Determining the Winner of a Dodgson Election is Hard
Michael R. Fellows, Bart M. P. Jansen, Daniel Lokshtanov, Frances Rosamond, Saket Saurabh · DROPS (Schloss Dagstuhl – Leibniz Center for Informatics) · 2010
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 $W[1]$.