Theory and Decision

, Volume 49, Issue 3, pp 223–234 | Cite as

Reconciliation with the Utility of Chance by Elaborated Outcomes Destroys the Axiomatic Basis of Expected Utility Theory

Article

Abstract

Expected utility theory does not directly deal with the utility of chance. It has been suggested in the literature (Samuelson, 1952, Markowitz, 1959) that this can be remedied by an approach which explicitly models the emotional consequences which give rise to the utility of chance. We refer to this as the elaborated outcomes approach. It is argued that the elaborated outcomes approach destroys the possibility of deriving a representation theorem based on the usual axioms of expected utility theory. This is shown with the help of an example due to Markowitz. It turns out that the space of conceivable lotteries over elaborated outcomes is too narrow to permit the application of the axioms. Moreover it is shown that a representation theorem does not hold for the example.

Utility of chance Elaborated outcomes Axiomatised expected utility theory Representation theorem 

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REFERENCES

  1. Aumann, R.J. (1997), Letter from Robert Aumann to Leonard Savage, 8 January 1971, in R.J. Aumann, Collected Papers, Vol. 1. Massachusetts Institute of Technology Press, Cambridge, Massachusetts, 305–306.Google Scholar
  2. Broome, J. (1984), Rationality and the sure-thing principle, Discussion Paper 84/158, University of Bristol, Bristol, September.Google Scholar
  3. Broome, J. (1986), Rationality and the sure-thing principle, paper presented to the Economics Seminar Series, Research School of Social Science, Australian National University, Canberra.Google Scholar
  4. Broome, J. (1991a), Rationality and the sure-thing principle, in J. Gay Tulip Meeks (ed.), Thoughtful Economic Man, Cambridge University Press, 74–102Google Scholar
  5. Broome, J. (1991b), Expected Utility and Rationality, in J. Broome, Weighing Goods, Blackwell, UK, 90–120.Google Scholar
  6. Canaan, E. (1926), Profit, Palgrave's Dictionary of Political Economy, New Edition 1963, Henry Higgs (ed.), Kelley, New York.Google Scholar
  7. Luce, R.D. and Raiffa, H. (1957), Games and Decisions, Wiley, New York.Google Scholar
  8. Machina, M. (1989), Dynamic Consistency and Non-Expected Utility Models of Choice under Uncertainty, Journal of Economic Literature 27: 1622–68.Google Scholar
  9. Markowitz, H.M. (1959), Portfolio Selection, Wiley, New York.Google Scholar
  10. Marshall, A. (1920 and 1956), Principles of Economics, Macmillan, London.Google Scholar
  11. Pope, R.E. (1983), The Pre-Outcome Period and the Utility of Gambling, in B.P. Stigum and F. Wenstøp (eds.), Foundations of Utility and Risk Theory with Applications, Reidel, Dordrecht, 137–177.Google Scholar
  12. Pope, R.E. (1985), Timing Contradictions in von Neumann and Morgenstern's Axioms and in Savage's Sure-Thing Proof, Theory and Decision 18: 229–261.Google Scholar
  13. Pope, R.E. (1988a), The Bayesian Approach: Irreconcilable with Expected Utility Theory?, in B. Munier (ed.), Risk, Decision and Rationality, Reidel, Dordrecht, 221–230.Google Scholar
  14. Pope, R.E. (1988b), Reality versus Intention in the Expected Utility Procedure, Fourth International Conference on the Foundations and Applications of Utility, Risk and Decision Theory, Budapest.Google Scholar
  15. Pope, R.E. (1991a), The Delusion of Certainty in Savage's Sure-Thing Principle, Journal of Economic Psychology 12(2): 209–241.Google Scholar
  16. Pope, R.E. (1991b), Lowered Welfare under the Expected Utility Procedure, in A. Chikán (ed.), Progress in Decision, Utility and Risk, Kluwer, Dordrecht, 125–133.Google Scholar
  17. Pope, R.E. (1996/7) and forthcoming, Debates on the Utility of Chance: A Look Back to Move Forward, Journal for Science of Research (Zeitschrift für Wissenschaftsforschung), 11/12: 43–92 to be reprinted in On the Dynamics of Modern, Complex Social and Democratic Systems, Theory and Decision Library, Series A, Kluwer Academic Publishers.Google Scholar
  18. Pope, R.E. (1998), Attractions to and Repulsions from Chance, in Werner Leinfellner and Eckehart Köhler (eds.), Game Theory, Experience, Rationality, Kluwer, Dordrecht, 95–107.Google Scholar
  19. Pope, R.E., forthcoming, Evidence of Deliberate Violations of Dominance due to Secondary Satisfactions – Attractions to Chance, Homo Economicus, 33pp.Google Scholar
  20. Savage, L.J. (1972), Foundations of Statistics, Dover, NewYork.Google Scholar
  21. Savage, L.J. (1997), Letter from Leonard Savage to Robert Aumann, 27 January 1971, in R.J. Aumann, Collected Papers, Vol. 1, Massachusetts Institute of Technology Press, Cambridge, Massachusetts, 307–310.Google Scholar
  22. Samuelson, P. (1952), Probability, Utility and the Independence Axiom, Econometrica 20: 670–678.Google Scholar
  23. Smith, A. (1788), The Principles which Lead and Direct Philosophical Enquiries: Illustrated by the History of Astronomy, reprinted by Liberty Press, Indianapolis, 1982.Google Scholar

Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  1. 1.Department of EconomicsUniversity of TennesseeTennesseeUSA

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