IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/50533.html
   My bibliography  Save this paper

Codifications of complete preorders that are compatible with Mahalanobis disconsensus measures

Author

Listed:
  • Rodríguez Alcantud, José Carlos
  • de Andrés Calle, Rocío
  • González-Arteaga, Teresa

Abstract

We introduce the use of the Mahalanobis distance for the analysis of the cohesiveness of a group of linear orders or complete preorders. We prove that arbitrary codifications of the preferences are incompatible with this formulation, while affine transformations permit to compare profiles on the basis of such a proposal. This measure seems especially fit for the cases where the alternatives are correlated, e.g., committee selection when the candidates are affiliated to political parties.

Suggested Citation

  • Rodríguez Alcantud, José Carlos & de Andrés Calle, Rocío & González-Arteaga, Teresa, 2013. "Codifications of complete preorders that are compatible with Mahalanobis disconsensus measures," MPRA Paper 50533, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:50533
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/50533/1/MPRA_paper_50533.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Duncan Black, 1976. "Partial justification of the Borda count," Public Choice, Springer, vol. 28(1), pages 1-15, December.
    2. Wade D. Cook & Lawrence M. Seiford, 1982. "On the Borda-Kendall Consensus Method for Priority Ranking Problems," Management Science, INFORMS, vol. 28(6), pages 621-637, June.
    3. Jorge Alcalde-Unzu & Marc Vorsatz, 2013. "Measuring the cohesiveness of preferences: an axiomatic analysis," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(4), pages 965-988, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. García-Lapresta, José Luis & Martínez-Panero, Miguel, 2024. "Two characterizations of the dense rank," Journal of Mathematical Economics, Elsevier, vol. 111(C).
    2. González-Arteaga, T. & Alcantud, J.C.R. & de Andrés Calle, R., 2016. "A cardinal dissensus measure based on the Mahalanobis distance," European Journal of Operational Research, Elsevier, vol. 251(2), pages 575-585.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. González-Arteaga, T. & Alcantud, J.C.R. & de Andrés Calle, R., 2016. "A cardinal dissensus measure based on the Mahalanobis distance," European Journal of Operational Research, Elsevier, vol. 251(2), pages 575-585.
    2. Cascón, J.M. & González-Arteaga, T. & de Andrés Calle, R., 2019. "Reaching social consensus family budgets: The Spanish case," Omega, Elsevier, vol. 86(C), pages 28-41.
    3. Jos'e Luis Garc'ia-Lapresta & Miguel Mart'inez-Panero, 2023. "Two characterizations of the dense rank," Papers 2306.17546, arXiv.org.
    4. Jorge Alcalde-Unzu & Marc Vorsatz, 2016. "Do we agree? Measuring the cohesiveness of preferences," Theory and Decision, Springer, vol. 80(2), pages 313-339, February.
    5. García-Lapresta, José Luis & Martínez-Panero, Miguel, 2024. "Two characterizations of the dense rank," Journal of Mathematical Economics, Elsevier, vol. 111(C).
    6. Ignacio Contreras, 2010. "A Distance-Based Consensus Model with Flexible Choice of Rank-Position Weights," Group Decision and Negotiation, Springer, vol. 19(5), pages 441-456, September.
    7. Matthew Gentzkow & Jesse M. Shapiro & Matt Taddy, 2019. "Measuring Group Differences in High‐Dimensional Choices: Method and Application to Congressional Speech," Econometrica, Econometric Society, vol. 87(4), pages 1307-1340, July.
    8. Aki Lehtinen, 2007. "The Borda rule is also intended for dishonest men," Public Choice, Springer, vol. 133(1), pages 73-90, October.
    9. Chao Fu & Wenjun Chang, 2024. "A Markov Chain-Based Group Consensus Method with Unknown Parameters," Group Decision and Negotiation, Springer, vol. 33(5), pages 1019-1048, October.
    10. Alessandro Albano & José Luis García-Lapresta & Antonella Plaia & Mariangela Sciandra, 2023. "A family of distances for preference–approvals," Annals of Operations Research, Springer, vol. 323(1), pages 1-29, April.
    11. P. Battiston & M. Magnani & D. Paolini & L. Rossi, 2024. "Country vs. Music: Strategic Incentives for Competing Voters," Economics Department Working Papers 2024-EP02, Department of Economics, Parma University (Italy).
    12. Peeters, R.J.A.P. & Wolk, K.L., 2015. "Forecasting with Colonel Blotto," Research Memorandum 025, Maastricht University, Graduate School of Business and Economics (GSBE).
    13. Jorge Alcalde-Unzu & Marc Vorsatz, 2008. "The Measurement of Consensus: An Axiomatic Analysis," Working Papers 2008-28, FEDEA.
    14. András Farkas, 2013. "The Depiction of Advertising Industry in Novels and Their Incorporation in Education," Proceedings- 11th International Conference on Mangement, Enterprise and Benchmarking (MEB 2013),, Óbuda University, Keleti Faculty of Business and Management.
    15. Kelin Luo & Yinfeng Xu & Bowen Zhang & Huili Zhang, 2018. "Creating an acceptable consensus ranking for group decision making," Journal of Combinatorial Optimization, Springer, vol. 36(1), pages 307-328, July.
    16. Kangas, Annika & Laukkanen, Sanna & Kangas, Jyrki, 2006. "Social choice theory and its applications in sustainable forest management--a review," Forest Policy and Economics, Elsevier, vol. 9(1), pages 77-92, November.
    17. Hanna Bury & Dariusz Wagner, 2009. "Group judgement with ties. A position-based approach," Operations Research and Decisions, Wroclaw University of Technology, Institute of Organization and Management, vol. 4, pages 9-26.
    18. Edith Elkind & Piotr Faliszewski & Arkadii Slinko, 2015. "Distance rationalization of voting rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(2), pages 345-377, September.
    19. Cook, Wade D. & Kress, Moshe & Seiford, Lawrence M., 1997. "A general framework for distance-based consensus in ordinal ranking models," European Journal of Operational Research, Elsevier, vol. 96(2), pages 392-397, January.
    20. Solís Baltodano, María José, 2016. "The Catalan health budget rationing problem," Working Papers 2072/290741, Universitat Rovira i Virgili, Department of Economics.

    More about this item

    Keywords

    Complete preorders; Mahalanobis disconsensus measure; codification;
    All these keywords.

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:50533. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.