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

Hugo Gilbert (1) , Tom Portoleau (2) , Olivier Spanjaard (3)

1 LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision
2 LAAS-ROC - Équipe Recherche Opérationnelle, Optimisation Combinatoire et Contraintes
3 DECISION

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.

Domaines: Intelligence artificielle [cs.AI]; Algorithme et structure de données [cs.DS]; Complexité [cs.CC]

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⟩