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

arXiv: https://arxiv.org/abs/1911.06226 · HTML: https://mlsanity.com/paper/1911.06226/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Nov 2019.

## Built on by (most cited first, 4 of 4)

- [Diversity in Kemeny Rank Aggregation: A Parameterized Approach](https://mlsanity.com/paper/2105.09413/) (2021)
- [Quantifying Human Bias and Knowledge to guide ML models during Training](https://mlsanity.com/paper/2211.10796/) (2022)
- [Optimal majority rules and quantitative Condorcet properties of setwise Kemeny voting schemes](https://mlsanity.com/paper/2304.14980/) (2023)
- [Space reduction techniques for the 3-wise Kemeny problem](https://mlsanity.com/paper/2305.00140/) (2023)

## Abstract (arXiv)

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.