Skip to main content
Log in

Towards a more precise decision framework

A separation of the negative utility of chance from diminishing marginal utility and the preference for safety

  • Published:
Theory and Decision Aims and scope Submit manuscript

Abstract

The terms ‘negative utility of gambling’ and ‘risk aversion’ conflate three things:

  1. (i)

    Disutility from the mere act of taking a chance: i.e. negative effects that would not exist if there were no risk or uncertainty, effects which include serious business considerations such as the availability of loans — exemplified in von Neumann and Morgenstern's famous 1947 Appendix;

  2. (ii)

    Diminishing marginal utility of money: — exemplified in Bernoulli and Cramer's expected utility procedure; and

  3. (iii)

    A preference for safety: — exemplified in the rank dependent utility models of Allais, Lopes, Quiggin and Yaari.

Factor (iii) has not been previously distinguished from (i). Factor (i) is regularly either confused with (ii) or ignored as elusive and unimportant.

The paper shows that (i) should not be ignored since it is crucial in many serious business decisions, and need not remain elusive. To separate (i) from (ii) and (iii), and consistently incorporate (i), (ii) and (iii) in decision models, the paper identifies progressive stages in people's knowledge of the future and decomposes people's overall valuation of an option into three steps: 1 utilities distinctive to each of its possible outcomes; 2 utility common to all its possible outcomes; 3 aggregation rules for forming the overall valuation out of 1 and 2. The separation procedure is illustrated and the ambiguity of current decision models with respect to (i), (ii) and (iii) delineated.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Allais, M.: 1952 reprinted in 1979a, ‘The 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 Hypotheses and the Allais Paradox, Reidel, Dordrecht, pp. 27–145.

    Google Scholar 

  • Allais, M.: 1979b, ‘The So-called Allais Paradox and Rational Decisions Under Uncertainty’, in M. Allais and O. Hagen (Eds.),Expected Utility Hypotheses and the Allais Paradox, Reidel, Dordrecht, pp. 437–681.

    Google Scholar 

  • Allais, M.: 1984, ‘The Foundations of the Theory of Utility and Risk. Some Central Points of the Discussions at the Oslo Conference’, in O. Hagen and F. Wenstøp (Eds.),Progress in Utility and Risk Theory, Reidel, Dordrecht, pp. 3–131.

    Google Scholar 

  • Allais, M.: 1986,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, paper presented to Third International Conference on the Foundations and Applications of Risk, Utility and Decision Theory, Aix-en-Provence, June.

  • Allais, M.: 1988, ‘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 Bertrand R. Munier (Ed.),Risk, Decision and Rationality, Reidel, Dordrecht, 231–289.

    Google Scholar 

  • Aristotle: 1961,The Metaphysics Books I–IX with an English Translation by Hugh Tredennick, Harvard University Press, Cambridge.

    Google Scholar 

  • Barnett, S.A. and Cowan, P.E.: 1976, ‘Activity, Exploration, Curiosity and Fear: An Ethological Study’,Interdisciplinary Science Reviews,1(1), 43–61.

    Google Scholar 

  • Bell, David E.: 1982, ‘Regret in Decision Making under Uncertainty’,Operations Research,30(5), 961–981.

    Google Scholar 

  • Bell, David: 1985, “Disappointment in Decision Making under Uncertainty’,Operations Research,33(1), 1–27.

    Google Scholar 

  • Bernard, Georges: 1974, ‘On Utility Functions. The Present State’,Theory and Decision,5, 205–242.

    Google Scholar 

  • Berne, Eric: 1967,Games People Play, Grove Press, New York.

    Google Scholar 

  • Bernoulli, D.: 1738, ‘Specimen Theoriae Novae de Mensura Sortis', an English translation by Dr Louise Sommer is “Exposition of a New Theory on the Measurement of Risk’,Econometrica (1954),22, 23–36.

    Google Scholar 

  • Brewer, K.R.W. and Fellner, William: 1965, ‘The Slanting of Subjective Probabilities — Agreement on Some Essentials’,Quarterly Journal of Economics,79, 657–663.

    Google Scholar 

  • Broome, J.: 1991, ‘Rationality and the Sure-Thing Principle’ in J. Meeks (Ed.),Thoughtful Economic Man: Essays on Rationality, Moral Rules and Benevolence, Cambridge University Press, Cambridge, pp. 74–102.

    Google Scholar 

  • Chew, Soo Hong and Epstein, Larry G.: 1990, ‘Nonexpected Utility Preferences in a Temporal Framework with an Application to Consumption-Savings Behaviour’,Journal of Economic Theory,50, 54–81.

    Google Scholar 

  • Darwin, Charles: 1874,The Descent of Man, Murray, London.

    Google Scholar 

  • Davidson, Donald and Suppes, Patrick: 1957,Decision Making: An Experimental Approach, Stanford University Press, California.

    Google Scholar 

  • Fishburn, Peter and Wakker, Peter: ‘A History of the Independence Axiom’,Management Science, forthcoming.

  • Friedman, Milton and Savage, L.J.: 1948, ‘The Utility Analysis of Choices Involving Risk’,Journal of Political Economy,LVI(4), 279–304.

    Google Scholar 

  • Griswold, Charles: 1991, ‘Rhetoric and Ethics: Adam Smith on Theorizing about the Moral Sentiments’,Philosophy and Rhetoric,24, 211–237.

    Google Scholar 

  • Griswold, Charles: 1992,Adam Smith on the Rhetoric of the Sciences: An Inaugural Lecture, Boston Colloquium for the Philosophy of Science, Boston University, Boston.

    Google Scholar 

  • Gul, F.: 1991, ‘A Theory of Disappointment Aversion’,Econometrica,59(3), 667–686.

    Google Scholar 

  • Hagen, O.: 1972, ‘A New Axiomatization of Utility under Risk’,Teorie A Metoda,IV(2), 55–80.

    Google Scholar 

  • Hagen, O.: 1985, ‘Rules of Behaviour and Expected Utility Theory. Compatibility versus Dependence’,Theory and Decision,18, 31–45.

    Google Scholar 

  • Harsanyi, J.: 1978, ‘Bayesian Decision Theory and Utilitarian Ethics’,American Economic Review (Papers and Proceedings),68(2), 223–228.

    Google Scholar 

  • Harsanyi, J.: 1983, ‘Use of Subjective Probabilities in Game Theory’, in B. Stigum and F. Wenstøp (Eds.),Foundations of Utility and Risk Theory with Applications, D. Reidel, Dordrecht, 297–310.

    Google Scholar 

  • Karni, Edi and Schlee, Edward E.: 1995, ‘Utility Theory with Probability Dependent Outcome Valuations: Extensions and Applications’,Journal of Risk and Uncertainty,10(2), 127–142.

    Google Scholar 

  • Keynes, John Maynard: 1921,A Treatise on Probability, Macmillan, London.

    Google Scholar 

  • Kreps, David M. and Porteus, Evan L.: 1978, ‘Temporal Resolution of Uncertainty and Dynamic Choice Theory’,Econometrica,46(1), 185–200.

    Google Scholar 

  • Leinfellner, Werner: 1966,Die Entstehung der Theorie (The Rise of Theoretical Thinking in Antiquity). Alber, Munchen.

    Google Scholar 

  • Levy, H. and Markowitz, H.M.: 1979, ‘Approximating Expected Utility by a Function of Mean and Variance’,American Economic Review,69(3), 308–317.

    Google Scholar 

  • Loomes, Graham and Sugden, Robert: 1982, ‘Regret Theory: An Alternative Theory of Rational Choice Under Uncertainty’,Economic Journal,92 (Dec.), 805–824.

    Google Scholar 

  • Lopes, Lola L.: 1984, ‘Risk and Distributional Inequality’,Journal of Experimental Psychology: Human Perception and Performance,10, 465–485.

    Google Scholar 

  • Lopes, Lola L.: 1990, ‘Re-Modelling Risk Aversion’, in George M. von Furstenberg (Ed.),Acting Under Uncertainty: Multidisciplinary Conceptions, Kluwer, Dordrecht.

    Google Scholar 

  • Lowenstein, George: 1987, ‘Anticipation and the Value of Delayed Consumption’,Economic Journal,97(3), 666–684.

    Google Scholar 

  • Luce, R. Duncan and Raiffa, Howard: 1967,Games and Decisions, John Wiley, New York.

    Google Scholar 

  • Machina, Mark J.: 1981, ‘“Rational” Decision Making versus “Rational” Decision Modelling?’,Journal of Mathematical Psychology,24, 163–175.

    Google Scholar 

  • Machina, Mark J.: 1982, ‘“Expected Utility” Analysis Without the Independence Axiom’,Econometrica,50(2), 277–323.

    Google Scholar 

  • Machina, Mark J.: 1984, ‘Temporal Risk and the Nature of Induced Preferences’,Journal of Economic Theory,33, 199–231.

    Google Scholar 

  • Markowitz, Harry M.: 1959,Portfolio Selection, Wiley, New York.

    Google Scholar 

  • Markowitz, Harry, M.: 1994,Robin Pope's Findings on Elaborated Outcomes, presentation to the Seventh International Conference on the Foundations and Applications of Utility, Risk and Decision Theory, Norwegian School of Business, Oslo, July 3.

  • Marschak, Jacob: 1950, ‘Rational Behavior, Uncertain Prospects, and Measurable Utility’,Econometrica,18(2), 111–141.

    Google Scholar 

  • Marschak, Jacob and Radner, Roy: 1972,Economic Theory of Teams, Yale University Press, New Haven.

    Google Scholar 

  • Marshall, Alfred: 1920,Principles of Economics, Macmillan and Co. Ltd., London.

    Google Scholar 

  • McClennen, Edward F.: 1983, ‘Sure-Thing Doubts’, in B. Stigum and F. Wenstøp (Eds.),Foundations of Utility and Risk Theory with Applications, D. Reidel, Dordrecht, pp. 117–136.

    Google Scholar 

  • Morgenstern, Oskar: 1974, ‘Some Reflections on Utility’, posthumously published in M. Allais and O. Hagen (Eds.),Expected Utility Hypotheses and the Allais Paradox; Contemporary Discussions of Decisions Under Uncertainty with Allais' Rejoinder, 1979, D. Reidel, Dordrecht, pp. 175–183.

    Google Scholar 

  • Munier, Bertrand: 1992, ‘Market Uncertainty and Belief Formation with a Finite Number of Events’, in John Geweke (Ed.),Decision Making under Risk and Uncertainty: New Models and Empirical Findings, Kluwer, Dordrecht, pp. 179–187.

    Google Scholar 

  • Plato, 1967,Theaetetus, in Francis MacDonald Cornford,Plato's Theory of Knowledge: The Theaetetus and the Sophist, translated with a running commentary, Routledge and Kegan Paul, London.

    Google Scholar 

  • Pope, Robin: 1982, ‘Risk Pooling, Firm Strategy and the Government’,Working Paper 82/83-2-5, Department of Finance, University of Texas, Austin.

    Google Scholar 

  • Pope, Robin: 1983, ‘The Pre-Outcome Period and the Utility of Gambling’, in B. Stigum and F. Wenstøp (Eds.),Foundations of Utility and Risk Theory with Applications, D. Reidel, Dordrecht, pp. 137–177.

    Google Scholar 

  • Pope, Robin: 1984, ‘The Utility of Gambling and of Outcomes: Inconsistent First Approximations’, in O. Hagen and F. Wenstøp (Eds.),Progress in Utility and Risk Theory, D. Reidel, Dordrecht, pp. 251–273.

    Google Scholar 

  • Pope, Robin: 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 

  • Pope, Robin: 1986, ‘Consistency and Expected Utility Theory’, in L. Daboni, A. Montesano and M. Lines (Eds.),Recent Developments in the Foundations of Utility and Risk Theory, D. Reidel, Dordrecht, pp. 215–229.

    Google Scholar 

  • Pope, Robin: 1988a, ‘The Bayesian Approach: Irreconcilable With Expected Utility Theory?’, in Bertrand R. Munier (Ed.),Risk, Decision and Rationality, D. Reidel, Dordrecht, pp. 221–230.

    Google Scholar 

  • Pope, Robin: 1988b, ‘Reality versus Intention in the Expected Utility Procedure’, paper presented to the1988 Australian Economics Congress, 28 August–2 September.

  • Pope, Robin: 1989, ‘Additional Perspectives on Modelling Health Insurance Decisions’, in C. Selby-Smith (Ed.),Economics and Health, Public Sector Management Institute, Monash University, Melbourne, pp. 189–205.

    Google Scholar 

  • Pope, Robin: 1990a, ‘Rational People do Not Always prefer first Order Stochastically Dominating Options’,Fifth International Conference on the Foundations and Applications of Utility, Risk and Decision Theory, Duke University, North Carolina, 10–3 June.

    Google Scholar 

  • Pope, R.: 1990b,The Riskless Nature of Utility in the Expected Utility Procedure, paper presented to 19th Conference of Economists, University of New South Wales, 24–26 September.

  • Pope, Robin: 1991a, ‘The Delusion of Certainty in Savage's Sure-Thing Principle’,Journal of Economic Psychology,12(2), 209–241.

    Google Scholar 

  • Pope, Robin: 1991b, ‘Lowered Welfare under the Expected Utility Procedure’, in A. Chikan (Ed.),Progress in Decision, Utility and Risk, Kluwer, Dordrecht, pp. 125–133.

    Google Scholar 

  • Pope, Robin: 1994a, ‘The Elusive Utility of Chance: A Formal Definition and Model’,Working Paper, Center for Technology, Policy and Industrial Development, Massachusetts Institute of Technology, January.

  • Pope, Robin: 1994b, ‘A Comparison and Contrast of the Ramsey and Friedman-Savage Versions of NM utility: the avoidance of schizophrenia and illusory possessions in the Ramsey version’,Working Paper, Center for Technology, Policy and Industrial Development, Massachusetts Institute of Technology, January.

  • Pope, R.: 1994c, ‘Multi versus Single Stage Decision Procedures: which is more Scientific?’,Working Paper, Center for Technology, Policy and Industrial Development, Massachusetts Institute of Technology, January.

  • Quiggin, John: 1982, ‘A Theory of Anticipated Utility’,Journal of Economic Behavior and Organisation,3, 323–43.

    Google Scholar 

  • Quiggin, John: 1993,Generalised Expected Utility Theory: The Rank Dependent Model, Kluwer, Boston.

    Google Scholar 

  • Ramsey, Frank Plumpton: 1926 reproduced in 1950, ‘Truth and Probability’, in R.B. Braithwaite (Ed.),The Foundations of Mathematics and Other Logical Essays, The Humanities Press, New York, pp. 156–184.

    Google Scholar 

  • Rothenberg, Jerome: 1992, ‘Consumption Style as Choice under Risk: State Choice, Dynamic Irrationality and Crimes of Passion’, in John Geweke (Ed.),Decision Making under Risk and Uncertainty: New Models and Empirical Findings, Kluwer, Dordrecht, pp. 105–114.

    Google Scholar 

  • Rothenberg, Jerome: 1994, ‘Embodied Risk, Dynamic Inconsistency and the Deterrence of Crimes and Passion’, in Bertrand Munier and Mark Machina (Eds.),Models and Experiments in Risk, and Rationality, Kluwer, Boston, pp. 91–115.

    Google Scholar 

  • Samuelson, Paul A.: 1952, ‘Probability, Utility, and the Independence Axiom’,Econometrica,20(4), 670–678.

    Google Scholar 

  • Savage, Leonard J.: 1954,The Foundations of Statistics, Wiley, New York.

    Google Scholar 

  • Schoemaker, Paul J.H.: 1982, ‘The Expected Utility Model: Its Variants, Purposes, Evidence and Limitations’,Journal of Economic Literature,20(2), 529–563.

    Google Scholar 

  • Segal, Uzi: 1984, ‘Nonlinear Decision Weights with the Independence Axiom’, University of California Los Angeles,Working Paper 353, November.

  • Shackle, G.L.S.: 1979,Imagination and the Nature of Choice, Edinburgh University Press, Great Britain.

    Google Scholar 

  • Smith, Adam, 1776,Wealth of Nations, re-published 1910, Dent, London.

    Google Scholar 

  • Smith, Adam, 1778,The Principles which Lead and Direct Philosophical Enquiries: Illustrated by the History of Astronomy, excerpts in Charles A. Griswold 1991 and 1992 listed above.

  • Spence, Michael and Zeckhauser, Richard: 1972, ‘The Effect of the Timing of Consumption Decisions and the Resolution of Lotteries on the Choice of Lotteries’,Econometrica,40(2), 401–403.

    Google Scholar 

  • Sylvan, R.: 1989, ‘Modern Myths Concerning Rationality: The Imperatives of Consistency and (Constrained) Maximality’, in S. Biderman and B. Scharfstein (Eds.).Rationality in Question, Brill, Leiden, pp. 29–56.

    Google Scholar 

  • Tobin, James: 1969, ‘Comment on Borch and Feldstein’,Review of Economic Studies,36(1), 13–14.

    Google Scholar 

  • Tversky Amos and Kahneman, Daniel: 1992, ‘Advances in Prospect Theory: Cumulative Representation of Uncertainty’,Journal of Risk and Uncertainty,5, 297–323.

    Google Scholar 

  • Vickrey, William: 1945, ‘Measuring Marginal Utility by Reactions to Risk’,Econometrica,13(4), 319–333.

    Google Scholar 

  • Von Neumann, John and Morgenstern, Oskar: 1944 and 1947,Theory of Games and Economic Behavior, Princeton University Press, Princeton, New Jersey.

    Google Scholar 

  • Wu, George: 1991,Anxiety and Decision Making Among Gambles with Delayed Resolution of Uncertainty, Ph.D. Thesis in Decision Sciences, Harvard University, Cambridge, Massachusetts.

    Google Scholar 

  • Yaari, Menahem E.: 1984, ‘Risk Aversion without Diminishing Marginal Utility’, ICERD,Report Series in Theoretical Economics, London School of Economics.

  • Yaari, Menahem, E.: 1987, ‘The Dual Theory of Choice Under Risk’,Econometrica,55, 95–115.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pope, R. Towards a more precise decision framework. Theor Decis 39, 241–265 (1995). https://doi.org/10.1007/BF01082054

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01082054

Key words

Navigation