{"type":"ScholarlyArticle","title":"On the Complexity of Calculating Approval-Based Winners in Candidates-Embedded Metrics","authors":[{"name":"Yongjie Yang","slug":"yongjie-yang","given":"Yongjie","family":"Yang","affiliation":"Chair of Economic Theory , Saarland University , Saarbrücken , Germany"}],"abstract":"We study approval-based multiwinner voting where candidates are in a metric space and committees are valuated in terms of their distances to the given votes. In particular, we consider three different distance functions, and for each of them we study both the utilitarian rules and the egalitarian rules, resulting in six variants of winners determination problems. We focus on the (parameterized) complexity of these problems for both the general metric and several special metrics. For hardness results, we also discuss their approximability.","doi":"10.24963/ijcai.2022/83","url":"https://ijcai.org/proceedings/2022/83","pdf":"https://ijcai.org/proceedings/2022/0083.pdf","markdown":"https://ijcai.org/proceedings/2022/83.md","bibtex":"https://ijcai.org/proceedings/2022/bibtex/83","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":83,"pages":{"first":585,"last":591},"keywords":["Agent-based and Multi-agent Systems: Algorithmic Game Theory","Agent-based and Multi-agent Systems: Computational Social Choice"],"videos":[{"label":"Video #1","url":"https://slideslive.com/38987084","length_sec":87,"provider":"slideslive"},{"label":"Video #2","url":"https://slideslive.com/38985227","length_sec":715,"provider":"slideslive"}],"references":[{"position":1,"raw":"[Anshelevich et al., 2018] Elliot Anshelevich, Onkar Bhard- waj, Edith Elkind, John Postl, and Piotr Skowron. Ap- proximating optimal social choice under metric prefer- ences. Artif. Intell., 264:27-51, 2018.","title":"Approximating optimal social choice under metric preferences","authors":"Anshelevich","year":"2018","venue":"Artif. Intell","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Arora et al., 1998] Sanjeev Arora, Prabhakar Raghavan, and Satish Rao. Approximation schemes for Euclidean k-medians and related problems. In STOC, pages 106- 113, 1998.","title":"Approximation schemes for Euclidean k-medians and related problems","authors":"Sanjeev Arora, Prabhakar Raghavan, Satish Rao","year":"1998","venue":"STOC","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Aziz et al., 2018] Haris Aziz, Edith Elkind, Shenwei Huang, Martin Lackner, Luis Sánchez-Fernández, and Piotr Skowron. On the complexity of extended and pro- portional justified representation. In AAAI, pages 902- 909, 2018.","title":"On the complexity of extended and proportional justified representation","authors":"Haris Aziz, Edith Elkind, Shenwei Huang, Martin Lackner, Luis Sánchez-Fernández, Piotr Skowron","year":"2018","venue":"AAAI","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Betzler et al., 2013] Nadja Betzler, Arkadii Slinko, and Jo- hannes Uhlmann. On the computation of fully propor- tional representation. J. Artif. Intell. Res., 47:475-519, 2013.","title":"On the computation of fully proportional representation","authors":"Nadja Betzler, Arkadii Slinko, Johannes Uhlmann","year":"2013","venue":"J. Artif. Intell. Res","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Brams and Kilgour, 2014] Steven J. Brams and D. Marc Kilgour. Satisfaction approval voting. In Rudolf Fara, Dennis Leech, and Maurice Salles, editors, Voting Power and Procedures, Studies in Choice and Welfare, pages 323-346. Springer, 2014.","title":"Satisfaction approval voting","authors":"Steven J Brams, D Marc Kilgour","year":"2014","venue":"Voting Power and Procedures, Studies in Choice and Welfare","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Brams et al., 2007] Steven J. Brams, D. Marc Kilgour, and M. Remzi Sanver. A minimax procedure for electing committees. Public Choice, 132(3-4):401-420, 2007.","title":"A minimax procedure for electing committees","authors":"Steven J Brams, D Marc Kilgour, M Remzi Sanver","year":"2007","venue":"Public Choice","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Brill et al., 2020] Markus Brill, Paul Gölz, Dominik Peters, Ulrike Schmidt-Kraepelin, and Kai Wilker. Approval- based apportionment. In AAAI, pages 1854-1861, 2020.","title":"Approvalbased apportionment","authors":"Markus Brill, Paul Gölz, Dominik Peters, Ulrike Schmidt-Kraepelin, Kai Wilker","year":"2020","venue":"AAAI","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Byrka et al., 2017] Jarosław Byrka, Thomas Pensyl, Bar- tosz Rybicki, Aravind Srinivasan, and Khoa Trinh. An improved approximation for k-median and positive cor- relation in budgeted optimization. ACM Trans. Algo- rithms, 13(2):23:1-23:31, 2017.","title":"An improved approximation for k-median and positive correlation in budgeted optimization","authors":"Jarosław Byrka, Thomas Pensyl, Bartosz Rybicki, Aravind Srinivasan, Khoa Trinh","year":"2017","venue":"ACM Trans. Algorithms","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Chamberlin and Courant, 1983] John. R. Chamberlin and Paul N. Courant. Representative deliberations and rep- resentative decisions: Proportional representation and the Borda rule. Am. Polit. Sci. Rev., 77(3):718-733, 1983.","title":"Representative deliberations and representative decisions: Proportional representation and the Borda rule","authors":"John R Chamberlin, Paul N Courant","year":"1983","venue":"Am. Polit. Sci. Rev","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Chen et al., 2020] Xujin Chen, Minming Li, and Chenhao Wang. Favorite-candidate voting for eliminating the least popular candidate in a metric space. In AAAI, pages 1894-1901, 2020.","title":"Favorite-candidate voting for eliminating the least popular candidate in a metric space","authors":"Chen","year":"2020","venue":"AAAI","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Cohen-Addad et al., 2022] Vincent Cohen-Addad, Hossein Esfandiari, Vahab Mirrokni, and Shyam Narayanan. Im- proved approximations for Euclidean k-means and k- median, via nested quasi-independent sets. In STOC, 2022.","title":"Improved approximations for Euclidean k-means and kmedian, via nested quasi-independent sets","authors":"Vincent Cohen-Addad, Hossein Esfandiari, Vahab Mirrokni, Shyam Narayanan","year":"2022","venue":"STOC","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Cohen-Addad et al., 2019] Vincent Cohen-Addad, Anupam Gupta, Amit Kumar, Euiwoong Lee, and Jason Li. Tight FPT approximations for k-median and k-means. In ICALP, pages 42:1-42:14, 2019.","title":"Tight FPT approximations for k-median and k-means","authors":"Vincent Cohen-Addad, Anupam Gupta, Amit Kumar, Euiwoong Lee, Jason Li","year":"2019","venue":"ICALP","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Downey, 2012] Rod Downey. A parameterized complexity tutorial. In LATA, pages 38-56, 2012.","title":"Rod Downey. A parameterized complexity tutorial","authors":"Downey","year":"2012","venue":"LATA","doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Duggan, 2007] John Duggan. Equilibrium existence for zero-sum games and spatial models of elections. Game. Econ. Behav., 60(1):52-74, 2007.","title":"Equilibrium existence for zero-sum games and spatial models of elections","authors":"John Duggan","year":"2007","venue":"Game. Econ. Behav","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Elkind and Lackner, 2015] Edith Elkind and Martin Lack- ner. Structure in dichotomous preferences. In IJCAI, pages 2019-2025, 2015.","title":"Structure in dichotomous preferences","authors":"Lackner Elkind","year":"2015","venue":"IJCAI","doi":null,"url":null,"internal_url":"/proceedings/2015/286"},{"position":16,"raw":"[Feldmann, 2019] Andreas Emil Feldmann. Fixed- parameter approximations for k-center problems in low highway dimension graphs. Algorithmica, 81(3):1031-1052, 2019.","title":"Fixedparameter approximations for k-center problems in low highway dimension graphs","authors":"Andreas Emil, Feldmann","year":"2019","venue":"Algorithmica","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Gawron and Faliszewski, 2019] Grzegorz Gawron and Piotr Faliszewski. Robustness of approval-based multiwinner voting rules. In ADT, pages 17-31, 2019.","title":"Robustness of approval-based multiwinner voting rules","authors":"Grzegorz Gawron, Piotr Faliszewski","year":"2019","venue":"ADT","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Gkatzelis et al., 2020] Vasilis Gkatzelis, Daniel Halpern, and Nisarg Shah. Resolving the optimal metric distor- tion conjecture. In FOCS, pages 1427-1438, 2020.","title":"Resolving the optimal metric distortion conjecture","authors":"Vasilis Gkatzelis, Daniel Halpern, Nisarg Shah","year":"2020","venue":"FOCS","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Gonzalez, 1985] Teofilo Francisco Gonzalez. Clustering to minimize the maximum intercluster distance. Theor. Comput. Sci., 38:293-306, 1985.","title":"Clustering to minimize the maximum intercluster distance","authors":"Francisco Teofilo, Gonzalez","year":"1985","venue":"Theor. Comput. Sci","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Guruswami and Indyk, 2003] Venkatesan Guruswami and Piotr Indyk. Embeddings and non-approximability of geometric problems. In SODA, pages 537-538, 2003.","title":"Embeddings and non-approximability of geometric problems","authors":"Venkatesan Guruswami, Piotr Indyk","year":"2003","venue":"SODA","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Hochbaum and Shmoys, 1986] Dorit S. Hochbaum and David Bernard Shmoys. A unified approach to approx- imation algorithms for bottleneck problems. J. ACM, 33(3):533-550, 1986.","title":"A unified approach to approximation algorithms for bottleneck problems","authors":"Dorit S Hochbaum, David Bernard, Shmoys","year":"1986","venue":"J. ACM","doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Hsu and Nemhauser, 1979] Wen-Lian Hsu and George Lann Nemhauser. Easy and hard bottleneck location problems. Discret. Appl. Math., 1(3):209-215, 1979.","title":"Easy and hard bottleneck location problems","authors":"Wen-Lian Hsu, George Lann, Nemhauser","year":"1979","venue":"Discret. Appl. Math","doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[Izsak et al., 2018] Rani Izsak, Nimrod Talmon, and Gerhard Woeginger. Committee selection with intraclass and in- terclass synergies. In AAAI, pages 1071-1078, 2018.","title":"Committee selection with intraclass and interclass synergies","authors":"Rani Izsak, Nimrod Talmon, Gerhard Woeginger","year":"2018","venue":"AAAI","doi":null,"url":null,"internal_url":null},{"position":24,"raw":"[Jesorsky et al., 2001] Oliver Jesorsky, Klaus J. Kirchberg, and Robert W. Frischholz. Robust face detection using the Hausdorff distance. In AVBPA, pages 90-95, 2001.","title":"Robust face detection using the Hausdorff distance","authors":"Oliver Jesorsky, Klaus J Kirchberg, Robert W Frischholz","year":"2001","venue":"AVBPA","doi":null,"url":null,"internal_url":null},{"position":25,"raw":"[Lackner and Skowron, 2020] Martin Lackner and Piotr Skowron. Multi-winner voting with approval prefer- ences. https://arxiv.org/pdf/2007.01795.pdf, 2020. Ac- cessed: 2022-05-15.","title":"Multi-winner voting with approval preferences","authors":"Skowron Lackner, Martin Lackner, Piotr Skowron","year":"2020","venue":null,"doi":null,"url":"-cessed:2022-05-15","internal_url":null},{"position":26,"raw":"[Liu and Guo, 2016] Hong Liu and Jiong Guo. Parameter- ized complexity of winner determination in minimax committee elections. In AAMAS, pages 341-349, 2016.","title":"Parameterized complexity of winner determination in minimax committee elections","authors":"Guo ; Liu, Hong Liu, Jiong Guo","year":"2016","venue":"AAMAS","doi":null,"url":null,"internal_url":null},{"position":27,"raw":"[Merrill, 1993] Samuel Merrill III. Voting behavior under the directional spatial model of electoral competition. Public Choice, 77:739-756, 1993.","title":"Samuel Merrill III. Voting behavior under the directional spatial model of electoral competition","authors":"Merrill","year":"1993","venue":"Public Choice","doi":null,"url":null,"internal_url":null},{"position":28,"raw":"[Peters, 2018] Dominik Peters. Single-peakedness and to- tal unimodularity: New polynomial-time algorithms for multi-winner elections. In AAAI, pages 1169-1176, 2018.","title":"Single-peakedness and total unimodularity: New polynomial-time algorithms for multi-winner elections","authors":"Dominik Peters","year":"2018","venue":"AAAI","doi":null,"url":null,"internal_url":null},{"position":29,"raw":"[Pierczynski and Skowron, 2019] Grzegorz Pierczyński and Piotr Skowron. Approval-based elections and distortion of voting rules. In IJCAI, pages 543-549, 2019.","title":"Approval-based elections and distortion of voting rules","authors":"Grzegorz Pierczyński, Piotr Skowron","year":"2019","venue":"IJCAI","doi":null,"url":null,"internal_url":"/proceedings/2019/77"},{"position":30,"raw":"[Thiele, 1895] Thorvald Nicolai Thiele. Om flerfoldsvalg. Oversigt over det Kongelige Danske Videnskabernes Selskabs Forhandlinger, pages 415-441, 1895.","title":"Om flerfoldsvalg. Oversigt over det Kongelige Danske Videnskabernes Selskabs Forhandlinger","authors":"Thorvald Nicolai, Thiele","year":"1895","venue":null,"doi":null,"url":null,"internal_url":null},{"position":31,"raw":"[West, 2000] Douglas Brent West. Introduction to Graph Theory. Prentice-Hall, 2000.","title":"Introduction to Graph Theory","authors":"Douglas Brent, West","year":"2000","venue":null,"doi":null,"url":null,"internal_url":null},{"position":32,"raw":"[Yang and Wang, 2018] Yongjie Yang and Jianxin Wang. Multiwinner voting with restricted admissible sets: Complexity and strategyproofness. In IJCAI, pages 576-582, 2018.","title":"Multiwinner voting with restricted admissible sets: Complexity and strategyproofness","authors":"Yang, Wang ; ] Yongjie Yang, Jianxin Wang","year":"2018","venue":"IJCAI","doi":null,"url":null,"internal_url":"/proceedings/2018/80"},{"position":33,"raw":"[Yang, 2019] Yongjie Yang. Complexity of manipulating and controlling approval-based multiwinner voting. In IJCAI, pages 637-643, 2019.","title":"Complexity of manipulating and controlling approval-based multiwinner voting","authors":"Yongjie Yang","year":"2019","venue":"IJCAI","doi":null,"url":null,"internal_url":"/proceedings/2019/90"}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}