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.

In this paper, we highlight an intriguing connection between the cryptographic attacks on Enigma’s code and local consistency reasoning in constraint programming. The coding challenge proposed to the students during the 2020 ACP summer school, to be solved by constraint programming, was to decipher a message encoded using the well known Enigma machine, with as only clue a tiny portion of the original message. A number of students quickly crafted a model, thus nicely showcasing CP technology - as well as their own brightness. The detail that is slightly less favorable to CP technology is that solving this model on modern hardware is challenging, whereas the "Bombe", an antique computing device, could solve it eighty years ago. We argue that from a constraint programming point of vue, the key aspects of the techniques designed by Polish and British cryptanalysts can be seen as, respectively, path consistency and singleton arc consistency on some constraint satisfaction problems.

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.