Copeland Voting Fully Resists Constructive Control
Control and bribery are settings in which an external agent seeks to influence the outcome of an election. Faliszewski et al.  proved that Llull voting (which is here denoted by Copeland1) and a variant (here denoted by Copeland0) of Copeland voting are computationally resistant to many, yet not all, types of constructive control and that they also provide broad resistance to bribery. We study a parameterized version of Copeland voting, denoted by Copelandα, where the parameter α is a rational number between 0 and 1 that specifies how ties are valued in the pairwise comparisons of candidates in Copeland elections. For each rational α, 0 < α< 1, and each previously studied control scenario, we either prove that Copelandα is computationally vulnerable to control in that scenario (i.e., we give a P-time algorithm that determines whether control is possible, and if so, determines exactly how to exert the control) or we prove that Copelandα is computationally resistant to control in that scenario (i.e., we prove that control problem to be NP-hard). In particular, we prove that Copeland0.5, the system commonly referred to as “Copeland voting,” provides full resistance to constructive control. Among systems with a polynomial-time winner problem, this is the first natural election system proven to have full resistance to constructive control. Looking at rational α, 0 < α< 1, we give a broad set of results on bribery and on the fixed-parameter tractability of bounded-case control for Copelandα (previously only Copeland0 and Copeland1 had been studied), and we introduce and obtain fixed-parameter tractability results even in a new, more flexible model of control (that we dub “extended control”).
KeywordsComputational social choice theory preference aggregation multiagent systems
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- 3.Conitzer, V., Sandholm, T., Lang, J.: When are elections with few candidates hard to manipulate? Journal of the ACM 54(3) (Article 14)(2007)Google Scholar
- 4.Copeland, A.: A “reasonable” social welfare function. Mimeographed notes from a Seminar on Applications of Mathematics to the Social Sciences, University of Michigan (1951)Google Scholar
- 5.Downey, R., Fellows, M.: Parameterized Complexity. Springer, Heidelberg (1999)Google Scholar
- 6.Erdélyi, G., Hemaspaandra, L., Rothe, J., Spakowski, H.: Frequency of correctness versus average polynomial time and generalized juntas (manuscript, December 2007)Google Scholar
- 7.Faliszewski, P., Hemaspaandra, E., Hemaspaandra, L.: The complexity of bribery in elections. In: Proc. AAAI 2006, pp. 641–646. AAAI Press, Menlo Park (2006)Google Scholar
- 8.Faliszewski, P., Hemaspaandra, E., Hemaspaandra, L., Rothe, J.: Llull and Copeland voting computationally resist bribery and control. Technical report, Department of Computer Science, University of Rochester, Rochester, NY (in preparation)Google Scholar
- 9.Faliszewski, P., Hemaspaandra, E., Hemaspaandra, L., Rothe, J.: Llull and Copeland voting broadly resist bribery and control. In: Proc. AAAI 2007, pp. 724–730. AAAI Press, Menlo Park (2007)Google Scholar
- 11.Hemaspaandra, E., Hemaspaandra, L., Rothe, J.: Hybrid elections broaden complexity-theoretic resistance to control. In: Proc. IJCAI 2007, pp. 1308–1314. AAAI Press, Menlo Park (2007)Google Scholar
- 12.Homan, C., Hemaspaandra, L.: Guarantees for the success frequency of an algorithm for finding Dodgson-election winners. Journal of Heuristics (to appear) Full version available as Google Scholar
- 13.Homan, C., Hemaspaandra, L.: Guarantees for the success frequency of an algorithm for finding Dodgson-election winners. Technical Report TR-881, Department of Computer Science, University of Rochester, Rochester, NY, September 2005. Revised (June 2007)Google Scholar
- 16.Procaccia, A., Rosenschein, J., Kaminka, G.: On the robustness of preference aggregation in noisy environments. In: Proc. AAMAS 2007, pp. 416–422. ACM Press, New York (2007)Google Scholar
- 17.Procaccia, A., Rosenschein, J., Zohar, A.: Multi-winner elections: Complexity of manipulation, control, and winner-determination. In: Proc. IJCAI 2007, pp. 1476–1481. AAAI Press, Menlo Park (2007)Google Scholar