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Preference aggregation and in particular ranking aggregation are mainly studied by the field of social choice theory but extensively applied in a variety of contexts. Among the most prominent methods for ranking aggregation, the Kemeny method has been proved to be the only one that satisfies some desirable properties such as neutrality, consistency and the Condorcet condition at the same time. Unfortunately, the problem of finding a Kemeny ranking is NP-hard, which prevents practitioners from using it in real-life problems. The state of the art of exact algorithms for the computation of the Kemeny ranking experienced a major boost last year with the presentation of an algorithm that provides searching time guarantee up to 13 alternatives. In this work, we propose an enhanced version of this algorithm based on pruning the search space when some Condorcet properties hold. This enhanced version greatly improves the performance in terms of runtime consumption.

The time required for solving the ranking aggregation problem using the Kemeny method increases factorially with the number of alternatives to be ranked, which prevents its use when this number is large. Exact algorithms use domain information to discard rankings as possible solution, thus saving runtime. The amount of rankings that can be discarded varies for each profile and cannot be known beforehand. For profiles of rankings with large number of alternatives, the amount of rankings discarded highly affects the feasibility of the computation of Kemeny ranking. How to identify the profiles that are more time-consuming when finding the Kemeny ranking is not trivial. In this work we propose the use of machine learning models to predict how difficult is to obtain the Kemeny ranking in terms of runtime. The results obtained are promising, with values of the area under the curve metric over 80%. Furthermore, it is possible to extract from the proposed models the characteristics of the profile of rankings that impact on the runtime.