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

2020-06-02

Proceedings of the AAAI Conference on Artificial Intelligence, 34

Volume

Vol. 34 No. 02: AAAI-20 Technical Tracks 2

AAAI Technical Track: Game Theory and Economic Paradigms

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.

10.1609/aaai.v34i02.5569