Determining the Winner of a Dodgson Election is Hard

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 has no 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 this problem. We also prove that DODGSON SCORE parameterized by the number n of votes is hard for W[1].

• Type: Journal
• Year: 2010
• Where: FSTTCS
• Authors: Michael R. Fellows, Bart M. P. Jansen, Daniel Lokshtanov, Frances A. Rosamond, Saket Saurabh
• Keywords: Dodgson Score, FSTTCS 2010, Hard Computational Problem, Software Engineering, Target Score Value