Abstract
In structuring a decision problem under uncertainty, the uncertain environment may be affected by the choice of an act. In decision analysis, the decision maker provides subjective probabilities and utilities through separate elicitation processes, and then both components are combined together to give an index of his preference over decision alternatives. Based upon this conceptualisation of decision analysis, a constructive approach to act-conditional subjective expected utility theory is proposed. Two utility models have been addressed: the linear utility model and the weighted utility model.
Similar content being viewed by others
References
Balch, M. (1973). On recent developments in subjective expected utility. In Blach and Wu (editors),Essays on Economic Behaviour under Uncertainty, Amsterdam, North Holland.
Balch, M. and P.C. Fishburn (1973). Subjective expected utility for conditional primitives. In Balch and Wu (editors),Essays on Economic Behaviour under Uncertainty, Amsterdam, North Holland.
Bolker, E. D. (1973). Remarks on ‘Subjective expected utility for conditional primatives’. In Balch and Wu (editors),Essays on Economic Behaviour under Uncertainty, Amsterdam, North Holland.
Chew, S. H. and K. R. MacCrimmon (1979). Alpha-Nu choice theory: a generalisation of expected utility theory. Working Paper 669, University of British Columbia Vancouver.
Chew, S. H. (1983).A generalisation of the quasilinear mean with applications to the measurement of income inequality and decision theory resolving the Allais Paradox.Econometrica 51,1065–1092.
DeGroot, M. H. (1970).Optimal Statistical Decisions, McGraw Hill, New York.
Finetti, de (1937).La Preévision: Ses Lois Logiques, ses Sources Subjectives, Annales de l'Institut Henri Poincare,7,1–68.
Fishburn, P. C. (1988).Non-linear Preference and Utility Theory, Wheatsheaf Books, Brighton.
French, S. (1986).Decision Theory: an introduction to the mathematics of rationality. Ellis Horwood, Chichester.
French, S. and Xie, Z. (1994). A perspective on recent developments in utility theory, inDecision Theory and Decision Analysis: Trends and Challenges, edited by Sixto Rios, Kluwer.
Herstein, I. N., Milnor (1953). An axiomatic approach to measurable utility,Econometrica 21, 291–297.
Luce, R. D. and D. H. Krantz (1971). Conditional expected utility,Econometrica 39, 253–271.
Luce, R. D. and P. C. Fishburn (1991). Rank and sign dependent linear utility models for finite first-order gambles,Journal of Risk and uncertainty,1, 29–59.
Pratt, J. W., H. Raiffa and R. Schlaifer (1964). The foundations of decision under uncertainty: an elementary exposition.Journal of the American Statistical Association,59, 353–375.
Pratt, J. W. (1973), Some comments on some axioms for decision making under uncertainty, in Balch and Wu (editors),Essays on Economic Behaviour under Uncertainty, Amsterdam, North Holland.
Ramsay, F. P. (1931). Truth and Probability, inThe Foundations of Mathematics and Other Logical Essays, ed. Ramsey, New York: Harcourt Brace.
Savage, L. J. (1954).The Foundation of Statistics, Wiley, New York.
Villegas, C. (1964). On qualitative probability σ-algebras,Annals of Mathematical Statistics,35, 1787–1796.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Xie, Z., French, S. Towards a constructive approach to act-conditional subjective expected utility models. Top 5, 167–186 (1997). https://doi.org/10.1007/BF02568547
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02568547