Beyond Pairwise Comparisons in Social Choice: A Setwise Kemeny Aggregation Problem

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

1 GSSI - Gran Sasso Science Institute
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. It reveals useful to divide the aggregation problem into several sub-problems. 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. Thirty-Fourth AAAI Conference on Artificial Intelligence (AAAI-20), Feb 2020, New York, United States. pp.1982-1989, ⟨10.1609/aaai.v34i02.5569⟩. ⟨hal-02979833⟩