Abstract
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.
Highlights
Elections in which several voters express their preferences over a set of alternatives in the form of rankings arise in many situations [1,2]
Condorcet set a majority criterion principle based on choosing as winner of the election the alternative that beats all other alternatives by a majority of the votes, whenever such alternative exists
The majority relation may be inconsistent with respect to any scoring method based on assigning points to the different alternatives according to their positions in the rankings, including the most prominent such method proposed by Borda [5]
Summary
Elections in which several voters express their preferences over a set of alternatives in the form of rankings arise in many situations [1,2]. Condorcet set a (simple) majority criterion principle based on choosing as winner of the election the alternative that beats all other alternatives by a majority of the votes, whenever such alternative exists. When applying this majority criterion for establishing a winning ranking instead of a single winner, it is considered that an alternative should be ranked at a better position than another alternative in the winning ranking if the former defeats the latter by a majority of the votes. The majority relation defined in this way is not necessarily transitive, and cycles of preferences might occur. This is referred to as the voting paradox.
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