IDEAS home Printed from https://ideas.repec.org/a/kap/jrisku/v31y2005i2p109-127.html
   My bibliography  Save this article

How Many Balance Functions Does it Take to Determine a Utility Function?

Author

Listed:
  • John Pratt

Abstract

Call b your balance function at wealth W if you are indifferent between W and a 50–50 lottery with outcomes x and b(x). Given one b, u is arbitrary on one side of W but then determined on the other. Given two b‘s, u is arbitrary between the two W′ s but then determined elsewhere. Additional properties of u restrict the b’s but do not ordinarily make u unique. Contradictions can occur. Given three b′ s, an algorithm is developed using minimal domains of definition that determines the relative utility of the W’s. If it is irrational, then the set S generated by applying all combinations of b’s to W′ s is dense and u is determined. If finitely many b’s are rationally related, then S is discrete, a further algorithm determines it, the values of u on S are equally spaced, and u is arbitrary between any two adjacent points of S but then determined elsewhere. Infinitely many balance functions determine u unless they are rationally related in a uniform way. Copyright Springer Science + Business Media, Inc. 2005

Suggested Citation

  • John Pratt, 2005. "How Many Balance Functions Does it Take to Determine a Utility Function?," Journal of Risk and Uncertainty, Springer, vol. 31(2), pages 109-127, September.
  • Handle: RePEc:kap:jrisku:v:31:y:2005:i:2:p:109-127
    DOI: 10.1007/s11166-005-3551-x
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s11166-005-3551-x
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1007/s11166-005-3551-x?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. Partha Dasgupta & Douglas Gale & Oliver Hart & Eric Maskin (ed.), 1992. "Economic Analysis of Markets and Games: Essays in Honor of Frank Hahn," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262541599, April.
    2. Gollier, Christian & Pratt, John W, 1996. "Risk Vulnerability and the Tempering Effect of Background Risk," Econometrica, Econometric Society, vol. 64(5), pages 1109-1123, September.
    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. Pérez-Gladish, B. & Gonzalez, I. & Bilbao-Terol, A. & Arenas-Parra, M., 2010. "Planning a TV advertising campaign: A crisp multiobjective programming model from fuzzy basic data," Omega, Elsevier, vol. 38(1-2), pages 84-94, February.

    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. Thorsten Hens & Beate Pilgrim & Janos Mayer, "undated". "Existence of Sunspot Equilibria and Uniqueness of Spot Market Equilibria: The Case of Intrinsically Complete Markets," IEW - Working Papers 188, Institute for Empirical Research in Economics - University of Zurich.
    2. Hens, Thorsten & Mayer, Janós & Pilgrim, Beate, 2004. "Existence of Sunspot Equilibria and Uniqueness of Spot Market Equilibria: The Case of Intrinsically Complete Markets," Discussion Papers 2004/15, Norwegian School of Economics, Department of Business and Management Science.
    3. Angrisani, Marco & Atella, Vincenzo & Brunetti, Marianna, 2018. "Public health insurance and household portfolio Choices: Unravelling financial “Side Effects” of Medicare," Journal of Banking & Finance, Elsevier, vol. 93(C), pages 198-212.
    4. Thomas Eichner & Andreas Wagener, 2002. "Increases in Risk and the Welfare State," CESifo Working Paper Series 685, CESifo.
    5. Nabil I. Al-Najjar & Luca Anderlini & Leonardo Felli, 2006. "Undescribable Events," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 73(4), pages 849-868.
    6. Goytom Abraha Kahsay & Daniel Osberghaus, 2018. "Storm Damage and Risk Preferences: Panel Evidence from Germany," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 71(1), pages 301-318, September.
    7. Barbera, S. & Bossert, W. & Pattanaik, P.K., 2001. "Ranking Sets of Objects," Cahiers de recherche 2001-02, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    8. Zubanov, Nick & Cadsby, Bram & Song, Fei, 2017. "The," IZA Discussion Papers 10542, Institute of Labor Economics (IZA).
    9. de Blasio, Guido & De Paola, Maria & Poy, Samuele & Scoppa, Vincenzo, 2018. "Risk Aversion and Entrepreneurship: New Evidence Exploiting Exposure to Massive Earthquakes in Italy," IZA Discussion Papers 12057, Institute of Labor Economics (IZA).
    10. Freudenreich, Hanna & Musshoff, Oliver & Wiercinski, Ben, 2017. "The Relationship between Farmers' Shock Experiences and their Uncertainty Preferences - Experimental Evidence from Mexico," GlobalFood Discussion Papers 256212, Georg-August-Universitaet Goettingen, GlobalFood, Department of Agricultural Economics and Rural Development.
    11. Michael Haliassos & Alexander Michaelides, 2003. "Portfolio Choice and Liquidity Constraints," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 44(1), pages 143-177, February.
    12. Annette Vissing-Jorgensen, 2000. "Towards an Explanation of Household Portfolio Choice Heterogeneity: Nonfinancial Income and Participation Cost Structures," Econometric Society World Congress 2000 Contributed Papers 1102, Econometric Society.
    13. Enriqueta Aragones & Itzhak Gilboa & Andrew Postlewaite & David Schmeidler, 2012. "Fact-Free Learning," World Scientific Book Chapters, in: Case-Based Predictions An Axiomatic Approach to Prediction, Classification and Statistical Learning, chapter 8, pages 185-210, World Scientific Publishing Co. Pte. Ltd..
    14. Christelis, Dimitris & Georgarakos, Dimitris & Sanz-de-Galdeano, Anna, 2020. "The impact of health insurance on stockholding: A regression discontinuity approach," Journal of Health Economics, Elsevier, vol. 69(C).
    15. Christian Rogg, 2006. "Asset Portfolios in Africa: Evidence from Rural Ethiopia," WIDER Working Paper Series RP2006-145, World Institute for Development Economic Research (UNU-WIDER).
    16. Richard Peter, 2024. "The economics of self-protection," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 49(1), pages 6-35, March.
    17. Modica, Salvatore & Scarsini, Marco, 2005. "A note on comparative downside risk aversion," Journal of Economic Theory, Elsevier, vol. 122(2), pages 267-271, June.
    18. Khanam, Taznoore & Pede, Valerien O. & Wheatley, W. Parker, 2020. "Climate Change and the Formation of Risk and Time Preferences: A Study of Rice Farmers in Bangladesh," 2020 Annual Meeting, July 26-28, Kansas City, Missouri 304414, Agricultural and Applied Economics Association.
    19. Steven Brams & D. Kilgour, 1998. "Backward Induction Is Not Robust: The Parity Problem and the Uncertainty Problem," Theory and Decision, Springer, vol. 45(3), pages 263-289, December.
    20. Nolan Miller & Karen Eggleston & Richard Zeckhauser, 2006. "Provider choice of quality and surplus," International Journal of Health Economics and Management, Springer, vol. 6(2), pages 103-117, June.

    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:31:y:2005:i:2:p:109-127. 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.