IDEAS home Printed from
MyIDEAS: Login to save this article or follow this journal

Continuous multi-utility representations of preorders

  • Bosi, Gianni
  • Herden, Gerhard

Let (X,t) be a topological space. Then a preorder ≾ on (X,t) has a continuous multi-utility representation if there exists a family F of continuous and isotonic real-valued functions f on (X,≾,t) such that for all x∈X and all y∈X the inequalities x≾y mean that for all f∈F the inequalities f(x)≤f(y) hold. We discuss the existence of a continuous multi-utility representation by using suitable concepts of continuity of a preorder. In addition, we clarify in detail the relation between the concept of a continuous multi-utility representation and Nachbin’s concept of a normally preordered space.

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:
Download Restriction: Full text for ScienceDirect subscribers only

As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 48 (2012)
Issue (Month): 4 ()
Pages: 212-218

in new window

Handle: RePEc:eee:mateco:v:48:y:2012:i:4:p:212-218
Contact details of provider: Web page:

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. Sondermann, Dieter, 1980. "Utility representations for partial orders," Journal of Economic Theory, Elsevier, vol. 23(2), pages 183-188, October.
  2. Ok, Efe A., 2002. "Utility Representation of an Incomplete Preference Relation," Journal of Economic Theory, Elsevier, vol. 104(2), pages 429-449, June.
  3. Michael Mandler, 2004. "Status quo maintenance reconsidered: changing or incomplete preferences?," Economic Journal, Royal Economic Society, vol. 114(499), pages F518-F535, November.
  4. Juan Dubra & Fabio Maacheroni & Efe A. Ok, 2001. "Expected Utility Theory without the Completeness Axiom," Cowles Foundation Discussion Papers 1294, Cowles Foundation for Research in Economics, Yale University.
  5. John E. Roemer, 1999. "The Democratic Political Economy of Progressive Income Taxation," Econometrica, Econometric Society, vol. 67(1), pages 1-20, January.
  6. Masatlioglu, Yusufcan & Ok, Efe A., 2005. "Rational choice with status quo bias," Journal of Economic Theory, Elsevier, vol. 121(1), pages 1-29, March.
  7. Sagi, Jacob S., 2006. "Anchored preference relations," Journal of Economic Theory, Elsevier, vol. 130(1), pages 283-295, September.
  8. Frank Niehaus, 2001. "The Influence of Heterogeneous Preferences on Asset Prices in an Incomplete Market Model," CeNDEF Workshop Papers, January 2001 2A.2, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
  9. Jaffray, Jean-Yves, 1975. "Semicontinuous extension of a partial order," Journal of Mathematical Economics, Elsevier, vol. 2(3), pages 395-406, December.
  10. Eliaz, Kfir & Ok, Efe A., 2006. "Indifference or indecisiveness? Choice-theoretic foundations of incomplete preferences," Games and Economic Behavior, Elsevier, vol. 56(1), pages 61-86, July.
  11. Evren, Özgür & Ok, Efe A., 2011. "On the multi-utility representation of preference relations," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 554-563.
  12. Michael Mandler, 2006. "Cardinality versus Ordinality: A Suggested Compromise," American Economic Review, American Economic Association, vol. 96(4), pages 1114-1136, September.
  13. David Kelsey & Erkan Yalcin, 2004. "The Arbitrage Pricing Theorem with Incomplete Preferences," GE, Growth, Math methods 0401002, EconWPA.
  14. Herden, G., 1989. "On the existence of utility functions ii," Mathematical Social Sciences, Elsevier, vol. 18(2), pages 107-117, October.
  15. Sophie Bade, 2005. "Nash equilibrium in games with incomplete preferences," Economic Theory, Springer, vol. 26(2), pages 309-332, 08.
  16. Herden, G., 1989. "On the existence of utility functions," Mathematical Social Sciences, Elsevier, vol. 17(3), pages 297-313, June.
  17. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
  18. Mehta, Ghanshyam, 1988. "Some general theorems on the existence of order-preserving functions," Mathematical Social Sciences, Elsevier, vol. 15(2), pages 135-143, April.
  19. Majumdar, Mukul & Sen, Amartya K, 1976. "A Note on Representing Partial Orderings," Review of Economic Studies, Wiley Blackwell, vol. 43(3), pages 543-45, October.
  20. Peleg, Bezalel, 1970. "Utility Functions for Partially Ordered Topological Spaces," Econometrica, Econometric Society, vol. 38(1), pages 93-96, January.
  21. Herden, G., 1989. "Some lifting theorems for continuous utility functions," Mathematical Social Sciences, Elsevier, vol. 18(2), pages 119-134, October.
  22. 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.
Full references (including those not matched with items on IDEAS)

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

When requesting a correction, please mention this item's handle: RePEc:eee:mateco:v:48:y:2012:i:4:p:212-218. 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: (Zhang, Lei)

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.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.