{"type":"ScholarlyArticle","title":"Insight into Voting Problem Complexity Using Randomized Classes","authors":[{"name":"Zack Fitzsimmons","slug":"zack-fitzsimmons","given":"Zack","family":"Fitzsimmons","affiliation":"College of the Holy Cross"},{"name":"Edith Hemaspaandra","slug":"edith-hemaspaandra","given":"Edith","family":"Hemaspaandra","affiliation":"Rochester Institute of Technology"}],"abstract":"The first step in classifying the complexity of an NP problem is typically showing the problem in P or NP-complete. This has been a successful first step for many problems, including voting problems. However, in this paper we show that this may not always be the best first step. We consider the problem of constructive control by replacing voters (CCRV) introduced by Loreggia et al. [2015, https://dl.acm.org/doi/10.5555/2772879.2773411] for the scoring rule First-Last, which is defined by (1, 0, ..., 0, -1). We show that this problem is equivalent to Exact Perfect Bipartite Matching, and so CCRV for First-Last can be determined in random polynomial time. So on the one hand, if CCRV for First-Last is NP-complete then RP = NP, which is extremely unlikely. On the other hand, showing that CCRV for First-Last is in P would also show that Exact Perfect Bipartite Matching is in P, which would solve a well-studied 40-year-old open problem.\r\n\r\nConsidering RP as an option for classifying problems can also help classify problems that until now had escaped classification. For example, the sole open problem in the comprehensive table from Erdélyi et al. [2021, https://doi.org/10.1007/s10458-021-09523-9] is CCRV for 2-Approval. We show that this problem is in RP, and thus easy since it is widely assumed that P = RP.","doi":"10.24963/ijcai.2022/42","url":"https://ijcai.org/proceedings/2022/42","pdf":"https://ijcai.org/proceedings/2022/0042.pdf","markdown":"https://ijcai.org/proceedings/2022/42.md","bibtex":"https://ijcai.org/proceedings/2022/bibtex/42","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":42,"pages":{"first":293,"last":299},"keywords":["Agent-based and Multi-agent Systems: Computational Social Choice"],"videos":[{"label":"Video #1","url":"https://slideslive.com/38986936","length_sec":83,"provider":"slideslive"},{"label":"Video #2","url":"https://slideslive.com/38985079","length_sec":342,"provider":"slideslive"}],"references":[{"position":1,"raw":"[Bartholdi et al., 1992] J. 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