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

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-02979833
Contributor : Olivier Spanjaard Connect in order to contact the contributor
Submitted on : Tuesday, October 27, 2020 - 12:14:38 PM
Last modification on : Tuesday, October 19, 2021 - 11:18:14 PM

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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⟩

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