Skip to main content
SpringerLink
Log in

On a Metric Kemeny’s Median

  • Conference paper
  • First Online:
Intelligent Data Processing (IDP 2016)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 794))

Abstract

The Kemeny’s median represents the coordinated ranking as the opinion of an expert group. Such an opinion is the least different from others in the group and is free of some contradictions (Arrow’s paradox) in the well-known majority rule problem. The new problem of building the Kemeny’s median with metric characteristics is being developed in this paper. It is assumed, rankings represented by pairwise distances between them are immersed as a set in some Euclidean space. In this case, we can define the mean element as the center of this set. Such central element is a ranking as well and must be similar to the Kemeny’s median. The mathematically correct Kemeny’s median needs to be seen as the center in its distances to other elements. A new procedure is developed to build the modified loss matrix and find the metric Kemeny’s median.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Litvak, B.G.: Expert Information: Methods of Acquisition and Analysis, 184 p. Radio i svyaz, Moscow (1982). (in Russian)

    Google Scholar 

  2. Charon, I., Guenoche, A., Hudry, O., Woirgard, F.: New results on the computation of median orders. Discrete Math. 165(166), 139–153 (1997). https://doi.org/10.1016/S0012-365X(96)00166-5

    Article  MathSciNet  MATH  Google Scholar 

  3. Biedl, T., Brandenburg, F.J., Deng, X.: Crossings and permutations. In: Healy, P., Nikolov, N.S. (eds.) GD 2005. LNCS, vol. 3843, pp. 1–12. Springer, Heidelberg (2006). https://doi.org/10.1007/11618058_1

    Chapter  Google Scholar 

  4. Conitzer, V., Davenport, A., Kalagnanam, J.: Improved bounds for computing Kemeny rankings. In: Proceedings of the 21st National Conference on Artificial Intelligence, vol. 1, pp. 620–626 (2006). http://www.cs.cmu.edu/conitzer/kemenyAAAI06.pdf

  5. Nogin, V.D.: Reducing of Pareto Set: an Axiomatic Approach. Fizmatlit, Moscow (2016). (in Russian)

    Google Scholar 

  6. Larichev, O.I., Moshkovich, E.M.: Qualitative Methods of Decision Making. Verbal Analysis of Decisions. Nauka, Fizmatlit, Moscow (1996). (in Russian)

    MATH  Google Scholar 

  7. Jiao, Y., Korba, A., Sibony, E.: Controlling the distance to a Kemeny consensus without computing it. In: Balcan, M.F., Weinberger, K.Q. (eds.) Proceedings of The 33rd International Conference on Machine Learning. PMLR, vol. 48, pp. 2971–2980 (2016)

    Google Scholar 

  8. Dvoenko, S.D., Pshenichny, D.O.: Optimal correction of metrical violations in matrices of pairwise comparisons. JMLDA 1(7), 885–890 (2014). (in Russian)

    Google Scholar 

  9. Dvoenko, S.D., Pshenichny, D.O.: On metric correction of matrices of pairwise comparisons. JMLDA 1(5), 606–620 (2013). (in Russian)

    Google Scholar 

  10. Dvoenko, S.D., Pshenichny, D.O.: A recovering of violated metrics in machine learning. In: Proceedings of the Seventh Symposium on Information and Communication Technology (SoICT’16), pp. 15–21. ACM, New York (2016). https://doi.org/10.1145/3011077.3011084

  11. Kemeny, J., Snell, J.: Mathematical Models in the Social Sciences. Blaisdell, New York (1963)

    MATH  Google Scholar 

  12. Mirkin, B.G.: The Problem of a Group Choice. Nauka, Moscow (1974). (in Russian)

    Google Scholar 

  13. Kemeny, J.: Mathematics without numbers. Daedalus 88(4), 577–591 (1959)

    Google Scholar 

  14. Young, G., Housholder, A.S.: Discussion of a set of points in terms of their mutual distances. Psychometrica 3(1), 19–22 (1938). https://doi.org/10.1007/BF02287916

    Article  Google Scholar 

  15. Torgerson, W.S.: Theory and Methods of Scaling, 460 p. Wiley, New York (1958). https://doi.org/10.1002/bs.3830040308

    Article  Google Scholar 

  16. Dvoenko, S.D.: Clustering and separating of a set of members in terms of mutual distances and similarities. Trans. MLDM 2(2), 80–99 (2009)

    Google Scholar 

Download references

Acknowledgments

This research was partially supported by the Russian Foundation for Basic Research (RFBR) grants 15-05-02228, 15-07-08967, 17-07-00319, 17-07-00436.

Author information

Authors and Affiliations

  1. Tula State University, Tula, Russia

    Sergey Dvoenko & Denis Pshenichny

Authors
  1. Sergey Dvoenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Denis Pshenichny
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sergey Dvoenko .

Editor information

Editors and Affiliations

  1. Moscow Institute of Physics and Technology, Dolgoprudny, Russia

    Vadim V. Strijov

  2. National Research University Higher School of Economics, Moscow, Russia

    Dmitry I. Ignatov

  3. Yandex School of Data Analysis, Moscow, Russia

    Konstantin V. Vorontsov

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Dvoenko, S., Pshenichny, D. (2019). On a Metric Kemeny’s Median. In: Strijov, V., Ignatov, D., Vorontsov, K. (eds) Intelligent Data Processing. IDP 2016. Communications in Computer and Information Science, vol 794. Springer, Cham. https://doi.org/10.1007/978-3-030-35400-8_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-35400-8_4

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-35399-5

  • Online ISBN: 978-3-030-35400-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation