{"type":"ScholarlyArticle","title":"Computational Aspects of Conditional Minisum Approval Voting in Elections with Interdependent Issues","authors":[{"name":"Evangelos Markakis","slug":"evangelos-markakis","given":"Evangelos","family":"Markakis","affiliation":"Athens University of Economics and Business , Department of Informatics"},{"name":"Georgios Papasotiropoulos","slug":"georgios-papasotiropoulos","given":"Georgios","family":"Papasotiropoulos","affiliation":"Athens University of Economics and Business , Department of Informatics"}],"abstract":"Approval voting provides a simple, practical framework for multi-issue elections, and the most representative example among such election rules is the classic Minisum approval voting rule. \r\nWe consider a generalization of Minisum, introduced by the work of Barrot and Lang [2016], referred to as Conditional Minisum, where voters are also allowed to express dependencies between issues.\r\nThe price we have to pay when we move to this higher level of expressiveness is that we end up with a computationally hard rule. Motivated by this, we focus on the computational aspects of Conditional Minisum, where progress has been rather scarce so far. \r\nWe identify restrictions to every voter's dependencies, under which we provide the first multiplicative approximation algorithms for the problem.\r\nThe restrictions involve upper bounds on the number of dependencies an issue can have on the others. At the same time, by additionally requiring certain structural properties for the union of dependencies cast by the whole electorate, we obtain optimal efficient algorithms for well-motivated special cases. \r\nOverall, our work provides a better understanding on the complexity implications introduced by conditional voting.","doi":"10.24963/ijcai.2020/43","url":"https://ijcai.org/proceedings/2020/43","pdf":"https://ijcai.org/proceedings/2020/0043.pdf","markdown":"https://ijcai.org/proceedings/2020/43.md","bibtex":"https://ijcai.org/proceedings/2020/bibtex/43","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":43,"pages":{"first":304,"last":310},"keywords":["Agent-based and Multi-agent Systems: Voting","Agent-based and Multi-agent Systems: Algorithmic Game Theory","Agent-based and Multi-agent Systems: Computational Social Choice"],"videos":[{"label":"Video","url":"https://videos.ijcai20.org/24835/file_24835.m3u8","length_sec":274,"provider":"hls"}],"references":[{"position":1,"raw":"[Airiau et al., 2011] Stéphane Airiau, Ulle Endriss, Umberto Grandi, Daniele Porello, and Joel Uckelman. 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