Skip to main content

Nonlinear Utility Theory and Prospect Theory: Eliminating the Paradoxes of Linear Expected Utility Theory

  • Chapter
  • First Online:
Foundations of Economic Psychology

Abstract

As introduced in the previous chapter, expected utility theory has counter-examples called theAllais paradox (Allais, 1953) and Ellsberg’s paradox (Ellsberg, 1961), and we know that these counter-examples are related to independence axioms.

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

Access this chapter

eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 119.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 119.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Allais, M. (1953). Le comportement de l’homme rationnel devant le risque: Critique des postulates et axiomes de l’ecole Americaine. Econometrica, 21, 503–546.

    Article  Google Scholar 

  • Anscombe, F. J., & Aumann, R. J. (1963). A definition of subjective probability. The Annals of Mathematical Statistics, 34, 199–205.

    Article  Google Scholar 

  • Benartzi, S., & Thaler, R. H. (1995). Myopic loss aversion and the equity premium puzzle. Quarterly Journal of Economics, 110, 73–92.

    Article  Google Scholar 

  • Camerer, C. (1995). Individual decision making. In J. H. Hagel & A. E. Roth (Eds.), Handbook of experimental economics (pp. 587–703). Princeton, NJ: Princeton University Press.

    Google Scholar 

  • Camerer, C. F. (2000). Prospect theory in the wild: Evidence from the field. In D. Kahneman & A. Tversky (Eds.), Choices, values, and frames (pp. 288–300). Cambridge, UK: Cambridge University Press.

    Chapter  Google Scholar 

  • Camerer, C. F., Loewenstein, G., & Rabin, M. (Eds.). (2004). Advances in behavioral economics. Princeton, NJ: Princeton University Press.

    Google Scholar 

  • Chiccheti, C., & Dubin, J. (1994). A microeconometric analysis of risk aversion and the self-insure. Journal of Political Economy, 102, 169–186.

    Article  Google Scholar 

  • Choquet, G. (1954). Theory of capacities. Annales de l’institut Fourier, 5, 131–195.

    Article  Google Scholar 

  • Dawes, R. M. (1979). The robust beauty of improper linear models in decision making. American Psychologist, 34(7), 571–582.

    Article  Google Scholar 

  • De Waegenaere, A., & Wakker, P. P. (2001). Nonmonotonic Choquet integrals. Journal of Mathematical Economics, 36, 45–60.

    Article  Google Scholar 

  • Edwards, W. (Ed.). (1992). Utility theories: Measurement and applications. Boston, MA: Kluwer Academic Publishers.

    Google Scholar 

  • Einhorn, H., & Hogarth, R. (1985). Ambiguity and uncertainty in probabilistic inference. Psychological Review, 92, 433–461.

    Article  Google Scholar 

  • Einhorn, H., & Hogarth, R. (1986). Decision-making under ambiguity. Journal of Business, 59, 225–250.

    Article  Google Scholar 

  • Ellsberg, D. (1961). Risk, ambiguity, and the Savage axiom. Quarterly Journal of Economics, 75, 643–669.

    Article  Google Scholar 

  • Fechner, G. (1860). Elemente der psychophysik. Leibzing, DE: Breitkopf & Hartel.

    Google Scholar 

  • Fishburn, P. C. (1988). Nonlinear preference and utility theory. Sussex, UK: Wheatsheaf Books.

    Google Scholar 

  • Gigerenzer, G., & Strube, G. (1983). Are there limits to binaural additivity of loudness? Journal of Experimental Psychology: Human Perception and Performance, 9(1), 126–136.

    Google Scholar 

  • Gilboa, I. (2009). Theory of Decision under Uncertainty. Cambridge, UK: Cambridge University Press.

    Book  Google Scholar 

  • Gonzalez, R., & Wu, G. (1999). On the shape of the probability weighting function. Cognitive Psychology, 38(1), 129–166.

    Article  Google Scholar 

  • Kahneman, D., Knetsch, J. L., & Thaler, R. H. (1990). Experiment tests of the endowment effect and coase theorem. Journal of Political Economy, 98, 1325–1348.

    Article  Google Scholar 

  • Kahneman, D., Knetsch, J. L., & Thaler, R. H. (1991). The endowment effect, loss aversion, and status quo bias. Journal of Economic Perspectives, 5, 193–206.

    Article  Google Scholar 

  • Kahneman, D., & Tversky, A. (1979). Prospect theory: an analysis of decision under risk. Econometrica, 47, 263–292.

    Article  Google Scholar 

  • Levelt, W. J., Riemersma, J. B., & Bunt, A. A. (1972). Binaural additivity of loudness. British Journal of Mathematical and Statistical Psychology, 25, 51–68.

    Article  Google Scholar 

  • Loewenstein, G., & Prelec, D. (1992). Anomalies in intertemporal choice: evidence and an interpretation. The Quarterly Journal of Economics, 107(2), 573–597.

    Article  Google Scholar 

  • Mazur, J. E. (1987). An adjusting procedure for studying delayed reinforcement. In M. L. Commons, J. E. Mazur, J. A. Nevin, & H. Rachlin (Eds.), The effect of delay and of intervening events on reinforcement value (pp. 55–73). Hillsdale, NJ: Erlbaum.

    Google Scholar 

  • Murakami, H., Ideno, T., Tamari, Y., & Takemura, K. (2014). Kakuritsu kajĹ« kansĹ« ni taisuru moderu no teian to sono hikaku kentĹŤ [Proposal of probability weighting function model and psychological experiment for the comparisons]. Poster session presented at The Proceedings of the 78th Annual Convention of the Japanese Psychological Association, Kyoto, JP.

    Google Scholar 

  • Murofushi, T., Sugeno, M., & Machida, M. (1994). Nonmonotonic fuzzy measures and choquet integral. Fuzzy Sets and System, 64, 73–86.

    Article  Google Scholar 

  • Nakamura, K. (1992). On the nature of intransitivity in human preferential judgments. In V. Novak, J. Ramik, M. Mares, M. Cherny, & J. Nekola (Eds.), Fuzzy approach to reasoning and decision making (pp. 147–162). Dordrecht, NL: Kluwer.

    Chapter  Google Scholar 

  • Odean, T. (1998). Are investors reluctant to realize their losses? Journal of Finance, 53, 1775–1798.

    Article  Google Scholar 

  • Payne, J. W., Bettman, J. R., & Johnson, E. J. (1993). The adaptive decision maker. New York, NY: Cambridge University Press.

    Book  Google Scholar 

  • Prelec, D. (1998). The probability weighting function. Econometrica, 66(3), 497–527.

    Article  Google Scholar 

  • Quiggin, J. (1993). Generalized expected utility theory: The rank dependent model. Boston, MA: Kluwer Academic Publishers.

    Book  Google Scholar 

  • Savage, L. J. (1954). The foundations of statistics. New York, NY: Wiley.

    Google Scholar 

  • Schmeidler, D. (1989). Subjective probability and expected utility without additivity. Econometrica, 57, 571–587.

    Article  Google Scholar 

  • Seo, F. (1994). ShikĹŤ no Gijutsu: Aimai kankyĹŤka no keiei ishikettei [Thinking techniques: Management decision making under ambiguity environment]. Tokyo, JP: Yuhikaku Publishing.

    Google Scholar 

  • Shefrin, H. M., & Statman, M. (1985). The disposition to sell winners too early and ride losers too long. Journal of Finance, 40, 777–790.

    Article  Google Scholar 

  • Starmer, C. (2000). Developments in non-expected utility theory: The hunt for descriptive theory of choice under risk. Journal of Economic Literature, 38, 332–382.

    Article  Google Scholar 

  • Stott, H. P. (2006). Cumulative prospect theory’s functional menagerie. Journal of Risk and Uncertainty, 32(2), 101–130.

    Article  Google Scholar 

  • Sugeno, M., & Murofushi, T. (1993). KĹŤza fajÄ« 3: FajÄ« sokudo [Fuzzy theory 3: Fuzzy measure]. Tokyo, JP: Nikkan Kogyo Shimbunsha.

    Google Scholar 

  • Tada, Y. (2003). KĹŤdĹŤ Keizaigaku NyĹ«mon [Introduction to behavioral economics]. Tokyo, JP: Nikkei Inc.

    Google Scholar 

  • Takemura, K. (1998). JĹŤkyĹŤ izonteki ishikettei no teiseiteki moderu: Shinteki monosashi riron niyoru setsumei [Qualitative model of contingent decision-making: An explanation of using the mental ruler theory]. Ninchi Kagaku [Cognitive Studies], 5(4), 17–34.

    Google Scholar 

  • Takemura, K. (2000). Vagueness in human judgment and decision making. In Z. Q. Liu & S. Miyamoto (Eds.), Soft computing for human centered machines (pp. 249–281). Tokyo, JP: Springer.

    Chapter  Google Scholar 

  • Takemura, K. (2001). Contingent decision making in the social world. In C. M. Allwood & M. Selart (Eds.), Decision making: Social and creative dimensions (pp. 153–173). Dordrecht, NL: Kluwer Academic Publishers.

    Chapter  Google Scholar 

  • Takemura, K. (2011). Tazokusei ishikettei no shinri moderu to “yoi ishikettei” [Psychological model of multi-attribute decision making and good decision]. Opereshonzu risachi [Journal of the Operations Research Society of Japan], 56, 583–590.

    Google Scholar 

  • Takemura, K. (2014). Behavioral decision theory: Psychological and mathematical representations of human choice behavior. Tokyo, JP: Springer.

    Book  Google Scholar 

  • Takemura, K., & Murakami, H. (2016). Probability weighting functions derived from hyperbolic time discounting: psychophysical models and their individual level testing., Frontiers in Psychology, 7, 778. https://doi.org/10.3389/fpsyg.2016.00778.

  • Takemura, K., & Murakami, H. (2018). A testing method of probability weighting functions from an axiomatic perspective. Frontiers in Applied Mathematics and Statistics, 4, 48. https://doi.org/10.3389/fams.2018.00048.

    Article  Google Scholar 

  • Takemura, K., Murakami, H., Tamari, Y., & Ideno, T. (2013). Probability weighting function and value function based on unified psychological model. Paper presented at 2013 Asia-Pacific Meeting of the Economic Science Association, Tokyo, JP.

    Google Scholar 

  • Takemura, K., Murakami, H., Tamari, Y., & Ideno, T. (2014). Probability weighting function models and psychological experiment for the comparisons. Paper presented at Soft Science Workshop of Japan Society for Fuzzy Theory and Intelligent Infomatics, Fukuoka, JP.

    Google Scholar 

  • Tamura, H., Nakamura, Y., & Fujita, S. (1997). KĹŤyĹŤ bunseki no sĹ«ri to ĹŤyĹŤ [Mathematical principles and application of utility analysis]. Tokyo, JP: Corona Publishing.

    Google Scholar 

  • Thaler, R. H., & Ziemba, W. T. (1988). Anomalies: Parimutuel betting markets: Racetracks and lotteries. Journal of Economic Perspectives, 2(2), 161–174.

    Article  Google Scholar 

  • Toshino, M. (2004). ShĹŤken shijĹŤ to kĹŤdĹŤ fainansu [Security market and behavioral finance]. Tokyo, JP: Toyo Keizai.

    Google Scholar 

  • Tversky, A., & Kahneman, D. (1983). Extensional versus intuitive reasoning: The conjunction fallacy in probability judgment. Psychological Review, 90(4), 293–315.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Wu, G., & Gonzalez, R. (1996). Curvature of the probability weighting function. Management Science, 42(12), 1676–1690.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Kazuhisa Takemura .

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Singapore Pte Ltd.

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Takemura, K. (2019). Nonlinear Utility Theory and Prospect Theory: Eliminating the Paradoxes of Linear Expected Utility Theory. In: Foundations of Economic Psychology. Springer, Singapore. https://doi.org/10.1007/978-981-13-9049-4_4

Download citation

Publish with us

Policies and ethics