{"type":"ScholarlyArticle","title":"Representation Matters: Characterisation and Impossibility Results for Interval Aggregation","authors":[{"name":"Ulle Endriss","slug":"ulle-endriss","given":"Ulle","family":"Endriss","affiliation":"Institute for Logic, Language and Computation (ILLC) , University of Amsterdam; Panthéon-Sorbonne"},{"name":"Arianna Novaro","slug":"arianna-novaro","given":"Arianna","family":"Novaro","affiliation":"Centre d'Economie de la Sorbonne (CES) , University of Paris"},{"name":"Zoi Terzopoulou","slug":"zoi-terzopoulou","given":"Zoi","family":"Terzopoulou","affiliation":"LAMSADE , Université Paris Dauphine-PSL"}],"abstract":"In the context of aggregating intervals reflecting the views of several agents into a single interval, we investigate the impact of the form of representation chosen for the intervals involved. Specifically, we ask whether there are natural rules we can define both as rules that aggregate separately the left and right endpoints of intervals and as rules that aggregate separately the left endpoints and the interval widths. We show that on discrete scales it is essentially impossible to do so, while on continuous scales we can characterise the rules meeting these requirements as those that compute a weighted average of the endpoints of the individual intervals.","doi":"10.24963/ijcai.2022/41","url":"https://ijcai.org/proceedings/2022/41","pdf":"https://ijcai.org/proceedings/2022/0041.pdf","markdown":"https://ijcai.org/proceedings/2022/41.md","bibtex":"https://ijcai.org/proceedings/2022/bibtex/41","volume":{"slug":"2022","title":"Proceedings of the Thirty-First International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2022","url":"https://ijcai.org/proceedings/2022/","year":2022,"location":"Vienna","dates":"23-29 July 2022","editors":"Luc De Raedt","isbn":"978-1-956792-00-3","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2022"},"section":"Agent-based and Multi-agent Systems","track":"Main Track","number":41,"pages":{"first":286,"last":292},"keywords":["Agent-based and Multi-agent Systems: Computational Social Choice"],"videos":[{"label":"Video #1","url":"https://slideslive.com/38986884","length_sec":82,"provider":"slideslive"},{"label":"Video #2","url":"https://slideslive.com/38985027","length_sec":362,"provider":"slideslive"}],"references":[{"position":1,"raw":"[Aczél and Wagner, 1980] János Aczél and Carl Wagner. 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