Subjective Probability under Additive Aggregation of Conditional Preferences

Abstract This paper provides an axiomatic basis for a representation of personal preferences in which the utility of an act can be expressed as an expected value of conditional utilities of the act given any set of mutually exclusive and exhaustive scenarios, under a unique subjective probability. The representation is general enough to incorporate state-dependent utilities and/or utilities with dependencies across states, as, for example, in the case of disappointment aversion. More generally, this is a model incorporating subjective probability and subjective consequences, since neither probabilities nor consequences are included among its primitives. The model reduces to subjective expected utility under the additional assumptions of separability and state-independence with respect to an objective state-contingent structure of acts.Journal of Economic LiteratureClassification Numbers: D81, D84.

[1]  Peter P. Wakker,et al.  Subjective probabilities for state-dependent continuous utility , 1987 .

[2]  Edi Karni,et al.  On State-Dependent Prefer-ences and Subjective Probabilities , 1983 .

[3]  Jacques Drèze,et al.  Essays on Economic Decisions under Uncertainty , 1990 .

[4]  Eddie Dekel An axiomatic characterization of preferences under uncertainty: Weakening the independence axiom , 1986 .

[5]  Peter P. Wakker,et al.  The algebraic versus the topological approach to additive representations , 1988 .

[6]  M. Machina "Expected Utility" Analysis without the Independence Axiom , 1982 .

[7]  P. Wakker Additive Representations of Preferences: A New Foundation of Decision Analysis , 1988 .

[8]  D. Schmeidler,et al.  A More Robust Definition of Subjective Probability , 1992 .

[9]  M. Machina Dynamic Consistency and Non-expected Utility Models of Choice under Uncertainty , 1989 .

[10]  Birgit Grodal,et al.  Additive Utility Functions and Other Special Functions in Economic Theory , 1990 .

[11]  David M. Kreps A Representation Theorem for , 1979 .

[12]  R. Luce,et al.  Conditional Expected Utility , 1971 .

[13]  Peter C. Fishburn,et al.  Nonlinear preference and utility theory , 1988 .

[14]  Werner Hildenbrand,et al.  Mathematical Economics: Valuation equilibrium and Pareto optimum , 1983 .

[15]  Yutaka Nakamura Subjective expected utility with non-additive probabilities on finite state spaces , 1990 .

[16]  Edi Karni,et al.  State-dependent Preferences , 1990 .

[17]  Edi Karni,et al.  A Definition of Subjective Probabilities with State-Dependent Preferences , 1993 .

[18]  David E. Bell,et al.  Disappointment in Decision Making Under Uncertainty , 1985, Oper. Res..

[19]  Robert Sugden,et al.  Disappointment and Dynamic Consistency in Choice under Uncertainty , 1986 .

[20]  Jean-Jacques Laffont,et al.  Advances in economic theory : Sixth World Congress , 1993 .

[21]  F. J. Anscombe,et al.  A Definition of Subjective Probability , 1963 .

[22]  J. Eatwell,et al.  The New Palgrave : utility and probability , 1990 .

[23]  D. Schmeidler,et al.  Bayes without Bernoulli: Simple Conditions for Probabilistically Sophisticated Choice , 1995 .

[24]  Costis Skiadas,et al.  Conditioning and Aggregation of Preferences , 1997 .

[25]  Jaap Van Brakel,et al.  Foundations of measurement , 1983 .

[26]  Faruk Gul A Theory of Disappointment Aversion , 1991 .

[27]  Peter P. Wakker,et al.  SUBJECTIVE PROBABILITIES FOR STATE DEPENDENT , 1987 .

[28]  Edi Karni,et al.  Utility Theory and Uncertainty , 1990 .

[29]  G. Debreu Topological Methods in Cardinal Utility Theory , 1959 .

[30]  L. J. Savage,et al.  The Foundations of Statistics , 1955 .

[31]  David M. Kreps A REPRESENTATION THEOREM FOR "PREFERENCE FOR FLEXIBILITY" , 1979 .

[32]  Robert Sugden,et al.  An Axiomatic Foundation for Regret Theory , 1993 .

[33]  Edi Karni,et al.  Choquet Expected Utility with a Finite State Space: Commutativity and Act-Independence , 1994 .

[34]  Peter C. Fishburn,et al.  A Mixture-Set Axiomatization of Conditional Subjective Expected Utility , 1973 .

[35]  Edi Karni,et al.  Utility theory with uncertainty , 1991 .

[36]  Aaas News,et al.  Book Reviews , 1893, Buffalo Medical and Surgical Journal.

[37]  Daniel McFadden,et al.  Essays on economic behavior under uncertainty , 1976 .

[38]  Edi Karni,et al.  Subjective Expected Utility Theory with State-Dependent Preferences , 1993 .

[39]  Jacques Drèze Essays on economic decisions under uncertainty: Markets and prices , 1987 .

[40]  Simon Grant,et al.  Subjective probability without monotonicity: or how Machina's mom may also be probabilistically sophisticated , 1995 .