IDEAS home Printed from https://ideas.repec.org/a/eee/mateco/v47y2011i6p706-717.html
   My bibliography  Save this article

Accounting for optimism and pessimism in expected utility

Author

Listed:
  • Webb, Craig S.
  • Zank, Horst

Abstract

We provide a preference foundation for decision under risk resulting in a model where probability weighting is linear as long as the corresponding probabilities are not extreme (i.e., 0 or 1). This way, most of the elegance and mathematical tractability of expected utility is maintained and also much of its normative foundation. Yet, the new model can accommodate the extreme sensitivity towards changes from 0 to almost impossible and from almost certain to 1 that has widely been documented in the experimental literature. The model can be viewed as “expected utility with the best and worst in mind” as suggested by Chateauneuf, Eichberger and Grant (Chateauneuf, Alain, Eichberger, Jürgen, Grant, Simon, 2007. Choice under uncertainty with the best and worst in mind: NEO-Additive capacities. Journal of Economic Theory 137, 538–567) or, following our preference foundation, interpreted as “expected utility with consistent optimism and pessimism”.

Suggested Citation

  • Webb, Craig S. & Zank, Horst, 2011. "Accounting for optimism and pessimism in expected utility," Journal of Mathematical Economics, Elsevier, vol. 47(6), pages 706-717.
    • Handle: RePEc:eee:mateco:v:47:y:2011:i:6:p:706-717
    DOI: 10.1016/j.jmateco.2011.09.007
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304406811000887
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmateco.2011.09.007?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 look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Wakker, Peter P, 2001. "Testing and Characterizing Properties of Nonadditive Measures through Violations of the Sure-Thing Principle," Econometrica, Econometric Society, vol. 69(4), pages 1039-1059, July.
    2. Mohammed Abdellaoui, 2002. "A Genuine Rank-Dependent Generalization of the Von Neumann-Morgenstern Expected Utility Theorem," Econometrica, Econometric Society, vol. 70(2), pages 717-736, March.
    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. Han Bleichrodt & Jose Luis Pinto, 2000. "A Parameter-Free Elicitation of the Probability Weighting Function in Medical Decision Analysis," Management Science, INFORMS, vol. 46(11), pages 1485-1496, November.
    5. Daniel Ellsberg, 2000. "Risk, Ambiguity and the Savage Axioms," Levine's Working Paper Archive 7605, David K. Levine.
    6. Quiggin, John & Horowitz, John, 1995. "Time and Risk," Journal of Risk and Uncertainty, Springer, vol. 10(1), pages 37-55, January.
    7. Peter Wakker & Daniel Deneffe, 1996. "Eliciting von Neumann-Morgenstern Utilities When Probabilities Are Distorted or Unknown," Management Science, INFORMS, vol. 42(8), pages 1131-1150, August.
    8. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    9. Chateauneuf, Alain & Wakker, Peter, 1993. "From local to global additive representation," Journal of Mathematical Economics, Elsevier, vol. 22(6), pages 523-545.
    10. Mohammed Abdellaoui & Frank Vossmann & Martin Weber, 2005. "Choice-Based Elicitation and Decomposition of Decision Weights for Gains and Losses Under Uncertainty," Management Science, INFORMS, vol. 51(9), pages 1384-1399, September.
    11. 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..
    12. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    13. 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.
    14. David E. Bell, 1985. "Disappointment in Decision Making Under Uncertainty," Operations Research, INFORMS, vol. 33(1), pages 1-27, February.
    15. Diecidue, Enrico & Schmidt, Ulrich & Zank, Horst, 2009. "Parametric weighting functions," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1102-1118, May.
    16. Horst Zank, 2010. "Consistent probability attitudes," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 44(2), pages 167-185, August.
    17. Machina, Mark J, 1989. "Dynamic Consistency and Non-expected Utility Models of Choice under Uncertainty," Journal of Economic Literature, American Economic Association, vol. 27(4), pages 1622-1668, December.
    18. Chateauneuf, Alain, 1999. "Comonotonicity axioms and rank-dependent expected utility theory for arbitrary consequences," Journal of Mathematical Economics, Elsevier, vol. 32(1), pages 21-45, August.
    19. Mohammed Abdellaoui & Olivier L’Haridon & Horst Zank, 2010. "Separating curvature and elevation: A parametric probability weighting function," Journal of Risk and Uncertainty, Springer, vol. 41(1), pages 39-65, August.
    20. Daniel Ellsberg, 1961. "Risk, Ambiguity, and the Savage Axioms," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 75(4), pages 643-669.
    21. Enrico Diecidue & Jeroen van de Ven, 2008. "Aspiration Level, Probability Of Success And Failure, And Expected Utility," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 49(2), pages 683-700, May.
    22. George Wu & Richard Gonzalez, 1996. "Curvature of the Probability Weighting Function," Management Science, INFORMS, vol. 42(12), pages 1676-1690, December.
    23. Drazen Prelec, 1998. "The Probability Weighting Function," Econometrica, Econometric Society, vol. 66(3), pages 497-528, May.
    24. Veronika Köbberling & Peter P. Wakker, 2003. "Preference Foundations for Nonexpected Utility: A Generalized and Simplified Technique," Mathematics of Operations Research, INFORMS, vol. 28(3), pages 395-423, August.
    25. Milton Friedman & L. J. Savage, 1948. "The Utility Analysis of Choices Involving Risk," Journal of Political Economy, University of Chicago Press, vol. 56(4), pages 279-279.
    26. Michael Kilka & Martin Weber, 2001. "What Determines the Shape of the Probability Weighting Function Under Uncertainty?," Management Science, INFORMS, vol. 47(12), pages 1712-1726, December.
    27. Camerer, Colin F, 1989. "An Experimental Test of Several Generalized Utility Theories," Journal of Risk and Uncertainty, Springer, vol. 2(1), pages 61-104, April.
    28. Mohammed Abdellaoui & Olivier l’Haridon & Horst Zank, 2009. "Separating Curvature and Elevation: A Parametric Weighting Function," Economics Discussion Paper Series 0901, Economics, The University of Manchester.
    29. Wakker, Peter, 1993. "Additive representations on rank-ordered sets : II. The topological approach," Journal of Mathematical Economics, Elsevier, vol. 22(1), pages 1-26.
    30. Mohammed Abdellaoui, 2000. "Parameter-Free Elicitation of Utility and Probability Weighting Functions," Management Science, INFORMS, vol. 46(11), pages 1497-1512, November.
    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. Jinrui Pan & Craig S. Webb & Horst Zank, 2019. "Delayed probabilistic risk attitude: a parametric approach," Theory and Decision, Springer, vol. 87(2), pages 201-232, September.
    2. Katarzyna M. Werner & Horst Zank, 2019. "A revealed reference point for prospect theory," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 67(4), pages 731-773, June.
    3. Craig Webb, 2015. "Piecewise additivity for non-expected utility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 60(2), pages 371-392, October.
    4. Meng, Jingyi & Webb, Craig S. & Zank, Horst, 2024. "Mixture independence foundations for expected utility," Journal of Mathematical Economics, Elsevier, vol. 111(C).
    5. Ulrich Schmidt & Horst Zank, 2013. "Chance Theory: A Separation of Riskless and Risky Utility," Economics Discussion Paper Series 1324, Economics, The University of Manchester.
    6. Mohammed Abdellaoui & Horst Zank, 2023. "Source and rank-dependent utility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 75(4), pages 949-981, May.
    7. Baillon, Aurélien & Placido, Lætitia, 2019. "Testing constant absolute and relative ambiguity aversion," Journal of Economic Theory, Elsevier, vol. 181(C), pages 309-332.
    8. 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.
    9. Katarzyna Werner & Horst Zank, 2012. "Foundations for Prospect Theory Through Probability Midpoint Consistency," Economics Discussion Paper Series 1210, Economics, The University of Manchester.
    10. Rémi Stellian & Gabriel I. Penagos & Jenny P. Danna-Buitrago, 2021. "Firms in financial distress: evidence from inter-firm payment networks with volatility driven by ‘animal spirits’," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 16(1), pages 59-101, January.
    11. Mark Schneider, 2019. "A Bias Aggregation Theorem," Working Papers 19-03, Chapman University, Economic Science Institute.
    12. Mohammed Abdellaoui & Olivier l’Haridon & Horst Zank, 2009. "Separating Curvature and Elevation: A Parametric Weighting Function," Economics Discussion Paper Series 0901, Economics, The University of Manchester.
    13. Craig S. Webb, 2017. "Piecewise linear rank-dependent utility," Theory and Decision, Springer, vol. 82(3), pages 403-414, March.
    14. Mohammed Abdellaoui & Horst Zank, 2022. "Source and Rank-dependent Utility," Post-Print hal-03924295, HAL.

    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. Katarzyna M. Werner & Horst Zank, 2019. "A revealed reference point for prospect theory," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 67(4), pages 731-773, June.
    2. Mohammed Abdellaoui & Olivier L’Haridon & Horst Zank, 2010. "Separating curvature and elevation: A parametric probability weighting function," Journal of Risk and Uncertainty, Springer, vol. 41(1), pages 39-65, August.
    3. Diecidue, Enrico & Schmidt, Ulrich & Zank, Horst, 2009. "Parametric weighting functions," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1102-1118, May.
    4. Jinrui Pan & Craig S. Webb & Horst Zank, 2019. "Delayed probabilistic risk attitude: a parametric approach," Theory and Decision, Springer, vol. 87(2), pages 201-232, September.
    5. Mohammed Abdellaoui & Horst Zank, 2023. "Source and rank-dependent utility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 75(4), pages 949-981, May.
    6. 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.
    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. Horst Zank, 2010. "On probabilities and loss aversion," Theory and Decision, Springer, vol. 68(3), pages 243-261, March.
    9. Laurent Denant-Boemont & Olivier L’Haridon, 2013. "La rationalité à l'épreuve de l'économie comportementale," Revue française d'économie, Presses de Sciences-Po, vol. 0(2), pages 35-89.
    10. Martina Nardon & Paolo Pianca, 2019. "Behavioral premium principles," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(1), pages 229-257, June.
    11. Horst Zank, 2010. "Consistent probability attitudes," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 44(2), pages 167-185, August.
    12. Meng, Jingyi & Webb, Craig S. & Zank, Horst, 2024. "Mixture independence foundations for expected utility," Journal of Mathematical Economics, Elsevier, vol. 111(C).
    13. Ulrich Schmidt & Horst Zank, 2012. "A genuine foundation for prospect theory," Journal of Risk and Uncertainty, Springer, vol. 45(2), pages 97-113, October.
    14. Jakusch, Sven Thorsten & Meyer, Steffen & Hackethal, Andreas, 2019. "Taming models of prospect theory in the wild? Estimation of Vlcek and Hens (2011)," SAFE Working Paper Series 146, Leibniz Institute for Financial Research SAFE, revised 2019.
    15. Matthew D. Rablen, 2023. "Loss Aversion, Risk Aversion, and the Shape of the Probability Weighting Function," Working Papers 2023013, The University of Sheffield, Department of Economics.
    16. Thomas Epper & Helga Fehr-Duda, 2012. "The missing link: unifying risk taking and time discounting," ECON - Working Papers 096, Department of Economics - University of Zurich, revised Oct 2018.
    17. Epper, Thomas & Fehr-Duda, Helga, 2017. "A Tale of Two Tails: On the Coexistence of Overweighting and Underweighting of Rare Extreme Events," Economics Working Paper Series 1705, University of St. Gallen, School of Economics and Political Science.
    18. Víctor González-Jiménez, 2021. "Incentive contracts when agents distort probabilities," Vienna Economics Papers vie2101, University of Vienna, Department of Economics.
    19. Gijs van de Kuilen & Peter P. Wakker, 2011. "The Midweight Method to Measure Attitudes Toward Risk and Ambiguity," Management Science, INFORMS, vol. 57(3), pages 582-598, March.
    20. Víctor González-Jiménez, 2021. "Incentive contracts when agents distort probabilities," Vienna Economics Papers 2101, University of Vienna, Department of Economics.

    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:eee:mateco:v:47:y:2011:i:6:p:706-717. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jmateco .

    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.