to approval-based preferences. First, we compute the distortion of Approval Voting. Second, we introduce the concept of acceptability-based distortion---the main idea behind is that the optimal candidate is the one that is acceptable to most voters. We determine acceptability-distortion for a number of rules, including Plurality, Borda, k-Approval, Veto, Copeland, Ranked Pairs, the Schulze's method, and STV.","doi":"10.24963/ijcai.2019/77","url":"https://ijcai.org/proceedings/2019/77","pdf":"https://ijcai.org/proceedings/2019/0077.pdf","markdown":"https://ijcai.org/proceedings/2019/77.md","bibtex":"https://ijcai.org/proceedings/2019/bibtex/77","volume":{"slug":"2019","title":"Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2019","url":"https://ijcai.org/proceedings/2019/","year":2019,"location":"Macao","dates":"10-16 August 2019","editors":"Sarit Kraus","isbn":"978-0-9992411-4-1","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2019"},"section":"Agent-based and Multi-agent Systems","track":"Main track","number":77,"pages":{"first":543,"last":549},"keywords":["Agent-based and Multi-agent Systems: Computational Social Choice","Agent-based and Multi-agent Systems: Voting"],"videos":[],"references":[{"position":1,"raw":"[Anshelevich and Postl, 2017] E. 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