Reducing the time required to find the Kemeny ranking by exploiting a necessary condition for being a winner

• Published in: European journal of operational research Vol. 305; no. 3; pp. 1323 - 1336
• Main Authors: Rico, Noelia, Vela, Camino R., Díaz, Irene
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01-03-2023
• Subjects: Combinatorial optimization; Computational social choice; Group decisions and negotiations; Kemeny method; Ranking aggregation; Computational social choice; Kemeny method; Group decisions and negotiations; Combinatorial optimization; Ranking aggregation
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2022.07.031

•Branch and bound algorithms for computing the exact solution to the Kemeny ranking aggregation problem are provided, establishing novel bounds for reducing the execution time. Results of the experimts prove that these algorithms improve the execution time of the available implementations.•The algorithms designed in this work are developed in Python and are available as open source code. The dataset used for the experiments is also available.•Empirical evidence obtained from the experiments hints that, despite having the same number of alternatives and voters, profiles of rankings might differ greatly in their execution time (specially for larger numbers of alternatives) and factors as the uncertainty of the voters may impact the execution time.
The ranking aggregation problem is gaining attention in different application fields due to its connection with decision making. One of the most famous ranking aggregation methods can be traced back to Kemeny in 1959. Unfortunately, the problem of determining the result of the aggregation proposed by Kemeny, known as Kemeny ranking as it minimizes the number of pairwise discrepancies from a set of rankings given by voters, has been proved to be NP-hard, which unfortunately prevents practitioners from using this method in most real-life problems. In this work, we introduce two exact algorithms for determining the Kemeny ranking. The best of these algorithms guarantees a reasonable search time up to 14 alternatives, showing an important reduction of the execution time in comparison to other algorithms found in the literature. Moreover, a dataset of profiles of rankings is provided and a study of additional aspects of the votes that may have impact on the execution time required to determine the winning ranking is also detailed.