Abstract
We show that, other than for standard complexity theory with known NP-completeness results, the computational complexity of the Dodgson and Young election systems is completely different from a parameterized complexity point of view. That is, on the one hand, we present an efficient fixed-parameter algorithm for determining a Condorcet winner in Dodgson elections by a minimum number of switches in the votes. On the other hand, we prove that the corresponding problem for Young elections, where one has to delete votes instead of performing switches, is W[2]-complete. In addition, we study Dodgson elections that allow ties between the candidates and give fixed-parameter tractability as well as W[2]-hardness results depending on the cost model for switching ties.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Bartholdi III, J., Tovey, C.A., Trick, M.A.: Voting schemes for which it can be difficult to tell who won the election. Social Choice and Welfare 6, 157–165 (1989)
Betzler, N., Fellows, M.R., Guo, J., Niedermeier, R., Rosamond, F.A.: Fixed-parameter algorithms for Kemeny scores. In: Proc. of 4th AAIM. LNCS, vol. 5034, pp. 60–71. Springer, Heidelberg (2008)
Chevaleyre, Y., Endriss, U., Lang, J., Maudet, N.: A short introduction to computational social choice (invited paper). In: van Leeuwen, J., Italiano, G.F., van der Hoek, W., Meinel, C., Sack, H., Plášil, F. (eds.) SOFSEM 2007. LNCS, vol. 4362, pp. 51–69. Springer, Heidelberg (2007)
Christian, R., Fellows, M.R., Rosamond, F.A., Slinko, A.M.: On complexity of lobbying in multiple referenda. Review of Economic Design 11(3), 217–224 (2007)
Conitzer, V., Sandholm, T., Lang, J.: When are elections with few candidates hard to manipulate? Journal of the ACM 54(3), 1–33 (2007)
Downey, R.G., Fellows, M.R.: Parameterized Complexity. Springer, Heidelberg (1999)
Faliszewski, P., Hemaspaandra, E., Hemaspaandra, L.A., Rothe, J.: A richer understanding of the complexity of election systems. In: Ravi, S., Shukla, S. (eds.) Fundamental Problems in Computing: Essays in Honor of Professor Daniel J. Rosenkrantz. Springer, Heidelberg (2008)
Fellows, M.R.: Personal communication (October 2007)
Flum, J., Grohe, M.: Parameterized Complexity Theory. Springer, Heidelberg (2006)
Hemaspaandra, E., Hemaspaandra, L.A.: Dichotomy for voting systems. Journal of Computer and System Sciences 73(1), 73–83 (2007)
Hemaspaandra, E., Hemaspaandra, L.A., Rothe, J.: Exact analysis of Dodgson elections: Lewis Caroll’s 1876 voting system is complete for parallel access to NP. Journal of the ACM 44(6), 806–825 (1997)
Homan, C.M., Hemaspaandra, L.A.: Guarantees for the success frequency of an algorithm for finding Dodgson-election winners. Journal of Heuristics (2007)
McCabe-Dansted, J.C.: Approximability and computational feasibility of Dodgson’s rule. Master’s thesis, University of Auckland (2006)
McCabe-Dansted, J.C., Pritchard, G., Slinko, A.: Approximability of Dodgson’s rule. Social Choice and Welfare (2007)
McLean, I., Urken, A.: Classics of Social Choice. University of Michigan Press, Ann Arbor, Michigan (1995)
Niedermeier, R.: Invitation to Fixed-Parameter Algorithms. Oxford University Press, Oxford (2006)
Procaccia, A.D., Feldman, M., Rosenschein, J.S.: Approximability and inapproximability of Dodgson and Young elections. Technical Report Discussion paper 466, Center for the Study of Rationality, Hebrew University (October 2007)
Rothe, J., Spakowski, H., Vogel, J.: Exact complexity of the winner problem for Young elections. Theory of Computing Systems 36, 375–386 (2003)
Young, H.P.: Extending Condorcet’s rule. Journal of Economic Theory 16, 335–353 (1977)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Betzler, N., Guo, J., Niedermeier, R. (2008). Parameterized Computational Complexity of Dodgson and Young Elections. In: Gudmundsson, J. (eds) Algorithm Theory – SWAT 2008. SWAT 2008. Lecture Notes in Computer Science, vol 5124. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69903-3_36
Download citation
DOI: https://doi.org/10.1007/978-3-540-69903-3_36
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-69900-2
Online ISBN: 978-3-540-69903-3
eBook Packages: Computer ScienceComputer Science (R0)