IDEAS home Printed from https://ideas.repec.org/a/kap/jrisku/v28y2004i1p55-71.html
   My bibliography  Save this article

A Note on Luce-Fishburn Axiomatization of Rank-Dependent Utility

Author

Listed:
  • Liping Liu

Abstract

In this paper, I provide a new axiomatization for rank-dependent utilities. I show that, along with weak order, dominance, and the binary rank-dependent representation, the decomposition of certainty equivalents is sufficient to derive the general rank-dependent model of Luce and Fishburn (1991, 1995). My axiomatization not only simplifies and generalizes the theory proposed by Luce and Fishburn (1991, 1995) but also is more empirically appealing. The result is comparable to that obtained by Quiggin (1982) in the sense that both involve a sort of decomposition of certainty equivalents and both do not use compound lotteries. However, my axiomatization does not have the restriction that the weight of probability 1/2 is 1/2. Copyright Kluwer Academic Publishers 2004

Suggested Citation

  • Liping Liu, 2004. "A Note on Luce-Fishburn Axiomatization of Rank-Dependent Utility," Journal of Risk and Uncertainty, Springer, vol. 28(1), pages 55-71, January.
    • Handle: RePEc:kap:jrisku:v:28:y:2004:i:1:p:55-71
    DOI: 10.1023/B:RISK.0000009436.14961.6a
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1023/B:RISK.0000009436.14961.6a
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1023/B:RISK.0000009436.14961.6a?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. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    2. Robin M. Hogarth & Hillel J. Einhorn, 1990. "Venture Theory: A Model of Decision Weights," Management Science, INFORMS, vol. 36(7), pages 780-803, July.
    3. Cho, Younghee & Luce, R. Duncan, 1995. "Tests of Hypotheses about Certainty Equivalents and Joint Receipt of Gambles," Organizational Behavior and Human Decision Processes, Elsevier, vol. 64(3), pages 229-248, December.
    4. Tversky, Amos & Kahneman, Daniel, 1992. "Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
    5. Luce, R. Duncan, 1991. "Rank- and sign-dependent linear utility models for binary gambles," Journal of Economic Theory, Elsevier, vol. 53(1), pages 75-100, February.
    6. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    7. Luce, R Duncan & Fishburn, Peter C, 1995. "A Note on Deriving Rank-Dependent Utility Using Additive Joint Receipts," Journal of Risk and Uncertainty, Springer, vol. 11(1), pages 5-16, July.
    8. Liu, Liping & Shenoy, Prakash P, 1995. "A Theory of Coarse Utility," Journal of Risk and Uncertainty, Springer, vol. 11(1), pages 17-49, July.
    9. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    10. Mellers, Barbara & Weiss, Robin & Birnbaum, Michael, 1992. "Violations of Dominance in Pricing Judgments," Journal of Risk and Uncertainty, Springer, vol. 5(1), pages 73-90, February.
    11. Wakker, Peter & Tversky, Amos, 1993. "An Axiomatization of Cumulative Prospect Theory," Journal of Risk and Uncertainty, Springer, vol. 7(2), pages 147-175, October.
    12. Liu, Liping, 1999. "Approximate portfolio analysis," European Journal of Operational Research, Elsevier, vol. 119(1), pages 35-49, November.
    13. Handa, Jagdish, 1977. "Risk, Probabilities, and a New Theory of Cardinal Utility," Journal of Political Economy, University of Chicago Press, vol. 85(1), pages 97-122, February.
    14. William Fellner, 1961. "Distortion of Subjective Probabilities as a Reaction to Uncertainty," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 75(4), pages 670-689.
    15. Marley, A A J & Luce, R Duncan, 2001. "Ranked-Weighted Utilities and Qualitative Convolution," Journal of Risk and Uncertainty, Springer, vol. 23(2), pages 135-163, September.
    16. Luce, R Duncan & Fishburn, Peter C, 1991. "Rank- and Sign-Dependent Linear Utility Models for Finite First-Order Gambles," Journal of Risk and Uncertainty, Springer, vol. 4(1), pages 29-59, 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


    Cited by:

    1. Mikhail Sokolov, 2011. "Interval scalability of rank-dependent utility," Theory and Decision, Springer, vol. 70(3), pages 255-282, March.

    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. repec:cup:judgdm:v:16:y:2021:i:6:p:1324-1369 is not listed on IDEAS
    2. Sudeep Bhatia & Graham Loomes & Daniel Read, 2021. "Establishing the laws of preferential choice behavior," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 16(6), pages 1324-1369, November.
    3. Liang Zou, 2006. "An Alternative to Prospect Theory," Annals of Economics and Finance, Society for AEF, vol. 7(1), pages 1-28, May.
    4. Liu, Liping, 1999. "Approximate portfolio analysis," European Journal of Operational Research, Elsevier, vol. 119(1), pages 35-49, November.
    5. Cho, Young-Hee & Duncan Luce, R. & Truong, Lan, 2002. "Duplex decomposition and general segregation of lotteries of a gain and a loss: An empirical evaluation," Organizational Behavior and Human Decision Processes, Elsevier, vol. 89(2), pages 1176-1193, November.
    6. Birnbaum, Michael H. & Zimmermann, Jacqueline M., 1998. "Buying and Selling Prices of Investments: Configural Weight Model of Interactions Predicts Violations of Joint Independence," Organizational Behavior and Human Decision Processes, Elsevier, vol. 74(2), pages 145-187, May.
    7. Henry Stott, 2006. "Cumulative prospect theory's functional menagerie," Journal of Risk and Uncertainty, Springer, vol. 32(2), pages 101-130, March.
    8. Ulrich Schmidt & Chris Starmer & Robert Sugden, 2008. "Third-generation prospect theory," Journal of Risk and Uncertainty, Springer, vol. 36(3), pages 203-223, June.
    9. Schmidt, Ulrich & Zank, Horst, 2009. "A simple model of cumulative prospect theory," Journal of Mathematical Economics, Elsevier, vol. 45(3-4), pages 308-319, March.
    10. Duncan Luce, R., 1997. "Associative joint receipts," Mathematical Social Sciences, Elsevier, vol. 34(1), pages 51-74, August.
    11. Birnbaum, Michael H. & Chavez, Alfredo, 1997. "Tests of Theories of Decision Making: Violations of Branch Independence and Distribution Independence," Organizational Behavior and Human Decision Processes, Elsevier, vol. 71(2), pages 161-194, August.
    12. Sneddon, Robert & Luce, R. Duncan, 2001. "Empirical Comparisons of Bilinear and Nonbilinear Utility Theories," Organizational Behavior and Human Decision Processes, Elsevier, vol. 84(1), pages 71-94, January.
    13. Bernard, Carole & Ghossoub, Mario, 2009. "Static Portfolio Choice under Cumulative Prospect Theory," MPRA Paper 15446, University Library of Munich, Germany.
    14. Horst Zank, 2010. "On probabilities and loss aversion," Theory and Decision, Springer, vol. 68(3), pages 243-261, March.
    15. Andersen, Steffen & Harrison, Glenn W. & Lau, Morten Igel & Rutström, Elisabet E., 2014. "Dual criteria decisions," Journal of Economic Psychology, Elsevier, vol. 41(C), pages 101-113.
      • Andersen, Steffen & Harrison, Glenn W. & Lau, Morten Igel & Rutström, Elisabet, 2009. "Dual Criteria Decisions," Working Papers 02-2009, Copenhagen Business School, Department of Economics.
    16. Ulrich Schmidt & Horst Zank, 2012. "A genuine foundation for prospect theory," Journal of Risk and Uncertainty, Springer, vol. 45(2), pages 97-113, October.
    17. Wakker, Peter P. & Zank, Horst, 2002. "A simple preference foundation of cumulative prospect theory with power utility," European Economic Review, Elsevier, vol. 46(7), pages 1253-1271, July.
    18. Birnbaum, Michael H. & Schmidt, Ulrich, 2010. "Allais paradoxes can be reversed by presenting choices in canonical split form," Kiel Working Papers 1615, Kiel Institute for the World Economy (IfW Kiel).
    19. Birnbaum, Michael H., 2004. "Tests of rank-dependent utility and cumulative prospect theory in gambles represented by natural frequencies: Effects of format, event framing, and branch splitting," Organizational Behavior and Human Decision Processes, Elsevier, vol. 95(1), pages 40-65, September.
    20. Amit Kothiyal & Vitalie Spinu & Peter Wakker, 2011. "Prospect theory for continuous distributions: A preference foundation," Journal of Risk and Uncertainty, Springer, vol. 42(3), pages 195-210, June.
    21. Ulrich Schmidt & Christian Seidl, 2014. "Reconsidering the common ratio effect: the roles of compound independence, reduction, and coalescing," Theory and Decision, Springer, vol. 77(3), pages 323-339, 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:jrisku:v:28:y:2004:i:1:p:55-71. 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.