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.
Cite
Text
Gilbert et al. "Beyond Pairwise Comparisons in Social Choice: A Setwise Kemeny Aggregation Problem." AAAI Conference on Artificial Intelligence, 2020. doi:10.1609/AAAI.V34I02.5569Markdown
[Gilbert et al. "Beyond Pairwise Comparisons in Social Choice: A Setwise Kemeny Aggregation Problem." AAAI Conference on Artificial Intelligence, 2020.](https://mlanthology.org/aaai/2020/gilbert2020aaai-beyond/) doi:10.1609/AAAI.V34I02.5569BibTeX
@inproceedings{gilbert2020aaai-beyond,
title = {{Beyond Pairwise Comparisons in Social Choice: A Setwise Kemeny Aggregation Problem}},
author = {Gilbert, Hugo and Portoleau, Tom and Spanjaard, Olivier},
booktitle = {AAAI Conference on Artificial Intelligence},
year = {2020},
pages = {1982-1989},
doi = {10.1609/AAAI.V34I02.5569},
url = {https://mlanthology.org/aaai/2020/gilbert2020aaai-beyond/}
}