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Rank-dependent, subjective expected-utility representations

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Abstract

Gambles are recursively generated from pure payoffs, events, and other gambles, and a preference order over them is assumed. Weighted average utility representations are studied that are strictly increasing in each payoff and for which the weights depend both on the events underlying the gamble and the preference ranking over the several component payoffs. Basically two results are derived: a characterization of monotonicity in terms of the weights, and an axiomatization of the representation. The latter rests on two important conditions: a decomposition of gambles into binary ones and a necessary commutativity condition on events in a particular class of binary gambles. A number of unsolved problems are cited.

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References

  • Aczél, J.Lectures on Functional Equations and Their Applications. New York: Academic Press, 1966.

    Google Scholar 

  • Aczél, J., Roberts, F.S. & Rosenbaum, Z. On Scientific Law without Dimensional Constants.Journal of Mathematical Analysis and Applications, (Vol. 119, 1986), pp 389–416.

    Google Scholar 

  • Aczél, J. & Saaty, T.L. Procedures for Synthesizing Ratio Judgements.Journal of Mathematical Psychology, (Vol. 27, 1983), pp 93–102.

    Google Scholar 

  • Allais, M. Foundations of a Positive Theory of Choice Involving Risk, and a Criticism of the Postulates and Axioms of the American School. In: M. Allais and O. Hagen eds.Expected Utility Hypothesis and the Allais' Paradox. Dordrecht: D. Reidel Publishing Co., 1952/1979.

    Google Scholar 

  • Allais, M. Le Comportement de l'Homme Rationnel devant le Risque: Critique des Postulats et Axiomes de l'Ecole Americaine.Econometrica (Vol. 21, 1953), pp 503–546.

    Google Scholar 

  • Allais, M. The So-Called Allais' Paradox and Rational Decisions under Uncertainty. In: M. Allais and O. Hagen, eds.Expected Utility Hypothesis and the Allais' Paradox. Dordrecht: D. Reidel Publishing Co., 1979.

    Google Scholar 

  • Allais, M. the Foundations of the Theory of Utility and Risk. In O. Hagen and F. Wenstop, eds.,Progress in Decision Theory. Dordrech: D. Reidel Publishing Co., 1984.

    Google Scholar 

  • Allais, M. (1988a). The General Theory of Random Choices in Relation to the Invariant Cardinal Utility Function and the Specific Probability Function. The (U, θ)-Model: A General Overview. In: B.R. Munier, ed.,Risk, Decision and Rationality. Dordrecht: D. Reidel Publishing Co., 1984.

    Google Scholar 

  • Allais, M. (1988b) Three Theorems on the Theory of Cardinal Utility and Random Choice. In:Essays in Honour of Werner Leinfellner. Theory and Decision, in press.

  • Anand, P. Are the Preference Axioms Really Rational?Theory and Decision, (Vol. 23, 1987), pp 189–214.

    Google Scholar 

  • Bostic, R., Herrnstein, R.J. & Luce R.D. the Effect on the Preference-Reversal Phenomenon of Using choice Indifferences. Submitted, 1988.

  • Chew, S.H. a Generalization of the Quasilinear Mean with Applications to Measurement of Income Inequality and Decision Theory Resolving the Allais Paradox.Econometrica (Vol. 51, 1983), pp 1065–1092.

    Google Scholar 

  • Chew, S.H. & Epstein, L.G. (1987a). A Unifying Approach to Axiomatic Non-Expected Utility Theories, Manuscript, 1987.

  • Chew, S.H. & Epstein, L.G. (1987b). Generalized and Implicit Gini Indices. Manuscript, 1987.

  • Chew, S.H. Epstein, L.G. & Segal, U. Invariant Mean Values and Measures of Income Inequality. Manuscript, 1987.

  • Ellsberg, D. Risk, Ambiguity, and the Savage Axioms.Quarterly Journal of Economics (Vol. 75, 1961), pp 643–669.

    Google Scholar 

  • Fishburn, P.C. Nontransitive Measurable Utility.Journal of Mathematical Psychology (Vol. 26, 1982), pp 31–67.

    Google Scholar 

  • Fishburn, P.C. Transitive Measurable Utility.Journal of Economic Theory (Vol. 31, 1983), pp 293–317.

    Google Scholar 

  • Gilboa, I. Expected Utility with Purely Subjective Non-Additive Probabilities.Journal of Mathematical Economics (Vol 16, 1987) pp 65–88.

    Google Scholar 

  • Grether, D.M. & Plott, C.R. Economic Theory of Choice and the Preference Reversal Phenomenon.The American Economic Review (Vol. 69, 1979) pp 623–638.

    Google Scholar 

  • Kahneman, D. & Tversky, A. Prospect Theory: An Analysis of Decision under Risk.Econometrica (Vol. 47, 1979), pp 263–291.

    Google Scholar 

  • Karmarkar, U.S. Subjectively Weighted Utility: A Descriptive Extension of the Expected Utility Model.Organizational Behavior and Human Performance (Vol. 21, 1978), pp 61–72.

    Google Scholar 

  • Lichtenstein, S. & Slovic, P. Reversals of Preference between Bids and Choices in Gambling Decisions.Journal of Experimental Psychology (Vol. 89, 1971), pp 46–55.

    Google Scholar 

  • Loomes, G. & Sugden, R. Regret Theory: An Alternative Theory of Rational Choice under Uncertainty.Economic Journal (Vol. 92, 1982), pp 805–824.

    Google Scholar 

  • Loomes, G. & Sugden, R. A Rationale for Preference Reversal.American Economic Review (Vol. 73, 1983), pp 428–432.

    Google Scholar 

  • Luce, R.D. Uniqueness and Homogeneity of Ordered Relational Structures.Journal of Mathematical Psychology (Vol. 30, 1986), pp 391–415.

    Google Scholar 

  • Luce, R.D. & Narens, L. Classification of Concatenation Measurement Structures According to Scale Type.Journal of Mathematical Psychology (Vol. 29, 1985), pp 1–72.

    Google Scholar 

  • Luce, R.D. & Narens, L. Measurement, Theory of. In: J. Eatwell, M. Milgate, and P. Newman, edsThe New Palgrave: A Dictionary of Economic Theory and Doctrine. New York: The Macmillan Press, 1987.

    Google Scholar 

  • Machina, M.J. “Expected Utility” Analysis without the Independence Axiom.Econometrica (Vol. 50, 1982), pp 277–323.

    Google Scholar 

  • Machina, M.J. Choice under Uncertainty: Problems Solved and Unsolved.Economic Perspectives (Vol. 1, 1987), pp 121–154.

    Google Scholar 

  • Munera, H.A. The Generalized Means Model (GMM) for Non-Deterministic Decision Making: Its Normative and Descriptive Power, Including Sketch of the Representation Theorem.Theory and Decision (Vol. 18, 1985), pp 173–202.

    Google Scholar 

  • Munera, H.A. The Generalized Means Model (GMM) for Non-Deterministic Decision Making: A Unified Treatment for the Two Contending Theories. In: L. Daboni et al, eds.Recent Developments in the Foundation of Utility and Risk Theory. Amsterdam: D. Reidel Publishing Co., 1986.

    Google Scholar 

  • Munera, H.A. & de Neufville, R. A Decision Analysis Model when the Substitution Principle is Not Acceptable. In: B.P. Stigum and F. Wenstop, eds.,Foundations of Utility and Risk Theory with Applications. Amsterdam: D. Reidel Publishiing Co., 1983.

    Google Scholar 

  • Pearson, T. Reversal of Preferences: Artifacts or Instransitivities. Manuscript, 1986.

  • Quiggin, J. A Theory of Anticipated Utility.Journal of Economic Behavior and Organization (Vol. 3, 1982), pp 323–343.

    Google Scholar 

  • Röell, A. Risk Aversion in Quiggin and Yarri's Rank-Order Model of Choice under Uncertainty.The Economic Journal (Vol. 97, 1987), pp 143–159.

    Google Scholar 

  • Segal, U (1987a). The Ellsberg Paradox and Risk Aversion: An Anticipated Utility Approach.International Economic Review (Vol. 28, 1987), pp 175–202.

    Google Scholar 

  • Segal, U. (1987b). Some Remarks on Quiggin's Anticipated Utility.Journal of Economic Behavior and Organization (Vol. 8, 1987), pp 145–154.

    Google Scholar 

  • Segal, U. (1987c). Axiomatic Representation of Expected Utility with Rank Dependent Probabilities. Manuscript, 1987.

  • Sen, A.On Economic Inequality, London: Oxford University Press, 1973.

    Google Scholar 

  • Tversky, A. & Kahnemann, D. Rational Choice and the Framing of Decisions.Journal of Business (Vol. 59, 1986), pp S251-S278.

    Google Scholar 

  • Tversky, A., Sattath, S. & Slovic, P. Contingent Weighting in Judgment and Choice.Psychological Review, in press, 1988.

  • Weber, M. & Camerer, C. Recent Developments in Modelling Preferences under Risk.OR Spektrum (Vol. 9, 1987), pp 129–151.

    Google Scholar 

  • Yaari, M.E. The Dual Theory of Choice under Risk.Econometrica (Vol. 55, 1987), pp 95–115.

    Google Scholar 

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Authors
  1. R. Duncan Luce
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Harvard University

APPENDIS: Kenneth L. Manders, University of Pittsburgh

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Luce, R.D. Rank-dependent, subjective expected-utility representations. J Risk Uncertainty 1, 305–332 (1988). https://doi.org/10.1007/BF00056140

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