Theory and Decision

, Volume 41, Issue 3, pp 281–301 | Cite as

Expected utility without utility

  • E. Castagnoli
  • M. Li Calzi


This paper advances an interpretation of Von Neumann-Morgenstern's expected utility model for preferences over lotteries which does not require the notion of a cardinal utility over prizes and can be phrased entirely in the language of probability. According to it, the expected utility of a lottery can be read as the probability that this lottery outperforms another given independent lottery. The implications of this interpretation for some topics and models in decision theory are considered.

Key words

Expected utility cardinal utility benchmark risk attitude stochastic dominance 


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  1. Arrow, K.J.: 1974, ‘The use of unbounded utility functions in expected utility maximization: Response’,Quarterly Journal of Economics 88, 136–138.Google Scholar
  2. Becker, J.L. and Sarin, R.K.: 1987, ‘Lottery dependent utility’,Management Science 33, 1367–1382.Google Scholar
  3. Berger, J.O.: 1985,Statistical Decision Theory and Bayesian Analysis, second edition, Springer, New York.Google Scholar
  4. Bernardo, J.M. and Smith, A.F.M.: 1994,Bayesian Theory, Wiley, New York and Chichester.Google Scholar
  5. Billingsley, P.: 1986,Probability and Measure, second edition, Wiley, New York and Chichester.Google Scholar
  6. Bordley, R.F.: 1992, ‘An intransitive expectations-based Bayesian variant of prospect theory’,Journal of Risk and Uncertainty 5, 127–144.Google Scholar
  7. Bordley, R.F. and Hazen, G.: 1992, ‘Nonlinear utility models arising from unmodelled small worlds intercorrelations,’Management Science 38, 1010–1017.Google Scholar
  8. Castagnoli, E.: 1990, ‘Qualche riflessione sull'utilità attesa,’Ratio Mathematica 1, 51–59.Google Scholar
  9. Castagnoli, E. and Li Calzi, M.: 1993, ‘Expected utility without utility: constant risk attitude’,Rendiconti del Comitato per gli Studi Economici 30–31, 145–160.Google Scholar
  10. Foldes, L.: 1972, ‘Expected utility and continuity’,Review of Economic Studies 39, 407–421.Google Scholar
  11. Grandmont, J.-M.: 1972, ‘Continuity properties of a von Neumann-Morgenstern utility’,Journal of Economic Theory 4, 45–57.Google Scholar
  12. Kahneman, D. and Tversky, A.: 1979, ‘Prospect theory: an analysis of decision under risk’,Econometrica 47, 263–291.Google Scholar
  13. Machina, M.J.: 1982, ‘Expected utility’ analysis without the independence Axiom’,Econometrica 50, 277–323.Google Scholar
  14. Machina, M.J.: 1983, ‘Generalized expected utility analysis and the nature of observed violations of the independence axiom’, In B.P. Stigum and F. Wenstøp (eds.),Foundations of Utility and Risk Theory, Reidel, Dordrecht, 263–293.Google Scholar
  15. Markowitz, H.: 1952, ‘The utility of wealth’,Journal of Political Economy 60, 151–158.Google Scholar
  16. Marshall, A.W. and Olkin, I.: 1979,Inequalities: Theory of Majorization and Its Applications, Academic Press, Orlando (Florida).Google Scholar
  17. Robson, A.J.: 1992, ‘Status, the distribution of wealth, private and social attitudes to risk’,Econometrica 60, 837–857.Google Scholar
  18. Viscusi, W.K.: 1989, ‘Prospective reference theory: toward an explanation of the Paradoxes’,Journal of Risk and Uncertainty 2, 235–264.Google Scholar

Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • E. Castagnoli
    • 1
  • M. Li Calzi
    • 2
  1. 1.Istituto di Metodi Quantitativi Università ‘L. Bocconi’MilanoItaly
  2. 2.Dipartimento di Matematica ApplicataUniversità di VeneziaVeneziaItaly

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