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Kemeny Elections with Bounded Single-peaked or Single-crossing Width

Cornaz, Denis; Galand, Lucie; Spanjaard, Olivier (2013), Kemeny Elections with Bounded Single-peaked or Single-crossing Width, Proceedings of the 23rd International Joint Conference on Artificial Intelligence (IJCAI 2013), AAAI Press / IJCAI, p. 76-82

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Type
Communication / Conférence
Date
2013
Book title
Proceedings of the 23rd International Joint Conference on Artificial Intelligence (IJCAI 2013)
Publisher
AAAI Press / IJCAI
ISBN
978-1-57735-633-2
Pages
76-82
Metadata
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Author(s)
Cornaz, Denis
Galand, Lucie
Spanjaard, Olivier
Abstract (EN)
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".
Subjects / Keywords
Computational Social Choice; Kemeny; Single-peaked; Single-crossing; Fixed-parameter Tractability

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