IDEAS home Printed from https://ideas.repec.org/p/iza/izadps/dp12701.html
   My bibliography  Save this paper

Foundations of the Rank-Dependent Probability Weighting Function

Author

Listed:
  • Rablen, Matthew D.

    (University of Sheffield)

Abstract

The psychological basis for rank-dependent probability weighting, and for an inverse-S probability weighting function (PWF) in particular, has often been questioned. I examine the existence and shape of the PWF in a model allowing for optimism/pessimism over probability distributions and for loss averse/gain loving stochastic reference dependence. I give commonly observed shapes of PWF a psychological interpretation. In particular, I establish a deep connection between two of the most established phenomena in decisionmaking: loss aversion and the inverse-S PWF: the former is a pre- condition for the latter.

Suggested Citation

  • Rablen, Matthew D., 2019. "Foundations of the Rank-Dependent Probability Weighting Function," IZA Discussion Papers 12701, Institute of Labor Economics (IZA).
    • Handle: RePEc:iza:izadps:dp12701
    as

    Download full text from publisher

    File URL: https://docs.iza.org/dp12701.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Diecidue, Enrico & Wakker, Peter P, 2001. "On the Intuition of Rank-Dependent Utility," Journal of Risk and Uncertainty, Springer, vol. 23(3), pages 281-298, November.
    2. Christian Gollier & Alexander Muermann, 2010. "Optimal Choice and Beliefs with Ex Ante Savoring and Ex Post Disappointment," Management Science, INFORMS, vol. 56(8), pages 1272-1284, August.
    3. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    4. Adam Booij & Bernard Praag & Gijs Kuilen, 2010. "A parametric analysis of prospect theory’s functionals for the general population," Theory and Decision, Springer, vol. 68(1), pages 115-148, February.
    5. Polkovnichenko, Valery & Zhao, Feng, 2013. "Probability weighting functions implied in options prices," Journal of Financial Economics, Elsevier, vol. 107(3), pages 580-609.
    6. 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.
    7. Bruno Jullien & Bernard Salanie, 2000. "Estimating Preferences under Risk: The Case of Racetrack Bettors," Journal of Political Economy, University of Chicago Press, vol. 108(3), pages 503-530, June.
    8. Botond Kőszegi & Matthew Rabin, 2006. "A Model of Reference-Dependent Preferences," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 121(4), pages 1133-1165.
    9. 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.
    10. Jianying Qiu & Eva-Maria Steiger, 2011. "Understanding the Two Components of Risk Attitudes: An Experimental Analysis," Management Science, INFORMS, vol. 57(1), pages 193-199, January.
    11. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    12. GlennW. Harrison & StevenJ. Humphrey & Arjan Verschoor, 2010. "Choice under Uncertainty: Evidence from Ethiopia, India and Uganda," Economic Journal, Royal Economic Society, vol. 120(543), pages 80-104, March.
    13. Segal, Uzi, 1987. "Some remarks on Quiggin's anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 8(1), pages 145-154, March.
    14. van de Kuilen, G. & Wakker, P.P., 2011. "The midweight method to measure attitudes towards risk and ambiguity," Other publications TiSEM c58a6884-24cc-4cab-ae2f-a, Tilburg University, School of Economics and Management.
    15. Levon Barseghyan & Francesca Molinari & Ted O'Donoghue & Joshua C. Teitelbaum, 2013. "The Nature of Risk Preferences: Evidence from Insurance Choices," American Economic Review, American Economic Association, vol. 103(6), pages 2499-2529, October.
    16. Goeree, Jacob K. & Holt, Charles A. & Palfrey, Thomas R., 2002. "Quantal Response Equilibrium and Overbidding in Private-Value Auctions," Journal of Economic Theory, Elsevier, vol. 104(1), pages 247-272, May.
    17. Gul, Faruk, 1991. "A Theory of Disappointment Aversion," Econometrica, Econometric Society, vol. 59(3), pages 667-686, May.
    18. 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..
    19. Botond Koszegi & Matthew Rabin, 2007. "Reference-Dependent Risk Attitudes," American Economic Review, American Economic Association, vol. 97(4), pages 1047-1073, September.
    20. Philippe Delquié & Alessandra Cillo, 2006. "Disappointment without prior expectation: a unifying perspective on decision under risk," Journal of Risk and Uncertainty, Springer, vol. 33(3), pages 197-215, December.
    21. 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.
    22. Karni, Edi & Safra, Zvi, 1987. ""Preference Reversal' and the Observability of Preferences by Experimental Methods," Econometrica, Econometric Society, vol. 55(3), pages 675-685, May.
    23. Matthew Rabin, 2000. "Risk Aversion and Expected-Utility Theory: A Calibration Theorem," Econometrica, Econometric Society, vol. 68(5), pages 1281-1292, September.
    24. repec:lmu:muenar:20868 is not listed on IDEAS
    25. David E. Bell, 1985. "Disappointment in Decision Making Under Uncertainty," Operations Research, INFORMS, vol. 33(1), pages 1-27, February.
    26. 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.
    27. Marc Oliver Rieger & Mei Wang & Thorsten Hens, 2017. "Estimating cumulative prospect theory parameters from an international survey," Theory and Decision, Springer, vol. 82(4), pages 567-596, April.
    28. John D. Hey & Chris Orme, 2018. "Investigating Generalizations Of Expected Utility Theory Using Experimental Data," World Scientific Book Chapters, in: Experiments in Economics Decision Making and Markets, chapter 3, pages 63-98, World Scientific Publishing Co. Pte. Ltd..
    29. Diecidue, Enrico & Wakker, Peter P., 2002. "Dutch books: avoiding strategic and dynamic complications, and a comonotonic extension," Mathematical Social Sciences, Elsevier, vol. 43(2), pages 135-149, March.
    30. Yusufcan Masatlioglu & Collin Raymond, 2016. "A Behavioral Analysis of Stochastic Reference Dependence," American Economic Review, American Economic Association, vol. 106(9), pages 2760-2782, September.
    31. Drazen Prelec, 1998. "The Probability Weighting Function," Econometrica, Econometric Society, vol. 66(3), pages 497-528, May.
    32. Tversky, Amos & Wakker, Peter, 1995. "Risk Attitudes and Decision Weights," Econometrica, Econometric Society, vol. 63(6), pages 1255-1280, November.
    33. Humphrey, Steven J. & Verschoor, Arjan, 2004. "The probability weighting function: experimental evidence from Uganda, India and Ethiopia," Economics Letters, Elsevier, vol. 84(3), pages 419-425, September.
    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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. Arjan Verschoor & Ben D’Exelle, 2022. "Probability weighting for losses and for gains among smallholder farmers in Uganda," Theory and Decision, Springer, vol. 92(1), pages 223-258, February.
    6. van de Kuilen, G. & Wakker, P.P., 2011. "The midweight method to measure attitudes towards risk and ambiguity," Other publications TiSEM c58a6884-24cc-4cab-ae2f-a, Tilburg University, School of Economics and Management.
    7. 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.
    8. Aurélien Baillon & Han Bleichrodt & Vitalie Spinu, 2020. "Searching for the Reference Point," Management Science, INFORMS, vol. 66(1), pages 93-112, January.
    9. Kpegli, Yao Thibaut & Corgnet, Brice & Zylbersztejn, Adam, 2023. "All at once! A comprehensive and tractable semi-parametric method to elicit prospect theory components," Journal of Mathematical Economics, Elsevier, vol. 104(C).
    10. repec:cup:judgdm:v:16:y:2021:i:6:p:1324-1369 is not listed on IDEAS
    11. 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.
    12. Georgalos, Konstantinos & Paya, Ivan & Peel, David, 2024. "The Kőszegi–Rabin expectations-based model and risk-apportionment tasks for elicitation of higher order risk preferences," Journal of Economic Behavior & Organization, Elsevier, vol. 224(C), pages 749-770.
    13. 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.
    14. Richard Gonzalez & George Wu, 2022. "Composition rules in original and cumulative prospect theory," Theory and Decision, Springer, vol. 92(3), pages 647-675, April.
    15. Johannes G. Jaspersen & Richard Peter & Marc A. Ragin, 2023. "Probability weighting and insurance demand in a unified framework," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 48(1), pages 63-109, March.
    16. Alex Gershkov & Benny Moldovanu & Philipp Strack & Mengxi Zhang, 2023. "Optimal Insurance: Dual Utility, Random Losses and Adverse Selection," ECONtribute Discussion Papers Series 242, University of Bonn and University of Cologne, Germany.
    17. Stephen G Dimmock & Roy Kouwenberg & Olivia S Mitchell & Kim Peijnenburg, 2021. "Household Portfolio Underdiversification and Probability Weighting: Evidence from the Field," The Review of Financial Studies, Society for Financial Studies, vol. 34(9), pages 4524-4563.
    18. Andersen, Steffen & Harrison, Glenn W. & Lau, Morten Igel & Rutström, Elisabet E., 2010. "Behavioral econometrics for psychologists," Journal of Economic Psychology, Elsevier, vol. 31(4), pages 553-576, August.
    19. Özalp Özer & Yanchong Zheng, 2016. "Markdown or Everyday Low Price? The Role of Behavioral Motives," Management Science, INFORMS, vol. 62(2), pages 326-346, February.
    20. 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.
    21. Aluma Dembo & Shachar Kariv & Matthew Polisson & John Quah, 2021. "Ever since Allais," IFS Working Papers W21/15, Institute for Fiscal Studies.

    More about this item

    Keywords

    probability weighting; rank dependent expected utility; loss aversion; reference dependence; optimism; pessimism;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:iza:izadps:dp12701. 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: Holger Hinte (email available below). General contact details of provider: https://edirc.repec.org/data/izaaade.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.