Beyond pairwise comparisons in social choice: A setwise Kemeny aggregation problem

In this paper, we advocate the use of setwise contests for aggregating a set input rankings into an output ranking. We propose generalization Kemeny rule where one minimizes number k-wise disagreements instead pairwise (one counts 1 disagreement each time top choice in subset alternatives cardinality at most k differs between ranking and ranking). After algorithmic study aggregation problem, introduce counterpart majority graph. This graph reveals useful to divide problem several sub-problems, which enables speed up exact computation consensus By introducing Spearman distance, also provide 2-approximation algorithm problem. conclude with numerical tests.