Skip to main content
SpringerLink
Log in

Solving the St. Petersburg Paradox in cumulative prospect theory: the right amount of probability weighting

  • Published:
Theory and Decision Aims and scope Submit manuscript

Abstract

Cumulative Prospect Theory (CPT) does not explain the St. Petersburg Paradox. We show that the solutions related to probability weighting proposed to solve this paradox, (Blavatskyy, Management Science 51:677–678, 2005; Rieger and Wang, Economic Theory 28:665–679, 2006) have to cope with limitations. In that framework, CPT fails to accommodate both gambling and insurance behavior. We suggest replacing the weighting functions generally proposed in the literature by another specification which respects the following properties: (1) to solve the paradox, the slope at zero has to be finite. (2) to account for the fourfold pattern of risk attitudes, the probability weighting has to be strong enough.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Abdellaoui M. (2000). Parameter-free elicitation of utility and probability weighting functions. Management Science 46: 1497–1512

    Article  Google Scholar 

  • Allais M. (1953). Le Comportement de l’Homme Rationnel Devant Le Risque, Critiques des Postulats et Axiomes de l’Ecole Américaine. Econometrica 21: 503–546

    Article  Google Scholar 

  • Arrow K.J. (1974). The use of unbounded functions in expected-utility maximization: Response. The Quaterly Journal of Economics 88: 136–138

    Article  Google Scholar 

  • Bernoulli D. (1738). Specimen Theoriae Novae de Mensura Sortis. Commentarii Academiae Scientiarum Imperialis Petropolitanae 5: 175–192

    Google Scholar 

  • Bernoulli, D. (1954, Original Edition, 1738). Exposition of a new theory of the measurement of risk. Econometrica, 22, 123–136.

    Google Scholar 

  • Blavatskyy P. (2005). Back to the St Petersburg Paradox?. Management Science 51: 677–678

    Article  Google Scholar 

  • Bleichrodt H. and Pinto J. (2000). A parameter-free elicitation of the probability weighting function in medical decision analysis. Management Science 46: 1485–1496

    Article  Google Scholar 

  • Camerer C. (1998). Bounded rationality in individual decision making. Experimental Economics 1: 163–183

    Google Scholar 

  • Camerer C.F. and Ho T. (1994). Violations of the betweenness axiom and nonlinearity in probability. Journal of Risk and Uncertainty 8: 167–196

    Article  Google Scholar 

  • De Giorgi E. and Hens S. (2006). Making prospect theory fit for finance. Financial Market Portfolio Management 20: 339–360

    Article  Google Scholar 

  • Ingersoll, J. (2008). Non-monotonicity of the Tversky-Kahneman probability-weighting function: A cautionary note. European Financial Management, 1–6.

  • Kahneman D. and Tversky A. (1979). Prospect theory: An analysis of decision under risk. Econometrica 47: 263–291

    Article  Google Scholar 

  • Köbberling V. and Wakker P. (2005). An index of loss aversion. Journal of Economic Theory 122: 119–131

    Article  Google Scholar 

  • Kilka M. and Weber M. (2001). What determines the shape of the probability weighting function under uncertainty. Management Science 47: 1712–1726

    Article  Google Scholar 

  • Menger K. (1934). Das Unsicherheitsmoment in der Wertlehre. Zeitschrift National[["o]]konomie 51: 459–485

    Article  Google Scholar 

  • Neilson W. and Stowe J. (2002). A further examination of cumulative prospect theory parameterizations. Journal of Risk and Uncertainty 24: 31–46

    Article  Google Scholar 

  • Quiggin J. (1982). A theory of anticipated utility. Journal of Economic Behavior and Organization 3: 323–343

    Article  Google Scholar 

  • Rieger M. and Wang M. (2006). Cumulative prospect theory and the St. Petersburg Paradox. Economic Theory 28: 665–679

    Article  Google Scholar 

  • Slovic P. and Lichtenstein S. (1968). The relative importance of probabilities and payoffs in risk taking. Journal of Experimental Psychology 78: 1–18

    Article  Google Scholar 

  • Tversky A. and Fox C.R. (1995). Weighting risk and uncertainty. Psychological Review 102: 269–283

    Article  Google Scholar 

  • Tversky A. and Kahneman D. (1992). Advances in prospect theory: Cumulative representation of uncertainty. Journal of Risk and Uncertainty 5: 297–323

    Article  Google Scholar 

  • Wu G. and Gonzalez R. (1996). Curvature of the probability weighting function. Management Science 42: 1676–1690

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. LaRGE Research Center, EM Strasbourg Business School, University of Strasbourg, Pôle Européen de Gestion et d’Economie, 61 avenue de la Forêt Noire, 67085, Strasbourg Cedex, France

    Marie Pfiffelmann

Authors
  1. Marie Pfiffelmann
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Marie Pfiffelmann.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pfiffelmann, M. Solving the St. Petersburg Paradox in cumulative prospect theory: the right amount of probability weighting. Theory Decis 71, 325–341 (2011). https://doi.org/10.1007/s11238-009-9191-x

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11238-009-9191-x

Keywords

Search

Navigation