IDEAS home Printed from https://ideas.repec.org/a/spr/joecth/v26y2005i3p729-740.html
   My bibliography  Save this article

Designer path independent choice functions

Author

Listed:
  • Mark Johnson
  • Richard Dean

Abstract

This paper provides an algorithm for the construction of all PICFs on a finite set of alternatives, V, designed by an a priori given set I of initial choices as well as the determination of whether the initial set I is consistent with path independence. The algorithm is based on a new characterization result for path independent choice functions (PICF) on finite domains and uses that characterization as the basis of the algorithm. The characterization result identifies two properties of a partition of the Boolean algebra as necessary and sufficient for a choice function C to be a PICF: (i): For every subset A of V the set ${\rm arc}(A)={\{}B: C (B)=C(A){\}}$ is an interval in the Boolean algebra 2 V . (ii): If A/B is an interval in the Boolean algebra such that C(A)=C(B) and if M/N is an upper transpose of A/B then C(M)=C(N). The algorithm proceeds by expanding on the implications of these two properties. Copyright Springer-Verlag Berlin/Heidelberg 2005

Suggested Citation

  • Mark Johnson & Richard Dean, 2005. "Designer path independent choice functions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(3), pages 729-740, October.
    • Handle: RePEc:spr:joecth:v:26:y:2005:i:3:p:729-740
    DOI: 10.1007/s00199-004-0544-y
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00199-004-0544-y
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00199-004-0544-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.

    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:joecth:v:26:y:2005:i:3:p:729-740. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.