IDEAS home Printed from https://ideas.repec.org/a/kap/theord/v79y2015i4p615-625.html
   My bibliography  Save this article

Two preference metrics provide settings for the study of properties of binary relations

Author

Listed:
  • Vicki Knoblauch

Abstract

The topological structures imposed on the collection of binary relations on a given set by the symmetric difference metric and the Hausdorff metric provide opportunities for learning about how collections of binary relations with various properties fit into the collection of all binary relations. For example, there is some agreement and some disagreement between conclusions drawn about the rarity of certain properties of binary relations using first the symmetric difference metric and then the Hausdorff metric. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Vicki Knoblauch, 2015. "Two preference metrics provide settings for the study of properties of binary relations," Theory and Decision, Springer, vol. 79(4), pages 615-625, December.
  • Handle: RePEc:kap:theord:v:79:y:2015:i:4:p:615-625
    DOI: 10.1007/s11238-015-9487-y
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s11238-015-9487-y
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1007/s11238-015-9487-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. Vicki Knoblauch, 2014. "Preference, topology and measure," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(2), pages 507-514, August.
    2. Balasko, Yves & Cres, Herve, 1997. "The Probability of Condorcet Cycles and Super Majority Rules," Journal of Economic Theory, Elsevier, vol. 75(2), pages 237-270, August.
    3. Chichilnisky, Graciela, 1980. "Social choice and the topology of spaces of preferences," MPRA Paper 8006, University Library of Munich, Germany.
    4. Paras Mehta, 1997. "Topological methods in social choice: an overview," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 14(2), pages 233-243.
    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. Knoblauch, Vicki, 2023. "Lexicographic preference representation: Intrinsic length of linear orders on infinite sets," Journal of Mathematical Economics, Elsevier, vol. 105(C).

    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. Ram Sewak Dubey & Giorgio Laguzzi, 2022. "How rare are the properties of binary relations?," Papers 2202.05229, arXiv.org.
    2. Lauwers, Luc, 2000. "Topological social choice," Mathematical Social Sciences, Elsevier, vol. 40(1), pages 1-39, July.
    3. Vicki Knoblauch, 2014. "Preference, topology and measure," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(2), pages 507-514, August.
    4. Guillaume Chèze, 2017. "Topological aggregation, the twin paradox and the No Show paradox," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(4), pages 707-715, April.
    5. Tanaka, Yasuhito, 2007. "A topological approach to Wilson's impossibility theorem," Journal of Mathematical Economics, Elsevier, vol. 43(2), pages 184-191, February.
    6. Tanaka, Yasuhito, 2009. "On the equivalence of the Arrow impossibility theorem and the Brouwer fixed point theorem when individual preferences are weak orders," Journal of Mathematical Economics, Elsevier, vol. 45(3-4), pages 241-249, March.
    7. Askoura, Youcef & Billot, Antoine, 2021. "Social decision for a measure society," Journal of Mathematical Economics, Elsevier, vol. 94(C).
    8. Mich Tvede & Hervé Crés, 2005. "Voting in assemblies of shareholders and incomplete markets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(4), pages 887-906, November.
    9. Luc Lauwers, 2002. "A note on Chichilnisky's social choice paradox," Theory and Decision, Springer, vol. 52(3), pages 261-266, May.
    10. Yasuhito Tanaka, 2005. "A topological proof of Eliaz's unified theorem of social choice theory (forthcoming in "Applied Mathematics and Computation")," Public Economics 0510021, University Library of Munich, Germany, revised 26 Oct 2005.
    11. Salvador Barberà & Dolors Berga & Bernardo Moreno, 2020. "Arrow on domain conditions: a fruitful road to travel," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 54(2), pages 237-258, March.
    12. Gustavo Bergantiños & Juan D. Moreno-Ternero, 2023. "Decentralized revenue sharing from broadcasting sports," Public Choice, Springer, vol. 194(1), pages 27-44, January.
    13. Eivind Stensholt, 2013. "What shall we do with the cyclic profile?," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(1), pages 229-262, January.
    14. Nikita Miku, 2022. "The connection between Arrow theorem and Sperner lemma," Papers 2212.12251, arXiv.org.
    15. Yasuhito Tanaka, 2005. "A topological approach to the Arrow impossibility theorem when individual preferences are weak orders (forcoming in ``Applied Mathematics and Compuation''(Elsevier))," Public Economics 0506013, University Library of Munich, Germany, revised 17 Jun 2005.
    16. Estelle Cantillon & Antonio Rangel, 2002. "A graphical analysis of some basic results in social choice," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 19(3), pages 587-611.
    17. repec:hal:spmain:info:hdl:2441/10283 is not listed on IDEAS
    18. Roger D. Congleton, 2016. "Gordon Tullock’s implicit analytical history of government," Constitutional Political Economy, Springer, vol. 27(2), pages 179-193, June.
    19. Graciela Chichilnisky, 1996. "A robust theory of resource allocation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 13(1), pages 1-10, January.
    20. Graciela Chichilnisky, 1990. "On The Mathematical Foundations Of Political Economy," Contributions to Political Economy, Oxford University Press, vol. 9(1), pages 25-41.
    21. Chichilnisky, Graciela & Heal, Geoffrey, 1983. "Necessary and sufficient conditions for a resolution of the social choice paradox," Journal of Economic Theory, Elsevier, vol. 31(1), pages 68-87, October.

    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:kap:theord:v:79:y:2015:i:4:p:615-625. 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.