{"type":"ScholarlyArticle","title":"On the Tree Representations of Dichotomous Preferences","authors":[{"name":"Yongjie Yang","slug":"yongjie-yang","given":"Yongjie","family":"Yang","affiliation":"Chair of Economic Theory , Saarland University , Saarbrücken , Germany"}],"abstract":"We study numerous restricted domains of dichotomous preferences with respect to some tree structures. Particularly, we study the relationships among these domains and the ones proposed by Elkind and Lackner [2015]. We also show that recognizing all the restricted domains proposed in this paper is polynomial-time solvable. Finally, we explore the complexity of winner determination for several important approval-based multiwinner voting rules when restricted to these domains.","doi":"10.24963/ijcai.2019/91","url":"https://ijcai.org/proceedings/2019/91","pdf":"https://ijcai.org/proceedings/2019/0091.pdf","markdown":"https://ijcai.org/proceedings/2019/91.md","bibtex":"https://ijcai.org/proceedings/2019/bibtex/91","volume":{"slug":"2019","title":"Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2019","url":"https://ijcai.org/proceedings/2019/","year":2019,"location":"Macao","dates":"10-16 August 2019","editors":"Sarit Kraus","isbn":"978-0-9992411-4-1","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2019"},"section":"Agent-based and Multi-agent Systems","track":"Main track","number":91,"pages":{"first":644,"last":650},"keywords":["Agent-based and Multi-agent Systems: Algorithmic Game Theory","Agent-based and Multi-agent Systems: Computational Social Choice"],"videos":[],"references":[{"position":1,"raw":"[Aziz et al., 2015] Haris Aziz, Serge Gaspers, Joachim Gud- mundsson, Simon Mackenzie, Nicholas Mattei, and Toby Walsh. Computational aspects of multi-winner ap- proval 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":2,"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":3,"raw":"[Black, 1948] Duncan Black. On the rationale of group decision-making. J. Polit. Econ., 56(1):23-34, 1948.","title":"On the rationale of group decision-making","authors":"Duncan Black","year":"1948","venue":"J. Polit. Econ","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Brandes et al., 2012] Ulrik Brandes, Sabine Cornelsen, Barbara Pampel, and Arnaud Sallaberry. Path-based sup- ports for hypergraphs. J. Discrete Algorithms, 14:248- 261, 2012.","title":"Path-based supports for hypergraphs","authors":"Brandes","year":"2012","venue":"J. Discrete Algorithms","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Brandt et al., 2015] Felix Brandt, Markus Brill, Edith Hemaspaandra, and Lane Hemaspaandra. Bypassing com- binatorial protections: Polynomial-time algorithms for single-peaked electorates. J. Artif. Intell. Res., 53:439- 496, 2015.","title":"Bypassing combinatorial protections: Polynomial-time algorithms for single-peaked electorates","authors":"Felix Brandt, Markus Brill, Edith Hemaspaandra, Lane Hemaspaandra","year":"2015","venue":"J. Artif. Intell. Res","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Bredereck et al., 2016] Robert Bredereck, Jiehua Chen, and Gerhard Woeginger. Are there any nicely structured pref- erence profiles nearby? Math. Soc. Sci., 79:61-73, 2016.","title":"Are there any nicely structured preference profiles nearby?","authors":"Robert Bredereck, Jiehua Chen, Gerhard Woeginger","year":"2016","venue":"Math. Soc. Sci","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Buchin et al., 2011] Kevin Buchin, Marc van Kreveld, Henk Meijer, Bettina Speckmann, and Kevin Verbeek. On planar supports for hypergraphs. J. Graph Algorithms Appl., 15(4):533-549, 2011.","title":"On planar supports for hypergraphs","authors":"Kevin Buchin, Marc Van Kreveld, Henk Meijer, Bettina Speckmann, Kevin Verbeek","year":"2011","venue":"J. Graph Algorithms Appl","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Caskurlu et al., 2017] Bugra Caskurlu, Vahan Mkrtchyan, Ojas Parekh, and Krishnamurthy Subramani. Partial ver- tex cover and budgeted maximum coverage in bipartite graphs. SIAM J. Discrete Math., 31(3):2172-2184, 2017.","title":"Partial vertex cover and budgeted maximum coverage in bipartite graphs","authors":"Bugra Caskurlu, Vahan Mkrtchyan, Ojas Parekh, Krishnamurthy Subramani","year":"2017","venue":"SIAM J. Discrete Math","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Chaplick et al., 2010] Steven Chaplick, Marisa Gutierrez, Benjamin Lévêque, and Silvia Tondato. From path graphs to directed path graphs. In WG, pages 256-265, 2010.","title":"From path graphs to directed path graphs","authors":"Steven Chaplick, Marisa Gutierrez, Benjamin Lévêque, Silvia Tondato","year":"2010","venue":"WG","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Clearwater et al., 2015] Adam Clearwater, Clemens Puppe, and Arkadii Slinko. Generalizing the single-crossing prop- erty on lines and trees to intermediate preferences on me- dian graphs. In IJCAI, pages 32-38, 2015.","title":"Generalizing the single-crossing property on lines and trees to intermediate preferences on median graphs","authors":"Clearwater","year":"2015","venue":"IJCAI","doi":null,"url":null,"internal_url":"/proceedings/2015/12"},{"position":11,"raw":"[Cormen et al., 2009] Thomas Cormen, Charles Leiserson, Ronald Rivest, and Clifford Stein. Introduction to Algo- rithms, 3rd Edition. MIT Press, 2009.","title":"Introduction to Algorithms","authors":"Thomas Cormen, Charles Leiserson, Ronald Rivest, Clifford Stein","year":"2009","venue":null,"doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Cornaz et al., 2012] Denis Cornaz, Lucie Galand, and Olivier Spanjaard. Bounded single-peaked width and pro- portional representation. In ECAI, pages 270-275, 2012.","title":"Bounded single-peaked width and proportional representation","authors":"Denis Cornaz, Lucie Galand, Olivier Spanjaard","year":"2012","venue":"ECAI","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Demange, 1983] Gabrielle Demange. Single-peaked orders on a tree. Math. Soc. Sci., 3(3):389-396, 1983.","title":"Single-peaked orders on a tree","authors":"Gabrielle Demange","year":"1983","venue":"Math. Soc. Sci","doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Demange, 2012] Gabrielle Demange. Majority relation and median representative ordering. SERIEs-J. Span. Econ., 3(1):95-109, 2012.","title":"Majority relation and median representative ordering","authors":"Gabrielle Demange","year":"2012","venue":"SERIEs-J. Span. Econ","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":"[Elkind et al., 2017] Edith Elkind, Martin Lackner, and Do- minik Peters. Structured preference. In Trends in Com- putational Social Choice, chapter 10, pages 187-207. AI Access, 2017.","title":"Structured preference","authors":"Elkind","year":"2017","venue":"Trends in Computational Social Choice","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Faliszewski et al., 2011] Piotr Faliszewski, Edith Hemas- paandra, Lane Hemaspaandra, and Jörg Rothe. The shield that never was: Societies with single-peaked preferences are more open to manipulation and control. Inf. Comput., 209(2):89-107, 2011.","title":"The shield that never was: Societies with single-peaked preferences are more open to manipulation and control","authors":"Piotr Faliszewski, Edith Hemaspaandra, Lane Hemaspaandra, Jörg Rothe","year":"2011","venue":"Inf. Comput","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Gibbard, 1973] Allan Gibbard. Manipulation of voting schemes: A general result. Econometrica, 41(4):587-601, 1973.","title":"Manipulation of voting schemes: A general result","authors":"Allan Gibbard","year":"1973","venue":"Econometrica","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Johnson and Pollak, 1987] David Johnson and Henry Pol- lak. Hypergraph planarity and the complexity of drawing Venn diagrams. J. Graph Theory, 11(3):309-325, 1987.","title":"David Johnson and Henry Pollak. Hypergraph planarity and the complexity of drawing Venn diagrams","authors":"Pollak Johnson","year":"1987","venue":"J. Graph Theory","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Kellerer, 2016] Hans Kellerer. Knapsack. In Encyclopedia of Algorithms, pages 1048-1051. Springer, 2016.","title":"Knapsack. In Encyclopedia of Algorithms","authors":"Hans Kellerer","year":"2016","venue":null,"doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Klemz et al., 2014] Boris Klemz, Tamara Mchedlidze, and Martin Nöllenburg. Minimum tree supports for hyper- graphs and low-concurrency Euler diagrams. In SWAT, pages 265-276, 2014.","title":"Minimum tree supports for hypergraphs and low-concurrency Euler diagrams","authors":"Boris Klemz, Tamara Mchedlidze, Martin Nöllenburg","year":"2014","venue":"SWAT","doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Korach and Stern, 2003] Ephraim Korach and Michal Stern. The clustering matroid and the optimal clustering tree. Math. Program., 98(1-3):385-414, 2003.","title":"Ephraim Korach and Michal Stern. The clustering matroid and the optimal clustering tree","authors":"Stern Korach","year":"2003","venue":"Math. Program","doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[Kung, 2015] Fan-Chin Kung. Sorting out single-crossing preferences on networks. Soc. Choice Welfare, 44(3):663- 672, 2015.","title":"Sorting out single-crossing preferences on networks","authors":"Fan-Chin Kung","year":"2015","venue":"Soc. Choice Welfare","doi":null,"url":null,"internal_url":null},{"position":24,"raw":"[LeGrand, 2004] Rob LeGrand. Analysis of the minimax procedure. Technical report, Department of Computer Sci- ence and Engineering, Washington University, St. Louis, Missouri., 2004.","title":"Analysis of the minimax procedure","authors":"Rob Legrand","year":"2004","venue":null,"doi":null,"url":null,"internal_url":null},{"position":25,"raw":"[Liu and Guo, 2016] Hong Liu and Jiong Guo. Parameter- ized complexity of winner determination in Minimax com- mittee 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":26,"raw":"[Moulin, 1980] Hervé Moulin. On strategy-proofness and single peakedness. Public Choice, 35(4):437-455, 1980.","title":"On strategy-proofness and single peakedness","authors":"Hervé Moulin","year":"1980","venue":"Public Choice","doi":null,"url":null,"internal_url":null},{"position":27,"raw":"[Peters and Elkind, 2016] Dominik Peters and Edith Elkind. Preferences single-peaked on nice trees. In AAAI, pages 594-600, 2016.","title":"Preferences single-peaked on nice trees","authors":"Elkind Peters, Dominik Peters, Edith Elkind","year":"2016","venue":"AAAI","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":"[Plesník, 1999] Ján Plesník. Constrained weighted match- ings and edge coverings in graphs. Discrete Appl. Math., 92(2-3):229-241, 1999.","title":"Ján Plesník. Constrained weighted matchings and edge coverings in graphs","authors":"Plesník","year":"1999","venue":"Discrete Appl. Math","doi":null,"url":null,"internal_url":null},{"position":30,"raw":"[Puppe and Slinko, 2019] Clemens Puppe and Arkadii Slinko. Condorcet domains, median graphs and the single-crossing property. Economic Theory, 67(1):285- 318, 2019.","title":"Condorcet domains, median graphs and the single-crossing property","authors":"Clemens Puppe, Arkadii Slinko","year":"2019","venue":"Economic Theory","doi":null,"url":null,"internal_url":null},{"position":31,"raw":"[Satterthwaite, 1975] Mark Allen Satterthwaite. Strategy- proofness and Arrow's conditions: Existence and corre- spondence theorems for voting procedures and social wel- fare functions. J. Econ. Theory, 10(2):187-217, 1975.","title":"Strategyproofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions","authors":"Mark Allen, Satterthwaite","year":"1975","venue":"J. Econ. Theory","doi":null,"url":null,"internal_url":null},{"position":32,"raw":"[Slater, 1978] Peter Slater. A characterization of Soft hyper- graphs. Canad. Math. Bull., 21(3):335-337, 1978.","title":"A characterization of Soft hypergraphs","authors":"Peter Slater","year":"1978","venue":"Canad. Math. Bull","doi":null,"url":null,"internal_url":null},{"position":33,"raw":"[Yang, 2015] Yongjie Yang. Manipulation with bounded single-peaked width: A parameterized study. In AAMAS, pages 77-85, 2015.","title":"Manipulation with bounded single-peaked width: A parameterized study","authors":"Yongjie Yang","year":"2015","venue":"AAMAS","doi":null,"url":null,"internal_url":null},{"position":34,"raw":"[Yang and Guo, 2014] Yongjie Yang and Jiong Guo. Con- trolling elections with bounded single-peaked width. In AAMAS, pages 629-636, 2014.","title":"Controlling elections with bounded single-peaked width","authors":"Yang, Guo ; ] Yongjie Yang, Jiong Guo","year":"2014","venue":"AAMAS","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}