Author:
Kavitha Telikepalli,Király Tamás,Matuschke Jannik,Schlotter Ildikó,Schmidt-Kraepelin Ulrike
Abstract
AbstractLet G be a digraph where every node has preferences over its incoming edges. The preferences of a node extend naturally to preferences over branchings, i.e., directed forests; a branching B is popular if B does not lose a head-to-head election (where nodes cast votes) against any branching. Such popular branchings have a natural application in liquid democracy. The popular branching problem is to decide if G admits a popular branching or not. We give a characterization of popular branchings in terms of dual certificates and use this characterization to design an efficient combinatorial algorithm for the popular branching problem. When preferences are weak rankings, we use our characterization to formulate the popular branching polytope in the original space and also show that our algorithm can be modified to compute a branching with least unpopularity margin. When preferences are strict rankings, we show that “approximately popular” branchings always exist.
Funder
DAE, Government of India
NKFIH
HAS
Hungarian Academy of Sciences
Cooperation of Excellences Grant
Deutsche Forschungsgemeinschaft
Publisher
Springer Science and Business Media LLC
Subject
General Mathematics,Software
Reference32 articles.
1. Abraham, D.J., Irving, R.W., Kavitha, T., Mehlhorn, K.: Popular matchings. SIAM J. Comput. 37(4), 1030–1034 (2007)
2. Biró, P., Irving, R.W., Manlove, D.F.: Popular matchings in the marriage and roommates problems. In: Proceedings of the 7th International Conference on Algorithms and Complexity (CIAC), Lecture Notes in Computer Science (LNCS), vol. 6078, pp. 97–108. Springer (2010)
3. Bloembergen, D., Grossi, D., Lackner, M.: On rational delegations in liquid democracy. In: Proceedings of the 33rd AAAI Conference on Artificial Intelligence (AAAI) (2019)
4. Blum, C., Zuber, C.I.: Liquid democracy: potentials, problems, and perspectives. J. Polit. Philos. 24(2), 162–182 (2016)
5. Brill, M.: Interactive democracy. In: Proceedings of the 17th International Conference on Autonomous Agents and Multiagent Systems (AAMAS) Blue Sky Ideas Track. pp. 1183–1187 (2018)
Cited by
3 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献