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

Denis Cornaz (1) , Lucie Galand (1) , Olivier Spanjaard (2)

1 LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision
2 DECISION

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".

Mots clés: Computational Social Choice; Kemeny; Single-peaked; Single-crossing; Fixed-parameter Tractability

Domaines: Informatique [cs]

Denis Cornaz, Lucie Galand, Olivier Spanjaard. Kemeny Elections with Bounded Single-peaked or Single-crossing Width. 23rd International Joint Conference on Artificial Intelligence (IJCAI 2013), Aug 2013, Beijing, China. pp.76-82. ⟨hal-01372505⟩