IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Log in (now much improved!) to save this paper

Axioms for Measuring without mixing apples and Oranges

Listed author(s):
  • O'Callaghan, Patrick
Registered author(s):

    A mixture set is path-connected via a suitable collection of paths, the most common example being a convex set. Yet in many economic settings, there are pairs of prospects that are not connected by a path of mixtures. Consider the thought experiment of von Neumann and Morgenstern involving a glass of milk, a glass of tea and a cup of coffee: we are often asked to choose between convex combinations of milk and tea, yet the same cannot be said of tea and coffee. We introduce partial mixture sets (which need not be path-connected) and provide a formal extension of the well-known axiomatisation of cardinal, linear utility by Herstein and Milnor. We show that partial mixture sets encompass a variety of settings in the literature and present a novel application to cardinal, nonlinear utility on a stochastic process.

    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: https://mpra.ub.uni-muenchen.de/81196/1/MPRA_paper_81196.pdf
    File Function: original version
    Download Restriction: no

    Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 81196.

    as
    in new window

    Length:
    Date of creation: 07 Sep 2017
    Handle: RePEc:pra:mprapa:81196
    Contact details of provider: Postal:
    Ludwigstraße 33, D-80539 Munich, Germany

    Phone: +49-(0)89-2180-2459
    Fax: +49-(0)89-2180-992459
    Web page: https://mpra.ub.uni-muenchen.de

    More information through EDIRC

    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. Karni, Edi & Safra, Zvi, 2000. "An extension of a theorem of von Neumann and Morgenstern with an application to social choice theory," Journal of Mathematical Economics, Elsevier, vol. 34(3), pages 315-327, November.
    2. Itzhak Gilboa & David Schmeidler, 2003. "Inductive Inference: An Axiomatic Approach," Econometrica, Econometric Society, vol. 71(1), pages 1-26, January.
    3. Simon Grant & Atsushi Kajii & Ben Polak & Zvi Safra, 2010. "Generalized Utilitarianism and Harsanyi's Impartial Observer Theorem," Econometrica, Econometric Society, vol. 78(6), pages 1939-1971, November.
    4. Burkhard Schipper, 2013. "Awareness-dependent subjective expected utility," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(3), pages 725-753, August.
    5. Gilboa,Itzhak & Schmeidler,David, 2001. "A Theory of Case-Based Decisions," Cambridge Books, Cambridge University Press, number 9780521802345, March.
    6. Chew, S H & Epstein, Larry G & Segal, U, 1991. "Mixture Symmetry and Quadratic Utility," Econometrica, Econometric Society, vol. 59(1), pages 139-163, January.
    7. Chew, Soo Hong & Epstein, Larry G & Segal, Uzi, 1994. "The Projective Independence Axiom," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(2), pages 189-215, March.
    8. Ball, Clifford A. & Torous, Walter N., 1983. "Bond Price Dynamics and Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 18(04), pages 517-531, December.
    9. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    10. Edi Karni, 2009. "A theory of medical decision making under uncertainty," Journal of Risk and Uncertainty, Springer, vol. 39(1), pages 1-16, August.
    11. Back, Kerry, 1992. "Insider Trading in Continuous Time," Review of Financial Studies, Society for Financial Studies, vol. 5(3), pages 387-409.
    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:pra:mprapa:81196. 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: (Joachim Winter)

    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.