{"type":"ScholarlyArticle","title":"Computational Complexity of Verifying the Group No-show Paradox","authors":[{"name":"Farhad Mohsin","slug":"farhad-mohsin","given":"Farhad","family":"Mohsin","affiliation":"College of the Holy Cross , Worcester , MA"},{"name":"Qishen Han","slug":"qishen-han","given":"Qishen","family":"Han","affiliation":"Rensselaer Polytechnic Institute , Troy , NY"},{"name":"Sikai Ruan","slug":"sikai-ruan","given":"Sikai","family":"Ruan","affiliation":"Rensselaer Polytechnic Institute , Troy , NY"},{"name":"Pin-Yu Chen","slug":"pin-yu-chen","given":"Pin-Yu","family":"Chen","affiliation":"IBM Research , Yorktown Heights , NY"},{"name":"Francesca Rossi","slug":"francesca-rossi","given":"Francesca","family":"Rossi","affiliation":"IBM Research , Yorktown Heights , NY"},{"name":"Lirong Xia","slug":"lirong-xia","given":"Lirong","family":"Xia","affiliation":"Rensselaer Polytechnic Institute , Troy , NY"}],"abstract":"The (group) no-show paradox refers to the undesirable situation where a group of agents have  incentive to abstain from voting to make the winner more favorable to them. To understand whether it is a critical concern in practice, in this paper, we take a  computational approach by examining the computational complexity of verifying whether the group no-show paradox exists given agents' preferences and the voting rule. We prove that, unfortunately, the verification problem is NP-hard to compute for some commonly studied voting rules, i.e., Copeland, maximin, single transferable vote, and all Condorcetified positional scoring rules such as Black's rule. We propose integer linear programming-based algorithms and a search-based algorithm for the verification problem for different voting rules. Experimental results on synthetic data illustrate that the former is efficient when the number of unique rankings in a profile is not too high, and the latter is efficient for a small number of agents. With the help of these algorithms, we observe that group no-show paradoxes rarely occur in real-world data.","doi":"10.24963/ijcai.2024/328","url":"https://ijcai.org/proceedings/2024/328","pdf":"https://ijcai.org/proceedings/2024/0328.pdf","markdown":"https://ijcai.org/proceedings/2024/328.md","bibtex":"https://ijcai.org/proceedings/2024/bibtex/328","volume":{"slug":"2024","title":"Proceedings of the Thirty-Third International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2024","url":"https://ijcai.org/proceedings/2024/","year":2024,"location":"Jeju, Korea","dates":"3-9 August 2024","editors":"Kate Larson","isbn":"978-1-956792-04-1","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2024"},"section":"Game Theory and Economic Paradigms","track":"Main Track","number":328,"pages":{"first":2958,"last":2966},"keywords":["Game Theory and Economic Paradigms: GTEP: Computational social choice"],"videos":[],"references":[{"position":1,"raw":"[Bartholdi and Orlin, 1991] John Bartholdi, III and James Orlin. 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