An Explanation and Characterization for the Buying of Lotteries

  • Hein Fennema
  • Peter Wakker


Popular lotteries typically give a very small probability to win a large prize and a moderate chance to win smaller prizes. In this paper, a rank dependent model is axiomatized, with an S-shaped weighting function, capable of giving an account for the popularity of these lotteries. Also, the role of utility, loss aversion and scale compatibility in the explanation of the buying of lotteries is discussed.


Weighting Function Decision Theory Gambling Behavior Loss Aversion Cumulative Prospect Theory 
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  1. Chateauneuf, A. (1990) On the Use of Comonotonicity in the Axiomatization of EURDP Theory for Arbitrary Consequences, CERMSEM, University of Paris I; presented at FUR VI, Paris.Google Scholar
  2. Chateauneuf, A. (1991) On the Use of Capacities in Modeling Uncertainty Aversion and Risk Aversion, J. Math. Econ., 20, 343–369.CrossRefGoogle Scholar
  3. Edwards, W. (1962) Subjective Probabilities Inferred from Decisions, Psychological Review, 69, 109–135.CrossRefGoogle Scholar
  4. Fishburn, P.C. (1978) On Handa’s ‘New Theory of Cardinal Utility’ and the Maximization of Expected return, J. Pol. Econ., 86, 321–324.CrossRefGoogle Scholar
  5. Friedman, M. and L.J. Savage (1948) The Utility Analysis of Choices Involving Risk, J. Pol. Econ., 56, 279–304.CrossRefGoogle Scholar
  6. Goldstein, W.M. and H.J. Einhorn (1987) Expression Theory and the Preference Reversal Phenomena, Psychological Review, 94, 236–254.CrossRefGoogle Scholar
  7. Kahneman, D. and A. Tversky (1979) Prospect Theory: An Analysis of Decision under Risk, Econometrica, 47, 263–291.CrossRefGoogle Scholar
  8. Kami, E. and Z. Safra (1990) Rank-Dependent Probabilities, Economic Journal, 100, 487–495.CrossRefGoogle Scholar
  9. Machina, M.J. (1982) ‘Expected Utility’ Analysis without the Independence Axiom, Econometrica, 50, 277–323.CrossRefGoogle Scholar
  10. Markowitz, H. (1952) The Utility of Wealth, J. Pol. Econ., 60, 151–158.CrossRefGoogle Scholar
  11. Quiggin, J. (1982) A Theory of Anticipated Utility, J. Econ. Beh. Organ., 3, 323–343.CrossRefGoogle Scholar
  12. Quiggin, J. (1991) On the Optimal Design of Lotteries, Economica, 58, 1–16.CrossRefGoogle Scholar
  13. Schmeidler, D. (1989) Subjective Probability and Expected Utility without Additivity, Econometrica, 57, 571–587.CrossRefGoogle Scholar
  14. Shapira, Z. and I. Venezia (1992) Size and Frequency of Prizes as Determinants of the Demand for Lotteries, Org. Beh. Hum. Dec. Proc., 52, 307–318.CrossRefGoogle Scholar
  15. Slovic, P. and S. Lichtenstein (1968) The Relative Influence of Probabilities and Payoffs upon Perceived Risk of a Gamble, J. Experim. Psych., 78, 646–654.CrossRefGoogle Scholar
  16. Tversky, A. and D. Kahneman (1992) Advances in Prospect Theory: Cumulative Representation of Uncertainty, J. Risk Unc., 5, 297–323.CrossRefGoogle Scholar
  17. Tversky, A., S. Sattath, and P. Slovic (1988) Contingent Weighting in Judgment and Choice, Psychological Review, 95, 371–384.CrossRefGoogle Scholar
  18. Tversky, A., P. Slovic, and D. Kahneman (1990) The Causes of Preference Reversal, American Economic Review, 80, 204–217.Google Scholar
  19. von Neumann, J. and O. Morgenstern (1944, 1947, 1953) Theory of Games and Economic Behavior, Princeton University Press.Google Scholar
  20. Wakker, P.P. (1987) From Decision Making under Uncertainty to Game Theory, in H.J.M. Peters and O. J. Vrieze (Eds.), Surveys of Game Theory and Related Topics, 163–180, CWI Tract 39, Centre for Mathematics and Computer Science, Amsterdam.Google Scholar
  21. Wakker, P.P. (1989) Transforming Probabilities without Violating Stochastic Dominance, in E. Roskam (Ed.), Mathematical Psychology in Progress, Springer, 29–47.Google Scholar
  22. Wakker, P.P. (1990a) Characterizing Optimism and Pessimism Directly through Comonotonicity, J. Econ. Theory, 52, 453–463.CrossRefGoogle Scholar
  23. Wakker, P.P. (1990b) A Behavioral Foundation for Fuzzy Measures, Fuzzy Sets and Systems, 37, 327–350.CrossRefGoogle Scholar
  24. Wakker, P.P. (1990c) Under Stochastic Dominance Choquet-Expected Utility and Anticipated Utility are Identical, Theory and Decision, 29, 119–132.CrossRefGoogle Scholar
  25. Wakker, P.P. and A. Tversky (1993) An Axiomatization of Cumulative Prospect Theory, J. Risk and Uncertainty 7, 147–176.CrossRefGoogle Scholar
  26. Weymark, J.A. (1981) Generalized Gini Inequality Indices, Mathematical Social Sciences, 1, 409–430.CrossRefGoogle Scholar
  27. Yaari, M.E. (1987) The Dual Theory of Choice under Risk, Econometrica, 55, 95–115.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

  • Hein Fennema
  • Peter Wakker

There are no affiliations available

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