Article Dans Une Revue Theoretical Computer Science Année : 2022

Beyond pairwise comparisons in social choice: A setwise Kemeny aggregation problem

Résumé

In this paper, we advocate the use of setwise contests for aggregating a set of input rankings into an output ranking. We propose a generalization of the Kemeny rule where one minimizes the number of k-wise disagreements instead of pairwise disagreements (one counts 1 disagreement each time the top choice in a subset of alternatives of cardinality at most k differs between an input ranking and the output ranking). After an algorithmic study of this k-wise Kemeny aggregation problem, we introduce a k-wise counterpart of the majority graph. This graph reveals useful to divide the aggregation problem into several sub-problems, which enables to speed up the exact computation of a consensus ranking. By introducing a k-wise counterpart of the Spearman distance, we also provide a 2-approximation algorithm for the k-wise Kemeny aggregation problem. We conclude with numerical tests.

Fichier principal
Vignette du fichier
S030439752100414X.pdf (690.13 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
Licence

Dates et versions

hal-03560807 , version 1 (22-07-2024)

Licence

Identifiants

Citer

Hugo Gilbert, Tom Portoleau, Olivier Spanjaard. Beyond pairwise comparisons in social choice: A setwise Kemeny aggregation problem. Theoretical Computer Science, 2022, 904, pp.27-47. ⟨10.1016/j.tcs.2021.07.004⟩. ⟨hal-03560807⟩
605 Consultations
430 Téléchargements

Altmetric

Partager

  • More