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
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.
