{"type":"ScholarlyArticle","title":"The Complexity of Election Problems with Group-Separable Preferences","authors":[{"name":"Piotr Faliszewski","slug":"piotr-faliszewski","given":"Piotr","family":"Faliszewski","affiliation":"AGH University , Krakow , Poland"},{"name":"Alexander Karpov","slug":"alexander-karpov","given":"Alexander","family":"Karpov","affiliation":"National Research University Higher School of Economics , Moscow , Russia; Institute of Control Sciences of Russian Academy of Sciences , Moscow , Russia"},{"name":"Svetlana Obraztsova","slug":"svetlana-obraztsova","given":"Svetlana","family":"Obraztsova","affiliation":"Nanyang Technological University , Singapore"}],"abstract":"We analyze the complexity of several NP-hard election-related problems under the assumptions that the voters have group-separable preferences. We show that under this assumption our problems typically remain NP-hard, but we provide more efficient algorithms if additionally the clone decomposition tree is of moderate height.","doi":"10.24963/ijcai.2020/29","url":"https://ijcai.org/proceedings/2020/29","pdf":"https://ijcai.org/proceedings/2020/0029.pdf","markdown":"https://ijcai.org/proceedings/2020/29.md","bibtex":"https://ijcai.org/proceedings/2020/bibtex/29","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":29,"pages":{"first":203,"last":209},"keywords":["Agent-based and Multi-agent Systems: Voting","Agent-based and Multi-agent Systems: Algorithmic Game Theory","Agent-based and Multi-agent Systems: Computational Social Choice"],"videos":[{"label":"Video","url":"https://videos.ijcai20.org/25179/file_25179.m3u8","length_sec":245,"provider":"hls"}],"references":[{"position":1,"raw":"[Bartholdi et al., 1992] J. Bartholdi, III, C. Tovey, and M. Trick. How hard is it to control an election? Math- ematical and Computer Modeling, 16(8/9):27-40, 1992.","title":"How hard is it to control an election?","authors":"J Bartholdi, C Iii, M Tovey, Trick","year":"1992","venue":"Mathematical and Computer Modeling","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Betzler et al., 2013] N. Betzler, A. Slinko, and J. Uhlmann. On the computation of fully proportional representation. Journal of Art. Int. Research, 47:475-519, 2013.","title":"On the computation of fully proportional representation","authors":"N Betzler, A Slinko, J Uhlmann","year":"2013","venue":"Journal of Art. Int. Research","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Black, 1958] D. Black. The Theory of Committees and Elec- tions. Cambridge University Press, 1958.","title":"The Theory of Committees and Elections","authors":"D Black","year":"1958","venue":null,"doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Booth and Lueker, 1976] K. Booth and G. Lueker. Test- ing for the consecutive ones property, interval graphs, and graph planarity using PQ-tree algorithms. Journal of Com- puter and System Sciences, 13(3):335-379, 1976.","title":"Testing for the consecutive ones property, interval graphs, and graph planarity using PQ-tree algorithms","authors":"K Booth, G Lueker","year":"1976","venue":"Journal of Computer and System Sciences","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Brandt et al., 2015] F. Brandt, M. Brill, E. Hemaspaandra, and L. Hemaspaandra. Bypassing combinatorial protec- tions: Polynomial-time algorithms for single-peaked elec- torates. Journal of Art. Int. Research, 53:439-496, 2015.","title":"Bypassing combinatorial protections: Polynomial-time algorithms for single-peaked electorates","authors":"F Brandt, M Brill, E Hemaspaandra, L Hemaspaandra","year":"2015","venue":"Journal of Art. Int. Research","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Bredereck et al., 2016] R. Bredereck, J. Chen, and G. Woeginger. Are there any nicely structured preference profiles nearby? Math. Social Sciences, 79:61-73, 2016.","title":"Are there any nicely structured preference profiles nearby?","authors":"R Bredereck, J Chen, G Woeginger","year":"2016","venue":"Math. Social Sciences","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Chamberlin and Courant, 1983] B. Chamberlin and P. Courant. Representative deliberations and representa- tive decisions: Proportional representation and the Borda rule. American Political Science Review, 77(3):718-733, 1983.","title":"Representative deliberations and representative decisions: Proportional representation and the Borda rule","authors":"B Chamberlin, P Courant","year":"1983","venue":"American Political Science Review","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Conitzer, 2009] V. Conitzer. Eliciting single-peaked prefer- ences using comparison queries. Journal of Art. Int. Re- search, 35:161-191, 2009.","title":"Eliciting single-peaked preferences using comparison queries","authors":"V Conitzer","year":"2009","venue":"Journal of Art. Int. Research","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Eisenbrand and Weismantel, 2018] F. Eisenbrand and R. Weismantel. Proximity results and faster algorithms for integer programming using the Steinitz lemma. In Proceedings of SODA-18, pages 808-816, 2018.","title":"Proximity results and faster algorithms for integer programming using the Steinitz lemma","authors":"F Eisenbrand, R Weismantel","year":"2018","venue":"Proceedings of SODA-18","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Elkind et al., 2012] E. Elkind, P. Faliszewski, and A. Slinko. Clone structures in voters' preferences. In Proceedings of EC-12, pages 496-513, June 2012.","title":"Clone structures in voters' preferences","authors":"E Elkind, P Faliszewski, A Slinko","year":"2012","venue":"Proceedings of EC-12","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Elkind et al., 2016] E. Elkind, M. Lackner, and D. Peters. Preference restrictions in computational social choice: Re- cent progress. In Proceedings of IJCAI-2016, pages 4062- 4065, 2016.","title":"Preference restrictions in computational social choice: Recent progress","authors":"E Elkind, M Lackner, D Peters","year":"2016","venue":"Proceedings of IJCAI-2016","doi":null,"url":null,"internal_url":"/proceedings/2016/601"},{"position":12,"raw":"[Faliszewski et al., 2011] P. Faliszewski, E. Hemaspaandra, L. Hemaspaandra, and J. Rothe. The shield that never was: Societies with single-peaked preferences are more open to manipulation and control. Information and Computation, 209(2):89-107, 2011.","title":"The shield that never was: Societies with single-peaked preferences are more open to manipulation and control","authors":"P Faliszewski, E Hemaspaandra, L Hemaspaandra, J Rothe","year":"2011","venue":"Information and Computation","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Gavenciak et al., 2018] T. Gavenciak, D. Knop, and M. Koutecký. Integer programming in parameterized complexity: Three miniatures. In Proceedings of IPEC-18, pages 21:1-21:16, 2018.","title":"Integer programming in parameterized complexity: Three miniatures","authors":"T Gavenciak, D Knop, M Koutecký","year":"2018","venue":"Proceedings of IPEC-18","doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Hemaspaandra et al., 2007] E. Hemaspaandra, L. Hemas- paandra, and J. Rothe. Anyone but him: The complexity of precluding an alternative. Artificial Intelligence, 171(5- 6):255-285, 2007.","title":"Anyone but him: The complexity of precluding an alternative","authors":"E Hemaspaandra, L Hemaspaandra, J Rothe","year":"2007","venue":"Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Inada, 1964] K. Inada. A note on the simple majority deci- sion rule. Econometrica, 32(32):525-531, 1964.","title":"A note on the simple majority decision rule","authors":"K Inada","year":"1964","venue":"Econometrica","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Inada, 1969] K. Inada. The simple majority decision rule. Econometrica, 37(3):490-506, 1969.","title":"The simple majority decision rule","authors":"K Inada","year":"1969","venue":"Econometrica","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Karpov, 2019] A. Karpov. On the number of group- separable preference profiles. Group Decision and Nego- tiation, 28(3):501-517, 2019.","title":"On the number of groupseparable preference profiles","authors":"A Karpov","year":"2019","venue":"Group Decision and Negotiation","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Lu and Boutilier, 2011] T. Lu and C. Boutilier. Budgeted social choice: From consensus to personalized decision making. In Proceedings of IJCAI-11, pages 280-286, 2011.","title":"Budgeted social choice: From consensus to personalized decision making","authors":"T Lu, C Boutilier","year":"2011","venue":"Proceedings of IJCAI-11","doi":null,"url":null,"internal_url":"/proceedings/2011/57"},{"position":19,"raw":"[Magiera and Faliszewski, 2017] K. Magiera and P. Fal- iszewski. How hard is control in single-crossing elections? Autonomous Agents and Multiagent Systems, 31(3):606- 627, 2017.","title":"How hard is control in single-crossing elections?","authors":"K Magiera, P Faliszewski","year":"2017","venue":"Autonomous Agents and Multiagent Systems","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Mirrlees, 1971] J. Mirrlees. An exploration in the theory of optimal income taxation. Review of Economic Studies, 38:175-208, 1971.","title":"An exploration in the theory of optimal income taxation","authors":"J Mirrlees","year":"1971","venue":"Review of Economic Studies","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Obraztsova and Elkind, 2011] S. Obraztsova and E. Elkind. On the complexity of voting manipulation under random- ized tie-breaking. In Proceedings of IJCAI-11, pages 319- 324, July 2011.","title":"On the complexity of voting manipulation under randomized tie-breaking","authors":"S Obraztsova, E Elkind","year":"2011","venue":"Proceedings of IJCAI-11","doi":null,"url":null,"internal_url":"/proceedings/2011/63"},{"position":22,"raw":"[Obraztsova et al., 2011] S. Obraztsova, E. Elkind, and N. Hazon. Ties matter: Complexity of voting manipula- tion revisited. In Proceedings of AAMAS-11, pages 71-78, May 2011.","title":"Ties matter: Complexity of voting manipulation revisited","authors":"S Obraztsova, E Elkind, N Hazon","year":"2011","venue":"Proceedings of AAMAS-11","doi":null,"url":null,"internal_url":"/proceedings/2011/449"},{"position":23,"raw":"[Peters and Elkind, 2016] D. Peters and E. Elkind. Prefer- ences single-peaked on nice trees. In Proceedings of AAAI- 16, pages 594-600, 2016.","title":"Preferences single-peaked on nice trees","authors":"D Peters, E Elkind","year":"2016","venue":"Proceedings of AAAI-16","doi":null,"url":null,"internal_url":null},{"position":24,"raw":"[Peters and Lackner, 2017] D. Peters and M. Lackner. Pref- erences single-peaked on a circle. In Proceedings of AAAI- 2017, pages 649-655, 2017.","title":"Preferences single-peaked on a circle","authors":"D Peters, M Lackner","year":"2017","venue":"Proceedings of AAAI-2017","doi":null,"url":null,"internal_url":null},{"position":25,"raw":"[Procaccia et al., 2008] A. Procaccia, J. Rosenschein, and A. Zohar. On the complexity of achieving proportional representation. Social Choice and Welfare, 30(3):353- 362, 2008.","title":"On the complexity of achieving proportional representation","authors":"A Procaccia, J Rosenschein, A Zohar","year":"2008","venue":"Social Choice and Welfare","doi":null,"url":null,"internal_url":null},{"position":26,"raw":"[Roberts, 1977] K. Roberts. Voting over income tax sched- ules. Journal of Public Economics, 8(3):329-340, 1977.","title":"Voting over income tax schedules","authors":"K Roberts","year":"1977","venue":"Journal of Public Economics","doi":null,"url":null,"internal_url":null},{"position":27,"raw":"[Rothe et al., 2003] J. Rothe, H. Spakowski, and J. Vogel. Exact complexity of the winner problem for Young elec- tions. Theory of Comp. Systems, 36(4):375-386, 2003.","title":"Exact complexity of the winner problem for Young elections","authors":"J Rothe, H Spakowski, J Vogel","year":"2003","venue":"Theory of Comp. Systems","doi":null,"url":null,"internal_url":null},{"position":28,"raw":"[Skowron et al., 2015a] P. Skowron, P. Faliszewski, and A. Slinko. Achieving fully proportional representation: Approximability result. Artificial Intelligence, 222:67- 103, 2015.","title":"Achieving fully proportional representation: Approximability result","authors":"Skowron","year":"2015","venue":"Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":29,"raw":"[Skowron et al., 2015b] P. Skowron, L. Yu, P. Faliszewski, and E. Elkind. The complexity of fully proportional repre- sentation for single-crossing electorates. Theoretical Com- puter Science, 569:43-57, 2015.","title":"The complexity of fully proportional representation for single-crossing electorates","authors":"Skowron","year":"2015","venue":"Theoretical Computer Science","doi":null,"url":null,"internal_url":null},{"position":30,"raw":"[Young, 1977] H. Young. Extending Condorcet's rule. Jour- nal of Economic Theory, 16(2):335-353, 1977.","title":"Extending Condorcet's rule","authors":"H Young","year":"1977","venue":"Journal of Economic Theory","doi":null,"url":null,"internal_url":null},{"position":31,"raw":"[Yu et al., 2013] Lan Yu, Hau Chan, and Edith Elkind. Mul- tiwinner elections under preferences that are single-peaked on a tree. In Proceedings of IJCAI-13, volume 13, pages 425-431, 2013.","title":"Multiwinner elections under preferences that are single-peaked on a tree","authors":"Lan Yu, Hau Chan, Edith Elkind","year":"2013","venue":"Proceedings of IJCAI-13","doi":null,"url":null,"internal_url":"/proceedings/2013/70"}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}