IDEAS home Printed from https://ideas.repec.org/a/eee/matsoc/v57y2009i3p333-338.html
   My bibliography  Save this article

Consensus rules based on decisive families: The case of hierarchies

Author

Listed:
  • McMorris, F.R.
  • Powers, Robert C.

Abstract

The notion of a decisive family of voters has played an important role in the analysis of various consensus functions defined on preference profiles. This role remains when the domain shifts to profiles of hierarchical classifications. The main result of this paper is a characterization of consensus rules defined on hierarchies where the output clusters are determined by a decisive family of sets.

Suggested Citation

  • McMorris, F.R. & Powers, Robert C., 2009. "Consensus rules based on decisive families: The case of hierarchies," Mathematical Social Sciences, Elsevier, vol. 57(3), pages 333-338, May.
    • Handle: RePEc:eee:matsoc:v:57:y:2009:i:3:p:333-338
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165-4896(08)00125-X
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. McMorris, F. R. & Neumann, Dean, 1983. "Consensus functions defined on trees," Mathematical Social Sciences, Elsevier, vol. 4(2), pages 131-136, April.
    2. Monjardet, B., 1990. "Arrowian characterizations of latticial federation consensus functions," Mathematical Social Sciences, Elsevier, vol. 20(1), pages 51-71, August.
    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. J.C.R. Alcantud & R. de Andrés Calle & J.M. Cascón, 2013. "Consensus and the Act of Voting," Studies in Microeconomics, , vol. 1(1), pages 1-22, June.

    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. Fred McMorris & Robert Powers, 2008. "A Characterization of Majority Rule for Hierarchies," Journal of Classification, Springer;The Classification Society, vol. 25(2), pages 153-158, November.
    2. McMorris, F. R. & Powers, R. C., 2004. "Consensus functions on tree quasi-orders that satisfy an independence condition," Mathematical Social Sciences, Elsevier, vol. 48(2), pages 183-192, September.
    3. Bruno Leclerc & Bernard Monjardet, 2010. "Aggregation and residuation," Post-Print halshs-00504982, HAL.
    4. Bruno Leclerc & Bernard Monjardet, 2010. "Aggregation et residuation," Documents de travail du Centre d'Economie de la Sorbonne 10058, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    5. Stefano Vannucci, 2019. "Majority judgment and strategy-proofness: a characterization," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(3), pages 863-886, September.
    6. McMorris, F.R. & Powers, R.C., 2013. "Majority decision on median semilattices," Mathematical Social Sciences, Elsevier, vol. 65(1), pages 48-51.
    7. Ernesto Savaglio & Stefano Vannucci, 2021. "Strategy-Proof Aggregation Rules in Median Semilattices with Applications to Preference Aggregation," Department of Economics University of Siena 867, Department of Economics, University of Siena.
    8. 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.
    9. Bernard Monjardet & Vololonirina Raderanirina, 2004. "Lattices of choice functions and consensus problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 23(3), pages 349-382, December.
    10. 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.
    11. Stefano Vannucci, 2017. "Symmetric Consequence Relations and Strategy-Proof Judgment Aggregation," Department of Economics University of Siena 754, Department of Economics, University of Siena.
    12. Stefano Vannucci, 2007. "Virtuous Circles and Contested Identities: on Collective Identification Procedures with Independent Qualified Certification," Department of Economics University of Siena 501, Department of Economics, University of Siena.
    13. Ralph Stinebrickner, 1986. "s-Consensus index method: An additional axiom," Journal of Classification, Springer;The Classification Society, vol. 3(2), pages 319-327, September.
    14. Stefano Vannucci, 2008. "The Libertarian Identification Rule in Finite Atomistic Lattices," Department of Economics University of Siena 526, Department of Economics, University of Siena.
    15. Stefano Vannucci, 2016. "Majority Judgment and Strategy-Proofness," Department of Economics University of Siena 730, Department of Economics, University of Siena.
    16. W. Vach, 1994. "Preserving consensus hierarchies," Journal of Classification, Springer;The Classification Society, vol. 11(1), pages 59-77, March.
    17. Ernesto Savaglio & Stefano Vannucci, 2012. "Strategy-proofness and unimodality in bounded distributive lattices," Department of Economics University of Siena 642, Department of Economics, University of Siena.
    18. Ernesto Savaglio & Stefano Vannucci, 2014. "Strategy-proofness and single-peackedness in bounded distributive lattices," Papers 1406.5120, arXiv.org.
    19. Ernesto Savaglio & Stefano Vannucci, 2022. "Strategy-proof aggregation rules in median semilattices with applications to preference aggregation," Papers 2208.12732, arXiv.org.
    20. Ernesto Savaglio & Stefano Vannucci, 2019. "Strategy-proof aggregation rules and single peakedness in bounded distributive lattices," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 52(2), pages 295-327, February.

    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:eee:matsoc:v:57:y:2009:i:3:p:333-338. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/505565 .

    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.