Advanced Search
MyIDEAS: Login to save this paper or follow this series

Szpilrajn-type theorems in economics

Contents:

Author Info

  • Andrikopoulos, Athanasios

Abstract

The Szpilrajn "constructive type" theorem on extending binary relations, or its generalizations by Dushnik and Miller [10], is one of the best known theorems in social sciences and mathematical economics. Arrow [1], Fishburn [11], Suzumura [22], Donaldson and Weymark [8] and others utilize Szpilrajn's Theorem and the Well-ordering principle to obtain more general "existence type" theorems on extending binary relations. Nevertheless, we are generally interested not only in the existence of linear extensions of a binary relation R, but in something more: the conditions of the preference sets and the properties which $R$ satisfies to be "inherited" when one passes to any member of some \textquotedblleft interesting\textquotedblright family of linear extensions of R. Moreover, in extending a preference relation $R$, the problem will often be how to incorporate some additional preference data with a minimum of disruption of the existing structure or how to extend the relation so that some desirable new condition is fulfilled. The key to addressing these kinds of problems is the szpilrajn constructive method. In this paper, we give two general "constructive type" theorems on extending binary relations, a Szpilrajn type and a Dushnik-Miller type theorem, which generalize and give a "constructive type" version of all the well known extension theorems in the literature.

Download Info

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
File URL: http://mpra.ub.uni-muenchen.de/14345/
File Function: original version
Download Restriction: no

Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 14345.

as in new window
Length:
Date of creation: 26 Feb 2009
Date of revision:
Handle: RePEc:pra:mprapa:14345

Contact details of provider:
Postal: Schackstr. 4, D-80539 Munich, Germany
Phone: +49-(0)89-2180-2219
Fax: +49-(0)89-2180-3900
Web page: http://mpra.ub.uni-muenchen.de
More information through EDIRC

Related research

Keywords: Consistent binary consistent binary relations; extension theorems; intersection of binary relations;

Find related papers by JEL classification:

This paper has been announced in the following NEP Reports:

References

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
as in new window
  1. Klaus Nehring & Clemens Puppe & Selva Demiralp, 2003. "Extended Partial Orders: A Unifying Structure For Abstract Choice Theory," Working Papers 976, University of California, Davis, Department of Economics.
  2. Clark, Stephen A, 1988. "An Extension Theorem for Rational Choice Functions," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 55(3), pages 485-92, July.
  3. Suzumura, Kataro, 1976. "Remarks on the Theory of Collective Choice," Economica, London School of Economics and Political Science, London School of Economics and Political Science, vol. 43(172), pages 381-90, November.
  4. Duggan, John, 1999. "A General Extension Theorem for Binary Relations," Journal of Economic Theory, Elsevier, vol. 86(1), pages 1-16, May.
  5. Herden, Gerhard & Pallack, Andreas, 2002. "On the continuous analogue of the Szpilrajn Theorem I," Mathematical Social Sciences, Elsevier, vol. 43(2), pages 115-134, March.
  6. Weymark, John A., 2000. "A generalization of Moulin's Pareto extension theorem," Mathematical Social Sciences, Elsevier, vol. 39(2), pages 235-240, March.
  7. Walter Bossert & David Donaldson & Charles Blackorby, 1999. "Rationalizable solutions to pure population problems," Social Choice and Welfare, Springer, vol. 16(3), pages 395-407.
  8. Sophie Bade, 2005. "Nash equilibrium in games with incomplete preferences," Economic Theory, Springer, vol. 26(2), pages 309-332, 08.
  9. Sholomov, Lev A., 2000. "Explicit form of neutral social decision rules for basic rationality conditions," Mathematical Social Sciences, Elsevier, vol. 39(1), pages 81-107, January.
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 in new window

Cited by:
  1. T. Demuynck, 2009. "Common ordering extensions," Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium, Ghent University, Faculty of Economics and Business Administration 09/593, Ghent University, Faculty of Economics and Business Administration.

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:14345. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Ekkehart Schlicht).

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 references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.

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