  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.
