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Determining the Winner of a Dodgson Election is Hard

Authors Michael Fellows, Bart M. P. Jansen, Daniel Lokshtanov, Frances A. Rosamond, Saket Saurabh



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Michael Fellows
Bart M. P. Jansen
Daniel Lokshtanov
Frances A. Rosamond
Saket Saurabh

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Michael Fellows, Bart M. P. Jansen, Daniel Lokshtanov, Frances A. Rosamond, and Saket Saurabh. Determining the Winner of a Dodgson Election is Hard. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2010). Leibniz International Proceedings in Informatics (LIPIcs), Volume 8, pp. 459-468, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2010)
https://doi.org/10.4230/LIPIcs.FSTTCS.2010.459

Abstract

Computing the Dodgson Score of a candidate in an election is a hard computational problem, which has been analyzed using classical and parameterized analysis. In this paper we resolve two open problems regarding the parameterized complexity of DODGSON SCORE. We show that DODGSON SCORE parameterized by the target score value $k$ does not have a polynomial kernel unless the polynomial hierarchy collapses to the third level; this complements a result of Fellows, Rosamond and Slinko who obtain a non-trivial kernel of exponential size for a generalization of this problem. We also prove that DODGSON SCORE parameterized by the number $n$ of votes is hard for $W[1]$.
Keywords
  • Dodgson Score
  • Parameterized Complexity
  • Kernelization Lower Bounds

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