IDEAS home Printed from https://ideas.repec.org/p/mnh/spaper/2756.html
   My bibliography  Save this paper

Security and potential level preferences with thresholds

Author

Listed:
  • Schmidt, Ulrich
  • Zimper, Alexander

Abstract

The security level models of Gilboa (1988) and of Jaffray (1988) as well as the security and potential level model of Cohen (1992) accomodate succesfully classical Allais paradoxa while they offer an interesting explanation for their occurrence. However, experimental data suggest a systematic violation of these models when lotteries with low probabilities of bad or good outcomes are involved. The present paper develops an axiomatic model that allows for thresholds in the perception of security and potential levels. The derived representation of preferences accommodates the observed violations of the original security and potential level models and provides a natural explanation for their occurence. Additionally, a more fundamental problem of the original models is resolved.

Suggested Citation

  • Schmidt, Ulrich & Zimper, Alexander, 2003. "Security and potential level preferences with thresholds," Papers 03-29, Sonderforschungsbreich 504.
  • Handle: RePEc:mnh:spaper:2756
    as

    Download full text from publisher

    File URL: https://madoc.bib.uni-mannheim.de/2756/1/dp03_29.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Itzhak Gilboa, 1988. "A Combination of Expected Utility and Maxmin Decision Criteria," Post-Print hal-00753244, HAL.
    2. Chateauneuf, Alain & Eichberger, Jurgen & Grant, Simon, 2007. "Choice under uncertainty with the best and worst in mind: Neo-additive capacities," Journal of Economic Theory, Elsevier, vol. 137(1), pages 538-567, November.
    3. 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.
    4. Matthew Rabin, 2000. "Risk Aversion and Expected-Utility Theory: A Calibration Theorem," Econometrica, Econometric Society, vol. 68(5), pages 1281-1292, September.
    5. Harless, David W & Camerer, Colin F, 1994. "The Predictive Utility of Generalized Expected Utility Theories," Econometrica, Econometric Society, vol. 62(6), pages 1251-1289, November.
    6. 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..
    7. Chris Starmer, 2000. "Developments in Non-expected Utility Theory: The Hunt for a Descriptive Theory of Choice under Risk," Journal of Economic Literature, American Economic Association, vol. 38(2), pages 332-382, June.
    8. Essid, Samir, 1997. "Choice under risk with certainty and potential effects: A general axiomatic model," Mathematical Social Sciences, Elsevier, vol. 34(3), pages 223-247, October.
    9. Birnbaum, Michael H & Navarrete, Juan B, 1998. "Testing Descriptive Utility Theories: Violations of Stochastic Dominance and Cumulative Independence," Journal of Risk and Uncertainty, Springer, vol. 17(1), pages 49-78, October.
    10. Jürgen Eichberger & David Kelsey, 1999. "E-Capacities and the Ellsberg Paradox," Theory and Decision, Springer, vol. 46(2), pages 107-138, April.
    11. Zvi Safra & Uzi Segal, 2005. "Are Universal Preferences Possible? Calibration Results for Non-Expected Utility Theories," Boston College Working Papers in Economics 633, Boston College Department of Economics.
    12. Stone, Eric R. & Yates, J. Frank & Parker, Andrew M., 1994. "Risk Communication: Absolute versus Relative Expressions of Low-Probability Risks," Organizational Behavior and Human Decision Processes, Elsevier, vol. 60(3), pages 387-408, December.
    Full references (including those not matched with items on IDEAS)

    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. Ulrich Schmidt & Horst Zank, 2022. "Chance theory: A separation of riskless and risky utility," Journal of Risk and Uncertainty, Springer, vol. 65(1), pages 1-32, August.
    2. Schmidt, Ulrich & Zimper, Alexander, 2003. "Security And Potential Level Preferences With," Sonderforschungsbereich 504 Publications 03-29, Sonderforschungsbereich 504, Universität Mannheim;Sonderforschungsbereich 504, University of Mannheim.
    3. Daniel Navarro-Martinez & Graham Loomes & Andrea Isoni & David Butler & Larbi Alaoui, 2018. "Boundedly rational expected utility theory," Journal of Risk and Uncertainty, Springer, vol. 57(3), pages 199-223, December.
    4. Peter Brooks & Horst Zank, 2005. "Loss Averse Behavior," Journal of Risk and Uncertainty, Springer, vol. 31(3), pages 301-325, December.
    5. Simone Cerreia‐Vioglio & David Dillenberger & Pietro Ortoleva, 2015. "Cautious Expected Utility and the Certainty Effect," Econometrica, Econometric Society, vol. 83, pages 693-728, March.
    6. Amit Kothiyal & Vitalie Spinu & Peter Wakker, 2014. "An experimental test of prospect theory for predicting choice under ambiguity," Journal of Risk and Uncertainty, Springer, vol. 48(1), pages 1-17, February.
    7. Peter Brooks & Simon Peters & Horst Zank, 2014. "Risk behavior for gain, loss, and mixed prospects," Theory and Decision, Springer, vol. 77(2), pages 153-182, August.
    8. Ryan O. Murphy & Robert H. W. ten Brincke, 2018. "Hierarchical Maximum Likelihood Parameter Estimation for Cumulative Prospect Theory: Improving the Reliability of Individual Risk Parameter Estimates," Management Science, INFORMS, vol. 64(1), pages 308-328, January.
    9. Michael Birnbaum & Ulrich Schmidt, 2008. "An experimental investigation of violations of transitivity in choice under uncertainty," Journal of Risk and Uncertainty, Springer, vol. 37(1), pages 77-91, August.
    10. 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).
    11. 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.
    12. Peter Wakker & Veronika Köbberling & Christiane Schwieren, 2007. "Prospect-theory’s Diminishing Sensitivity Versus Economics’ Intrinsic Utility of Money: How the Introduction of the Euro can be Used to Disentangle the Two Empirically," Theory and Decision, Springer, vol. 63(3), pages 205-231, November.
    13. Andrew J. Keith & Darryl K. Ahner, 2021. "A survey of decision making and optimization under uncertainty," Annals of Operations Research, Springer, vol. 300(2), pages 319-353, May.
    14. Groneck, Max & Ludwig, Alexander & Zimper, Alexander, 2024. "Who saves more, the naive or the sophisticated agent?," Journal of Economic Theory, Elsevier, vol. 219(C).
    15. Enrico Diecidue & Peter Wakker & Marcel Zeelenberg, 2007. "Eliciting decision weights by adapting de Finetti’s betting-odds method to prospect theory," Journal of Risk and Uncertainty, Springer, vol. 34(3), pages 179-199, June.
    16. 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.
    17. P Brooks & H Zank, 2004. "Attitudes on Gain and Loss Lotteries: A Simple Experiment," Economics Discussion Paper Series 0402, Economics, The University of Manchester.
    18. Pavlo Blavatskyy, 2018. "A second-generation disappointment aversion theory of decision making under risk," Theory and Decision, Springer, vol. 84(1), pages 29-60, January.
    19. Krzysztof Kontek & Michal Lewandowski, 2018. "Range-Dependent Utility," Management Science, INFORMS, vol. 64(6), pages 2812-2832, June.
    20. Ferdinand Vieider, 2016. "Certainty Preference, Random Choice, and Loss Aversion: A Comment on "Violence and Risk Preference: Experimental Evidence from Afghanistan"," Economics Discussion Papers em-dp2016-06, Department of Economics, University of Reading.

    More about this item

    Keywords

    Allais paradoxa ; security level ; potential level ; thresholds;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

    Statistics

    Access and download statistics

    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:mnh:spaper:2756. 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: Katharina Rautenberg (email available below). General contact details of provider: https://edirc.repec.org/data/sfmande.html .

    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.