Kemeny elections with bounded single-peaked or single-crossing width

Authors:
Denis Cornaz;Lucie Galand;Olivier Spanjaard
Affiliations:
LAMSADE-CNRS, UMR, Université Paris Dauphine, Paris, France;LAMSADE-CNRS, UMR, Université Paris Dauphine, Paris, France;LIP6-CNRS, UMR, UPMC, Paris, France
Venue:
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
Year:
2013

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Abstract

This paper is devoted to complexity results regarding specific measures of proximity to single-peakedness and single-crossingness, called "single-peaked width" [Cornaz et al., 2012] and "single-crossing width". Thanks to the use of the PQ-tree data structure [Booth and Lueker, 1976], we show that both problems are polynomial time solvable in the general case (while it was only known for single-peaked width and in the case of narcissistic preferences). Furthermore, we establish one of the first results (to our knowledge) concerning the effect of nearly single-peaked electorates on the complexity of an NP-hard voting system, namely we show the fixed-parameter tractability of Kemeny elections with respect to the parameters "single-peaked width" and "single-crossing width".