{"type":"ScholarlyArticle","title":"Tight Approximation for Proportional Approval Voting","authors":[{"name":"Szymon Dudycz","slug":"szymon-dudycz","given":"Szymon","family":"Dudycz","affiliation":"University of Wrocław , Poland"},{"name":"Pasin Manurangsi","slug":"pasin-manurangsi","given":"Pasin","family":"Manurangsi","affiliation":"Google Research , US"},{"name":"Jan Marcinkowski","slug":"jan-marcinkowski","given":"Jan","family":"Marcinkowski","affiliation":"University of Wrocław , Poland"},{"name":"Krzysztof Sornat","slug":"krzysztof-sornat","given":"Krzysztof","family":"Sornat","affiliation":"University of Wrocław , Poland; Ben-Gurion University , Israel"}],"abstract":"In approval-based multiwinner elections, we are given a set of voters, a set of candidates, and, for each voter, a set of candidates approved by the voter. The goal is to find a committee of size k that maximizes the total utility of the voters. In this paper, we study approximability of Thiele rules, which are known to be NP-hard to solve exactly. We provide a tight polynomial time approximation algorithm for a natural class of geometrically dominant weights that includes such voting rules as Proportional Approval Voting or p-Geometric. The algorithm is relatively simple: first we solve a linear program and then we round a solution by employing a framework called pipage rounding due to Ageev and Sviridenko (2004) and Calinescu et al. (2011). We provide a matching lower bound via a reduction from the Label Cover problem. Moreover, assuming a conjecture called Gap-ETH, we show that better approximation ratio cannot be obtained even in time f(k)*pow(n,o(k)).","doi":"10.24963/ijcai.2020/39","url":"https://ijcai.org/proceedings/2020/39","pdf":"https://ijcai.org/proceedings/2020/0039.pdf","markdown":"https://ijcai.org/proceedings/2020/39.md","bibtex":"https://ijcai.org/proceedings/2020/bibtex/39","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":39,"pages":{"first":276,"last":282},"keywords":["Agent-based and Multi-agent Systems: Computational Social Choice","Agent-based and Multi-agent Systems: Voting"],"videos":[{"label":"Video","url":"https://videos.ijcai20.org/25332/file_25332.m3u8","length_sec":279,"provider":"hls"}],"references":[{"position":1,"raw":"[Ageev and Sviridenko, 2004] Alexander A. Ageev and Maxim Sviridenko. Pipage Rounding: A New Method of Constructing Algorithms with Proven Performance Guar- antee. J. Comb. Optim., 8(3):307-328, 2004.","title":"Pipage Rounding: A New Method of Constructing Algorithms with Proven Performance Guarantee","authors":"Alexander A Ageev, Maxim Sviridenko","year":"2004","venue":"J. Comb. Optim","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Aziz et al., 2015] Haris Aziz, Serge Gaspers, Joachim Gud- mundsson, Simon Mackenzie, Nicholas Mattei, and Toby Walsh. Computational Aspects of Multi-Winner Approval Voting. In AAMAS, pages 107-115, 2015.","title":"Computational Aspects of Multi-Winner Approval Voting","authors":"Haris Aziz, Serge Gaspers, Joachim Gudmundsson, Simon Mackenzie, Nicholas Mattei, Toby Walsh","year":"2015","venue":"AAMAS","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Barman et al., 2020] Siddharth Barman, Omar Fawzi, Suprovat Ghoshal, and Emirhan Gürpinar. Tight Approxi- mation Bounds for Maximum Multi-Coverage. In IPCO, pages 66-77, 2020.","title":"Tight Approximation Bounds for Maximum Multi-Coverage","authors":"Siddharth Barman, Omar Fawzi, Suprovat Ghoshal, Emirhan Gürpinar","year":"2020","venue":"IPCO","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Bredereck et al., 2020] Robert Bredereck, Piotr Fal- iszewski, Andrzej Kaczmarczyk, Dusan Knop, and Rolf Niedermeier. Parameterized Algorithms for Finding a Collective Set of Items. In AAAI, 2020.","title":"Parameterized Algorithms for Finding a Collective Set of Items","authors":"Robert Bredereck, Piotr Faliszewski, Andrzej Kaczmarczyk, Dusan Knop, Rolf Niedermeier","year":"2020","venue":"AAAI","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Brill et al., 2018] Markus Brill, Jean-Franc ¸ois Laslier, and Piotr Skowron. Multiwinner Approval Rules as Appor- tionment Methods. J. Theor. Politics, 30(3):358-382, 2018.","title":"Multiwinner Approval Rules as Apportionment Methods","authors":"Markus Brill, Jean-Franc ¸ois Laslier, Piotr Skowron","year":"2018","venue":"J. Theor. Politics","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Byrka et al., 2017] Jarosław Byrka, Thomas Pensyl, Bar- tosz Rybicki, Aravind Srinivasan, and Khoa Trinh. An Im- proved Approximation for k-Median and Positive Correla- tion in Budgeted Optimization. ACM Trans. Algorithms, 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":7,"raw":"[Byrka et al., 2018] Jarosław Byrka, Piotr Skowron, and Krzysztof Sornat. Proportional Approval Voting, Har- monic k-Median, and Negative Association. In ICALP, pages 26:1-26:14, 2018.","title":"Proportional Approval Voting, Harmonic k-Median, and Negative Association","authors":"Jarosław Byrka, Piotr Skowron, Krzysztof Sornat","year":"2018","venue":"ICALP","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Cȃlinescu et al., 2011] Gruia Cȃlinescu, Chandra Chekuri, Martin Pál, and Jan Vondrák. Maximizing a Monotone Submodular Function Subject to a Matroid Constraint. SIAM J. Comput., 40(6):1740-1766, 2011.","title":"Maximizing a Monotone Submodular Function Subject to a Matroid Constraint","authors":"Gruia Cȃlinescu, Chandra Chekuri, Martin Pál, Jan Vondrák","year":"2011","venue":"SIAM J. Comput","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Chalermsook et al., 2017] Parinya Chalermsook, Marek Cygan, Guy Kortsarz, Bundit Laekhanukit, Pasin Manu- rangsi, Danupon Nanongkai, and Luca Trevisan. From Gap-ETH to FPT-Inapproximability: Clique, Dominating Set, and More. In FOCS, pages 743-754, 2017.","title":"From Gap-ETH to FPT-Inapproximability: Clique, Dominating Set, and More","authors":"Parinya Chalermsook, Marek Cygan, Guy Kortsarz, Bundit Laekhanukit, Pasin Manurangsi, Danupon Nanongkai, Luca Trevisan","year":"2017","venue":"FOCS","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Chamberlin and Courant, 1983] John R. Chamberlin and Paul N. Courant. Representative Deliberations and Repre- sentative Decisions: Proportional Representation and the Borda Rule. Am. Political Sci. Rev, 77:718-733, 9 1983.","title":"Representative Deliberations and Representative Decisions: Proportional Representation and the Borda Rule","authors":"John R Chamberlin, Paul N Courant","year":"1983","venue":"Am. Political Sci. Rev","doi":null,"url":null,"internal_url":null},{"position":11,"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":12,"raw":"[Cygan et al., 2018] Marek Cygan, Łukasz Kowalik, Arka- diusz Socała, and Krzysztof Sornat. Approximation and Parameterized Complexity of Minimax Approval Voting. J. Artif. Intell. Res., 63:495-513, 2018.","title":"Approximation and Parameterized Complexity of Minimax Approval Voting","authors":"Marek Cygan, Łukasz Kowalik, Arkadiusz Socała, Krzysztof Sornat","year":"2018","venue":"J. Artif. Intell. Res","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Faliszewski et al., 2017] Piotr Faliszewski, Piotr Skowron, Arkadii Slinko, and Nimrod Talmon. Multiwinner Rules on Paths From k-Borda to Chamberlin-Courant. In IJCAI, pages 192-198, 2017.","title":"Multiwinner Rules on Paths From k-Borda to Chamberlin-Courant","authors":"Piotr Faliszewski, Piotr Skowron, Arkadii Slinko, Nimrod Talmon","year":"2017","venue":"IJCAI","doi":null,"url":null,"internal_url":"/proceedings/2017/28"},{"position":14,"raw":"[Faliszewski et al., 2018] Piotr Faliszewski, Piotr Skowron, Arkadii Slinko, and Nimrod Talmon. Multiwinner Ana- logues of the Plurality Rule: Axiomatic and Algorithmic Perspectives. Soc. Choice Welf., 51(3):513-550, 2018.","title":"Multiwinner Analogues of the Plurality Rule: Axiomatic and Algorithmic Perspectives","authors":"Piotr Faliszewski, Piotr Skowron, Arkadii Slinko, Nimrod Talmon","year":"2018","venue":"Soc. Choice Welf","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Feige, 1998] Uriel Feige. A Threshold of ln(n) for Approx- imating Set Cover. J. ACM, 45(4):634-652, 1998.","title":"A Threshold of ln(n) for Approximating Set Cover","authors":"Uriel Feige","year":"1998","venue":"J. ACM","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Fluschnik et al., 2019] Till Fluschnik, Piotr Skowron, Mervin Triphaus, and Kai Wilker. Fair Knapsack. In AAAI, pages 1941-1948, 2019.","title":"Till Fluschnik","authors":"Fluschnik","year":"2019","venue":"Fair Knapsack","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Guha and Khuller, 1999] Sudipto Guha and Samir Khuller. Greedy Strikes Back: Improved Facility Location Algo- rithms. J. Algorithms, 31(1):228-248, 1999.","title":"Greedy Strikes Back: Improved Facility Location Algorithms","authors":"Khuller Guha, Sudipto Guha, Samir Khuller","year":"1999","venue":"J. Algorithms","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Jain et al., 2020] Pallavi Jain, Krzysztof Sornat, and Nim- rod Talmon. Participatory Budgeting with Project Interac- tions. In IJCAI, 2020.","title":"Participatory Budgeting with Project Interactions","authors":"Pallavi Jain, Krzysztof Sornat, Nimrod Talmon","year":"2020","venue":"IJCAI","doi":null,"url":null,"internal_url":"/proceedings/2020/54"},{"position":19,"raw":"[Janson, 2016] Svante Janson. Phragmén's and Thiele's Election Methods. CoRR, abs/1611.08826, 2016.","title":"Phragmén's and Thiele's Election Methods","authors":"Svante Janson","year":"2016","venue":null,"doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Khuller et al., 1999] Samir Khuller, Anna Moss, and Joseph Naor. The Budgeted Maximum Coverage Problem. Inf. Process. Lett., 70(1):39-45, 1999.","title":"The Budgeted Maximum Coverage Problem","authors":"Samir Khuller, Anna Moss, Joseph Naor","year":"1999","venue":"Inf. Process. Lett","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Kilgour, 2010] D. Marc Kilgour. Approval Balloting for Multi-Winner Elections. In Jean-Franc ¸ois Laslier and Remzi M. Sanver, editors, Handbook on Approval Voting, pages 105-124. Springer, 2010.","title":"Approval Balloting for Multi-Winner Elections","authors":"D Marc Kilgour","year":"2010","venue":"Handbook on Approval Voting","doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Lackner and Skowron, 2019] Martin Lackner and Piotr Skowron. A Quantitative Analysis of Multi-Winner Rules. In IJCAI, pages 407-413, 2019.","title":"A Quantitative Analysis of Multi-Winner Rules","authors":"Skowron Lackner, Martin Lackner, Piotr Skowron","year":"2019","venue":"IJCAI","doi":null,"url":null,"internal_url":"/proceedings/2019/58"},{"position":23,"raw":"[Manurangsi, 2020] Pasin Manurangsi. Tight Running Time Lower Bounds for Strong Inapproximability of Maximum k-Coverage, Unique Set Cover and Related Problems (via t-Wise Agreement Testing Theorem). In SODA, pages 62- 81, 2020.","title":"Tight Running Time Lower Bounds for Strong Inapproximability of Maximum k-Coverage, Unique Set Cover and Related Problems (via t-Wise Agreement Testing Theorem)","authors":"Pasin Manurangsi","year":"2020","venue":"SODA","doi":null,"url":null,"internal_url":null},{"position":24,"raw":"[Nemhauser et al., 1978] George L. Nemhauser, Lau- rence A. Wolsey, and Marshall L. Fisher. An Analysis of Approximations for Maximizing Submodular Set Functions -I. Math. Program., 14(1):265-294, 1978.","title":"An Analysis of Approximations for Maximizing Submodular Set Functions -I","authors":"George L Nemhauser, Laurence A Wolsey, Marshall L Fisher","year":"1978","venue":"Math. Program","doi":null,"url":null,"internal_url":null},{"position":25,"raw":"[Procaccia et al., 2008] Ariel D. Procaccia, Jeffrey S. Rosen- schein, and Aviv Zohar. On the Complexity of Achiev- ing Proportional Representation. Soc. Choice Welf., 30(3):353-362, 2008.","title":"On the Complexity of Achieving Proportional Representation","authors":"Ariel D Procaccia, Jeffrey S Rosenschein, Aviv Zohar","year":"2008","venue":"Soc. Choice Welf","doi":null,"url":null,"internal_url":null},{"position":26,"raw":"[Skowron and Faliszewski, 2017] Piotr Skowron and Piotr Faliszewski. Chamberlin-Courant Rule with Approval Ballots: Approximating the MaxCover Problem with Bounded Frequencies in FPT Time. J. Artif. Intell. Res., 60:687-716, 2017.","title":"Chamberlin-Courant Rule with Approval Ballots: Approximating the MaxCover Problem with Bounded Frequencies in FPT Time","authors":"Piotr Skowron, Piotr Faliszewski","year":"2017","venue":"J. Artif. Intell. Res","doi":null,"url":null,"internal_url":null},{"position":27,"raw":"[Skowron et al., 2016] Piotr Skowron, Piotr Faliszewski, and Jérôme Lang. Finding a Collective Set of Items: From Pro- portional Multirepresentation to Group Recommendation. Artif. Intell., 241:191-216, 2016.","title":"Finding a Collective Set of Items: From Proportional Multirepresentation to Group Recommendation","authors":"Piotr Skowron, Piotr Faliszewski, Jérôme Lang","year":"2016","venue":"Artif. Intell","doi":null,"url":null,"internal_url":null},{"position":28,"raw":"[Sviridenko, 2004] Maxim Sviridenko. A Note on Maxi- mizing a Submodular Set Function Subject to a Knapsack Constraint. Oper. Res. Lett., 32(1):41-43, 2004.","title":"A Note on Maximizing a Submodular Set Function Subject to a Knapsack Constraint","authors":"Maxim Sviridenko","year":"2004","venue":"Oper. Res. Lett","doi":null,"url":null,"internal_url":null},{"position":29,"raw":"[Swamy and Shmoys, 2008] Chaitanya Swamy and David B. Shmoys. Fault-Tolerant Facility Location. ACM Trans. Algorithms, 4(4):51:1-51:27, 2008.","title":"Fault-Tolerant Facility Location","authors":"Chaitanya Swamy, David B Shmoys","year":"2008","venue":"ACM Trans. Algorithms","doi":null,"url":null,"internal_url":null},{"position":30,"raw":"[Talmon and Faliszewski, 2019] Nimrod Talmon and Piotr Faliszewski. A Framework for Approval-Based Budget- ing Methods. In AAAI, pages 2181-2188, 2019.","title":"Nimrod Talmon and Piotr Faliszewski. A Framework for Approval-Based Budgeting Methods","authors":"Faliszewski Talmon","year":"2019","venue":"AAAI","doi":null,"url":null,"internal_url":null},{"position":31,"raw":"[Thiele, 1895] Thorvald Thiele. Om Flerfoldsvalg. In Over- sigt over det Kongelige Danske Videnskabernes Selskabs Forhandlinger (in Danish), pages 415-441.","title":"Om Flerfoldsvalg","authors":"Thorvald Thiele","year":null,"venue":"Oversigt over det Kongelige Danske Videnskabernes Selskabs Forhandlinger","doi":null,"url":null,"internal_url":null},{"position":32,"raw":"København: A.F. Høst, 1895.","title":null,"authors":"; A F København, Høst","year":"1895","venue":null,"doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}