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Series:   Elements in Decision Theory and Philosophy

The History and Methodology of Expected Utility

Published online by Cambridge University Press:  29 July 2023

Ivan Moscati
Ivan Moscati
Affiliation:
Università degli Studi dell'Insubria, Italy and Baffi Carefin, Università Bocconi, Milan

Summary

This Element offers an accessible but technically detailed review of expected utility theory (EU), which is a model of individual decision-making under uncertainty that is central for both economics and philosophy. The Element's approach falls between the history of ideas and economic methodology. At the historical level, it reviews EU by following its conceptual evolution from its original formulation in the eighteenth century through its transformations and extensions in the mid-twentieth century to its more recent supersession by post-EU theories such as prospect theory. In reconstructing the history of EU, it focuses on the methodological issues that have accompanied its evolution, such as whether the utility function and the other components of EU correspond to actual mental entities. On many of these issues, no consensus has yet been reached, and in this Element the author offers his view on them.
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Keywords

expected utility theoryhistory of expected utilitymethodology of expected utilityrisk and uncertaintyprospect theory
Type
Element
Information
Series: Elements in Decision Theory and Philosophy
Online ISBN: 9781009198295
Publisher: Cambridge University Press
Print publication: 31 August 2023

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References

Abdellaoui, M., Klibanoff, P., and Placido, L.. 2015. “Ambiguity and Compound Risk Attitudes: An Experiment.” Management Science 61: 1306–1322.Google Scholar
Abdellaoui, M., Li, C., Wakker, P. P., and Wu, G.. 2020. “A Defense of Prospect Theory in Bernheim & Sprenger’s Experiment.” Unpublished working paper. https://personal.eur.nl/wakker/pdf/wak.bernh.r.sp.pdf.Google Scholar
Allais, M. 1953. “Le comportement de l’homme rationnel devant le risque.” Econometrica 21: 503–546.CrossRefGoogle Scholar
Andersen, S., Harrison, G., Lau, M., and Rutström, E.. 2008. “Lost in State Space: Are Preferences Stable?” International Economic Review 49: 1091–1112.Google Scholar
Anscombe, F. and Aumann, R.. 1963. “A Definition of Subjective Probability.” Annals of Mathematical Statistics 34: 199–205.CrossRefGoogle Scholar
Aumann, R. 1962. “Utility Theory without the Completeness Axiom.” Econometrica 30: 445–462.CrossRefGoogle Scholar
Aumann, R. [1971] 2000. “Letter from Robert Aumann to Leonard Savage and Letter from Leonard Savage to Robert Aumann.” In Aumann, R., Collected Papers, Vol. 2, 305–310.Google Scholar
Baccelli, J. 2017. “Do Bets Reveal Beliefs?” Synthese 194: 3393–3419.Google Scholar
Baccelli, J. 2021. “The Problem of State-Dependent Utility: A Reappraisal.” British Journal for the Philosophy of Science 72: 617–634.Google Scholar
Baccelli, J. and Mongin, P.. 2022. “Can Redescriptions of Outcomes Salvage the Axioms of Decision Theory?” Philosophical Studies 179: 1621–1648.CrossRefGoogle Scholar
Barseghyan, L., Prince, J., and Teitelbaum, J. C.. 2011. “Are Risk Preferences Stable across Contexts? Evidence from Insurance Data.” American Economic Review 101: 591–631.CrossRefGoogle Scholar
Beauchamp, J. P., Benjamin, D. J., Laibson, D. I., and Chabris, C. F.. 2020. “Measuring and Controlling for the Compromise Effect When Estimating Risk Preference Parameters.” Experimental Economics 23: 1069–1099.Google Scholar
Berg, N. and Gigerenzer, G.. 2010. “As-If Behavioral Economics: Neoclassical Economics in Disguise?” History of Economic Ideas 18: 133–165.Google Scholar
Bernheim, B. D., Royer, R., and Sprenger, C.. 2022. “Robustness of Rank Independence in Risky Choice.” American Economic Review, Papers and Proceedings 112: 415–420.CrossRefGoogle Scholar
Bernheim, B. D. and Sprenger, C.. 2020. “On the Empirical Validity of Cumulative Prospect Theory.” Econometrica 88: 1363–1409.Google Scholar
Bernoulli, D. [1738] 1954. “Exposition of a New Theory on the Measurement of Risk.” Econometrica 22: 23–36.CrossRefGoogle Scholar
Bernoulli, D. [1738] 1982. Specimen theoriae novae de mensura sortis. In Speiser, D., ed., Die Werke von Daniel Bernoulli, Vol. 2, 223–234. Basel: Birkhäuser.Google Scholar
Bernoulli, J. [1713] 2006. The Art of Conjecturing. Baltimore, MD: Johns Hopkins University Press.Google Scholar
Bernoulli, N. [1709] 1975. De usu artis conjectandi in iure. In van der Waerden, B. L., ed., Die Werke von Jakob Bernoulli, Vol. 3, 287–326. Basel: Birkhäuser.Google Scholar
Binmore, K. 2009. Rational Decisions. Princeton, NJ: Princeton University Press.Google Scholar
Bordalo, P., Gennaioli, N., and Shleifer, A.. 2022. “Salience.” Annual Review of Economics 14, 521–544.Google Scholar
Bradley, R. 2017. Decision Theory with a Human Face. Cambridge: Cambridge University Press.Google Scholar
Brandstätter, E., Gigerenzer, G., and Hertwig, R.. 2006. “The Priority Heuristic.” Psychological Review 113: 409–432.Google Scholar
Broome, J. 1990. “Bolker–Jeffrey Expected Utility Theory and Axiomatic Utilitarianism.” Review of Economic Studies 57: 477–502.Google Scholar
Buchak, L. 2013. Risk and Rationality. Oxford: Oxford University Press.Google Scholar
Cairnes, J. E. 1872. “New Theories in Political Economy.” Fortnightly Review 9: 71–76.Google Scholar
Camerer, C. F. and Loewenstein, G.. 2004. “Behavioral Economics.” In C. F. Camerer, Loewenstein, G., and Rabin, M., eds., Advances in Behavioral Economics, 3–51. Princeton, NJ: Princeton University Press.CrossRefGoogle Scholar
Chateauneuf, A. 1985. “On the Existence of a Probability Measure Compatible with a Total Preorder on a Boolean Algebra.” Journal of Mathematical Economics 14: 43–52.CrossRefGoogle Scholar
Davidson, D., McKinsey, J. C. C., and Suppes, P.. 1955. “Outlines of a Formal Theory of Value, I.” Philosophy of Science 22: 140–160.Google Scholar
de Finetti, B. [1937] 1980. “Foresight: Its Logical Flaws, Its Subjective Sources.” In Kyburg, H. E. and Smokler, H. E., eds., Studies in Subjective Probability, 93–158. New York: Wiley.Google Scholar
Einav, L., Finkelstein, A., Pascu, I., and Cullen, M. R.. 2012. “How General Are Risk Preferences?” American Economic Review 102: 2606–2638.Google Scholar
Ellsberg, D. 1961. “Risk, Ambiguity, and the Savage Axioms.” Quarterly Journal of Economics 75: 643–669.CrossRefGoogle Scholar
Fishburn, P. C. 1978. “On Handa’s ‘New Theory of Cardinal Utility’ and the Maximization of Expected Return.” Journal of Political Economy 86: 321–324.Google Scholar
Friedman, M. 1953. “The Methodology of Positive Economics.” In M. Friedman, Essays in Positive Economics, 3–43. Chicago, IL: University of Chicago Press.Google Scholar
Friedman, M. and Savage, L. J.. 1948. “The Utility Analysis of Choices Involving Risk.” Journal of Political Economy 56: 279–304.Google Scholar
Friedman, M. and Savage, L. J.. 1952. “The Expected-Utility Hypothesis and the Measurability of Utility.” Journal of Political Economy 60: 463–474.Google Scholar
Gilboa, I. 2009. Theory of Decision under Uncertainty. Cambridge: Cambridge University Press.Google Scholar
Gilboa, I. and Marinacci, M.. 2013. “Ambiguity and the Bayesian Paradigm.” In Acemoglu, D., Arellano, M., and Dekel, E., eds., Advances in Economics and Econometrics, Vol. 1, 179–242. New York: Cambridge University Press.Google Scholar
Gilboa, I., Postlewaite, A., and Schmeidler, D.. 2008. “Probability and Uncertainty in Economic Modeling.” Journal of Economic Perspectives 22: 173–188.Google Scholar
Gilboa, I., Postlewaite, A., and Schmeidler, D.. 2012. “Rationality of Belief or: Why Savage’s Axioms Are Neither Necessary Nor Sufficient for Rationality.” Synthese 187: 11–31.Google Scholar
Gilboa, I., Postlewaite, A., and Schmeidler, D.. 2021. “The Complexity of the Consumer Problem.” Research in Economics 75: 96–103.Google Scholar
Gustafsson, J. E. 2022. Money-Pump Arguments. Cambridge: Cambridge University Press.Google Scholar
Hacking, I. 1975. The Emergence of Probability. Cambridge: Cambridge University Press.Google Scholar
Handa, J. 1977. “Risk, Probabilities, and a New Theory of Cardinal Utility.” Journal of Political Economy 85: 97–122.Google Scholar
Harrison, G. W., Martínez-Correa, J., and Swarthout, J. T.. 2015. “Reduction of Compound Lotteries with Objective Probabilities.” Journal of Economic Behavior & Organization 119: 32–55.Google Scholar
Herne, K. 1999. “The Effects of Decoy Gambles on Individual Choice.” Experimental Economics 2: 31–40.Google Scholar
Hicks, J. R. 1931. “The Theory of Uncertainty and Profit.” Economica 32: 170–189.Google Scholar
Hicks, J. R. 1934. “The Application of Mathematical Methods to the Theory of Risk.” Econometrica 2: 194–195.Google Scholar
Hicks, J. R. 1939. Value and Capital. Oxford: Clarendon Press.Google Scholar
Huber, J., Payne, J. W., and Puto, C.. 1982. “Adding Asymmetrically Dominated Alternatives.” Journal of Consumer Research 9: 90–98.Google Scholar
Huygens, C. [1657] 1920. De ratiociniis in ludo aleae. In Œuvres complètes de Christiaan Huygens, vol. 14, 50–175. La Haye: Nijhoff.Google Scholar
Jeffrey, R. C. [1965] 1990. The Logic of Decision. Chicago, IL: University of Chicago Press.Google Scholar
Jevons, W. S. 1871. The Theory of Political Economy. London: Macmillan.Google Scholar
Kahneman, D. and Tversky, A.. 1979. “Prospect Theory: An Analysis of Decision under Risk.” Econometrica 47: 263–292.Google Scholar
Karni, E. 1996. “Probabilities and Beliefs.” Journal of Risk and Uncertainty 13: 249–262.Google Scholar
Karni, E. 2008. “State-Dependent Utility.” In Anand, P., Pattanaik, P., and Puppe, C., eds., The Handbook of Rational and Social Choice, 223–238. Oxford: Oxford University Press.Google Scholar
Keynes, J. M. 1921. A Treatise on Probability. London: Macmillan.Google Scholar
Knight, F. H. 1921. Risk, Uncertainty, and Profit. Boston, MA: Houghton Mifflin.Google Scholar
Kolmogorov, A. 1933. Grundbegriffe der Wahrscheinlichkeitsrechnung. Berlin: Springer.Google Scholar
Koopman, B. O. 1940. “The Axioms and Algebra of Intuitive Probability.” Annals of Mathematics 41: 269–262.Google Scholar
Kraft, H. C., Pratt, W. J., and Seidenberg, A.. 1959. “Intuitive Probability on Finite Sets.” Annals of Mathematical Statistics 30: 408–419.Google Scholar
Kreps, D. 1988. Notes on the Theory of Choice. Boulder, CO: Westview Press.Google Scholar
Laplace, P.-S. 1812. Théorie analytique des probabilités. Paris: Courcier.Google Scholar
Leonard, R. 1995. “From Parlor Games to Social Science.” Journal of Economic Literature 33: 730–761.Google Scholar
Lewis, D. 1974. “Radical Interpretation.” Synthese 23: 331–344.Google Scholar
Lewis, D. [1980] 1987. “A Subjectivist’s Guide to Objective Chance.” In D. Lewis, Philosophical Papers, Vol. 2, 83–113. New York: Oxford University Press.Google Scholar
Lichtenstein, S. and Slovic, P.. 1971. “Reversals of Preference between Bids and Choices in Gambling Decisions.” Journal of Experimental Psychology 89: 46–55.Google Scholar
Lichtenstein, S. and Slovic, P., eds. 2006. The Construction of Preference. New York: Cambridge University Press.Google Scholar
Lipman, B. L. and Pesendorfer, W.. 2013. “Temptation.” In Acemoglu, D., Arellano, M., and Dekel, E., eds., Advances in Economics and Econometrics, 243–288. New York: Cambridge University Press.Google Scholar
Luce, R. D. and Raiffa, H.. 1957. Games and Decisions. New York: Wiley.Google Scholar
Marschak, J. 1950. “Rational Behavior, Uncertain Prospects, and Measurable Utility.” Econometrica 18: 111–141.Google Scholar
Marshall, A. 1890. Principles of Economics. London: Macmillan.Google Scholar
Mas-Colell, A., Whinston, M. D., and Green, J. R.. 1995. Microeconomic Theory. New York: Oxford University Press.Google Scholar
Mata, R. and Nagel, F.. 2023. “On an Unknown Early Version of Daniel Bernoulli’s Specimen theoriae novae de mensura sortis.” Unpublished working paper. https://doi.org/10.31234/osf.io/49f6s.Google Scholar
Menger, C. [1871] 1981. Principles of Economics. New York: New York University Press.Google Scholar
Montesano, A. 1985. “The Ordinal Utility under Uncertainty and the Measure of Risk Aversion in Terms of Preferences.” Theory and Decision 18: 73–85.CrossRefGoogle Scholar
Moscati, I. 2007. “History of Consumer Demand Theory 1871–1971.” European Journal of the History of Economic Thought 14: 119–156.Google Scholar
Moscati, I. 2013. “How Cardinal Utility Entered Economic Analysis: 1909–1944.” European Journal of the History of Economic Thought 20: 906–939.CrossRefGoogle Scholar
Moscati, I. 2016. “How Economists Came to Accept Expected Utility Theory: The Case of Samuelson and Savage.” Journal of Economic Perspectives 30: 219–236.Google Scholar
Moscati, I. 2018. Measuring Utility: From the Marginal Revolution to Behavioral Economics. New York: Oxford University Press.Google Scholar
Moscati, I. In press “Behavioural and Heuristic Models Are As-If Models Too – And That’s Ok.” Economics and Philosophy. http://doi:10.1017/S0266267123000093.Google Scholar
Mosteller, F. and Nogee, P.. 1951. “An Experimental Measurement of Utility.” Journal of Political Economy 59: 371–404.Google Scholar
Nuerk, H.-C., Moeller, K., and Willmes, K.. 2015. “Multi-Digit Number Processing.” In Kadosh, R. C. and Dowker, A., eds., The Oxford Handbook of Numerical Cognition, 106–139. Oxford: Oxford University Press.Google Scholar
O’Donoghue, T. and Somerville, J.. 2018. “Modeling Risk Aversion in Economics.” Journal of Economic Perspectives 32: 91–114.Google Scholar
Okasha, S. 2016. “On the Interpretation of Decision Theory.” Economics and Philosophy 32: 409–433.Google Scholar
Pareto, V. 1896. Cours d’économie politique, Vol. 1. Lausanne: Rouge.Google Scholar
Pareto, V. [1906/9] 2014. Manual of Political Economy, ed. by Montesano, A., Zanni, A., Bruni, L., Chipman, J. S., and McLure, M.. New York: Oxford University Press.Google Scholar
Peterson, M. 2004. “From Outcomes to Acts: A Non-Standard Axiomatization of the Expected Utility Principle.” Journal of Philosophical Logic 33: 361–378.Google Scholar
Peterson, M. 2017. An Introduction to Decision Theory. New York: Cambridge University Press.Google Scholar
Prelec, D. 1998. “The Probability Weighting Function.” Econometrica 66: 497–527.Google Scholar
Quiggin, J. 1982. “A Theory of Anticipated Utility.” Journal of Economic Behavior and Organization 3: 323–343.Google Scholar
Rabin, M. 1998. “Psychology and Economics.” Journal of Economic Literature 36: 11–46.Google Scholar
Ramsey, F. P. [1926] 1931. “Truth and Probability.” In Braithwaite, R. B., ed., Foundations of Mathematics and Other Logical Essays, 156–198. London: Kegan Paul.Google Scholar
Rubinstein, A. 1988. “Similarity and Decision-Making under Risk.” Journal of Economic Theory 46: 145–153.Google Scholar
Samuelson, P. A. 1947. Foundations of Economic Analysis. Cambridge, MA: Harvard University Press.Google Scholar
Samuelson, P. A. 1950. “Probability and the Attempts to Measure Utility.” Economic Review 1: 167–173.Google Scholar
Samuelson, P. A. 1952. “Probability, Utility, and the Independence Axiom.” Econometrica 20: 670–678.Google Scholar
Savage, L. J. [1954] 1972. The Foundations of Statistics. New York: Dover.Google Scholar
Schmoller, G. 1883. “Zur Methodologie der Staats und Sozialwissenschaften.” Jahrbuch für Gesetzgebung, Verwaltung und Volkswirtschaft im deutschen Reich 8: 974–994.Google Scholar
Schoemaker, P. J. H. 1982. “The Expected Utility Model: Its Variants, Purposes, Evidence and Limitations.” Journal of Economic Literature 20: 529–563.Google Scholar
Segal, U. 1992. “The Independence Axiom versus the Reduction Axiom.” In Edwards, W., ed., Utility Theories: Measurements and Applications, 165–183. Boston, MA: Kluwer.Google Scholar
Shafer, G. 1981. “Constructive Probability.” Synthese 48: 1–60.Google Scholar
Simonson, I. 1989. “Choice Based on Reasons: The Case of Attraction and Compromise Effects.” Journal of Consumer Research 16: 158–174.Google Scholar
Spiess, O. 1975. “Zur Vorgeschichte des Petersburger Problems.” In van der Waerden, B. L., ed., Die Werke von Jakob Bernoulli, Vol. 3, 557–567. Basel: Birkhäuser.Google Scholar
Starmer, C. 2000. “Developments in Non-expected Utility Theory.” Journal of Economic Literature 38: 332–382.Google Scholar
Steele, K. and Orri Stefánsson, H.. 2020. “Decision Theory.” In Zalta, E. N., ed., Stanford Encyclopedia of Philosophy (Winter 2020 ed.). https://plato.stanford.edu/archives/win2020/entries/decision-theory/.Google Scholar
Thaler, R. 1980. “Toward a Positive Theory of Consumer Choice.” Journal of Economic Behavior & Organization 1: 39–60.Google Scholar
Thaler, R. 2016. “Behavioral Economics.” American Economic Review 106: 1577–1600.Google Scholar
Tversky, A. 1969. “Intransitivity of Preferences.” Psychological Review 76: 31–48.Google Scholar
Tversky, A. and Kahneman, D.. 1992. “Advances in Prospect Theory: Cumulative Representation of Uncertainty.” Journal of Risk and Uncertainty 5: 297–323.Google Scholar
von Neumann, J. and Morgenstern, O.. [1944] 1953. Theory of Games and Economic Behavior. Princeton, NJ: Princeton University Press.Google Scholar
Wakker, P. P. 2010. Prospect Theory. Cambridge: Cambridge University Press.Google Scholar
Wakker, P. P. and Tversky, A.. 1993. “An Axiomatization of Cumulative Prospect Theory.” Journal of Risk and Uncertainty 7: 147–175.Google Scholar
Walras, L. [1874] 1954. Elements of Pure Economics. London: Allen and Unwin.Google Scholar
Zeisberger, S., Vrecko, D., and Langer, T.. 2012. “Measuring the Time Stability of Prospect Theory Preferences.” Theory and Decision 72: 359–386.Google Scholar
Zynda, L. 2000. “Representation Theorems and Realism about Degrees of Belief.” Philosophy of Science 67: 45–69.Google Scholar

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The History and Methodology of Expected Utility
  • Ivan Moscati, Università degli Studi dell'Insubria, Italy and Baffi Carefin, Università Bocconi, Milan
  • Online ISBN: 9781009198295
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The History and Methodology of Expected Utility
  • Ivan Moscati, Università degli Studi dell'Insubria, Italy and Baffi Carefin, Università Bocconi, Milan
  • Online ISBN: 9781009198295
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The History and Methodology of Expected Utility
  • Ivan Moscati, Università degli Studi dell'Insubria, Italy and Baffi Carefin, Università Bocconi, Milan
  • Online ISBN: 9781009198295
Available formats
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