Abstract
A coordinated ranking as an opinion of an expert group can be represented by the well-known Kemeny’s median. Such a decision is a least different from other rankings, and is free of some contradictions of the majority rule problem. As a mathematical principle, the Kemeny’s median gives a decision in any case, in particular, for conflicting experts or groups. In practice, competing opinions are usually identified, and special procedures are used to achieve the required level of consensus. One known approach consists in assigning weights to expert opinions. In this paper, the correct mathematical basis is formulated for new types on the Kemeny’s median, like metric and weighted ones. The problem to find the median for a linear combination of expert rankings is investigated based on the well-known locally optimal Kemeny’s algorithm. It is proposed to investigate the rank aggregation problem based on new types of the median.
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Funding
This investigation is supported by the Russian Foundation for Basic Research (RFBR) under grants 20-07-00055, 18-07-01087, 18-07-00942.
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Sergei D. Dvoenko received Dr. Sci. (Phys.-Math.) in 2002 at the Dorodnitsyn Computing Center of the Russian Academy of Sciences (CC of RAS) in the field of Theoretical Foundations of Informatics (05.13.17 of RAS) with the thesis “Pattern Recognition Methods for Arrays of Interconnected Data,” received Ph. D. in 1992 at the Institute of Control Sciences of the Russian Academy of Sciences (ICS of RAS) in the field of Computer Sciences (05.13.16 of RAS) with the thesis “Learning Algorithms for Event Recognition in Experimental Waveforms.” He is a professor at the Tula State University, Russia. Research interests are machine learning and pattern recognition, cluster-analysis and data mining, image processing, hidden Markov models. He is a member of the Russian Association for Pattern Recognition and Image Analysis (RAPRIA).
Denis O. Pshenichny completed postgraduate studies at the Tula State University, Russia. He is an assistant lecturer at the Tula State University. Research interests are machine learning and pattern recognition, immersing data of pairwise comparisons in a metric space. He is a member of the Russian Association for Pattern Recognition and Image Analysis (RAPRIA).
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Dvoenko, S.D., Pshenichny, D.O. Rank Aggregation Based on New Types of the Kemeny’s Median. Pattern Recognit. Image Anal. 31, 185–196 (2021). https://doi.org/10.1134/S1054661821020061
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DOI: https://doi.org/10.1134/S1054661821020061