IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v163y2008i1p63-8810.1007-s10479-008-0353-y.html
   My bibliography  Save this article

NP-hardness results for the aggregation of linear orders into median orders

Author

Listed:
  • Olivier Hudry

Abstract

Given a collection Π of individual preferences defined on a same finite set of candidates, we consider the problem of aggregating them into a collective preference minimizing the number of disagreements with respect to Π and verifying some structural properties. We study the complexity of this problem when the individual preferences belong to any set containing linear orders and when the collective preference must verify different properties, for instance transitivity. We show that the considered aggregation problems are NP-hard for different types of collective preferences (including linear orders, acyclic relations, complete preorders, interval orders, semiorders, quasi-orders or weak orders), if the number of individual preferences is sufficiently large. Copyright Springer Science+Business Media, LLC 2008

Suggested Citation

  • Olivier Hudry, 2008. "NP-hardness results for the aggregation of linear orders into median orders," Annals of Operations Research, Springer, vol. 163(1), pages 63-88, October.
    • Handle: RePEc:spr:annopr:v:163:y:2008:i:1:p:63-88:10.1007/s10479-008-0353-y
    DOI: 10.1007/s10479-008-0353-y
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-008-0353-y
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-008-0353-y?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Pierre Barthelemy, Jean & Monjardet, Bernard, 1981. "The median procedure in cluster analysis and social choice theory," Mathematical Social Sciences, Elsevier, vol. 1(3), pages 235-267, May.
    2. Nathalie Caspard & Bruno Leclerc & Bernard Monjardet, 2007. "Ensembles ordonnés finis : concepts, résultats, usages," Post-Print halshs-00197128, HAL.
    3. Jean-Pierre Barthélemy & Bruno Leclerc & Bernard Monjardet, 1986. "On the use of ordered sets in problems of comparison and consensus of classifications," Journal of Classification, Springer;The Classification Society, vol. 3(2), pages 187-224, September.
    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. Irène Charon & Olivier Hudry, 2010. "An updated survey on the linear ordering problem for weighted or unweighted tournaments," Annals of Operations Research, Springer, vol. 175(1), pages 107-158, March.
    2. Olivier Hudry, 2015. "Complexity results for extensions of median orders to different types of remoteness," Annals of Operations Research, Springer, vol. 225(1), pages 111-123, February.
    3. Olivier Hudry & Bernard Monjardet, 2010. "Consensus theories: an oriented survey," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00504974, HAL.
    4. Hudry, Olivier, 2012. "On the computation of median linear orders, of median complete preorders and of median weak orders," Mathematical Social Sciences, Elsevier, vol. 64(1), pages 2-10.

    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. Olivier Hudry & Bernard Monjardet, 2010. "Consensus theories: An oriented survey," Documents de travail du Centre d'Economie de la Sorbonne 10057, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    2. David Banks & Kathleen Carley, 1994. "Metric inference for social networks," Journal of Classification, Springer;The Classification Society, vol. 11(1), pages 121-149, March.
    3. Irène Charon & Olivier Hudry, 2010. "An updated survey on the linear ordering problem for weighted or unweighted tournaments," Annals of Operations Research, Springer, vol. 175(1), pages 107-158, March.
    4. Jean-Pierre Barthélemy, 1988. "Thresholded consensus for n-trees," Journal of Classification, Springer;The Classification Society, vol. 5(2), pages 229-236, September.
    5. Hudry, Olivier, 2009. "A survey on the complexity of tournament solutions," Mathematical Social Sciences, Elsevier, vol. 57(3), pages 292-303, May.
    6. Hannu Salonen, 2014. "Aggregating and Updating Information," Czech Economic Review, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, vol. 8(2), pages 55-67, October.
    7. McMorris, F.R. & Powers, R.C., 2013. "Majority decision on median semilattices," Mathematical Social Sciences, Elsevier, vol. 65(1), pages 48-51.
    8. Nehring, Klaus & Pivato, Marcus & Puppe, Clemens, 2014. "The Condorcet set: Majority voting over interconnected propositions," Journal of Economic Theory, Elsevier, vol. 151(C), pages 268-303.
    9. Nehring, Klaus & Pivato, Marcus & Puppe, Clemens, 2011. "Condorcet admissibility: Indeterminacy and path-dependence under majority voting on interconnected decisions," MPRA Paper 32434, University Library of Munich, Germany.
    10. Marcus Pivato, 2013. "Voting rules as statistical estimators," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(2), pages 581-630, February.
    11. Dewan F. Wahid & Elkafi Hassini, 2022. "A Literature Review on Correlation Clustering: Cross-disciplinary Taxonomy with Bibliometric Analysis," SN Operations Research Forum, Springer, vol. 3(3), pages 1-42, September.
    12. Stephen Hirtle, 1987. "On the classification of recall strings using lattice-theoretic measures," Journal of Classification, Springer;The Classification Society, vol. 4(2), pages 227-242, September.
    13. Pivato, Marcus, 2017. "Epistemic democracy with correlated voters," Journal of Mathematical Economics, Elsevier, vol. 72(C), pages 51-69.
    14. Bernard Monjardet, 2011. "G. Th. Guilbaud et la théorie du choix social," Documents de travail du Centre d'Economie de la Sorbonne 11047, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    15. Bernard Monjardet, 2006. "Condorcet domains and distributive lattices," Post-Print halshs-00119141, HAL.
    16. Katherine Baldiga & Jerry Green, 2013. "Assent-maximizing social choice," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(2), pages 439-460, February.
    17. Olivier Hudry & Bruno Leclerc & Bernard Monjardet & Jean-Pierre Barthélemy, 2004. "Médianes métriques et latticielles," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-03322636, HAL.
    18. McMorris, F.R. & Novick, B. & Mulder, H.M. & Powers, R.C., 2015. "An ABC-Problem for Location and Consensus Functions on Graphs," Econometric Institute Research Papers EI 2015-16, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    19. Mishra, Debasis & Roy, Souvik, 2012. "Strategy-proof partitioning," Games and Economic Behavior, Elsevier, vol. 76(1), pages 285-300.
    20. Nehring, Klaus & Puppe, Clemens, 2019. "Resource allocation by frugal majority rule," Working Paper Series in Economics 131, Karlsruhe Institute of Technology (KIT), Department of Economics and Management.

    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:spr:annopr:v:163:y:2008:i:1:p:63-88:10.1007/s10479-008-0353-y. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.