Abstract
This article offers an exegesis of the passages in von Neumann and Morgenstern (1944, 1947, 1953) that discuss their conception of utility. It is occasioned by two factors. First, as we approach the semicentennial of the publication of Theory of Games and Economic Behavior, its immense impact on economic thought in the intervening years encourages serious reflection on its authors' ideas. Second, misleading statements about the theory continue to appear. The article will have accomplished its purpose if it helps others appreciate the genius and spirit of the theory of utility fashioned by John von Neumann and Oskar Morgenstern.
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References
Allais, Maurice. (1979). “The Foundations of a Positive Theory of Choice involving Risk and a Criticism of the Postulates and Axioms of the American School (1952).” In Maurice Allais and Ole Hagen (eds.), Expected Utility Hypotheses and the Allais Paradox. Dordrecht: Reidel, pp. 27–145. Translation of “Fondements d'une théorie positive des choix comportant un risque et critique des postulats et axiomes de l'école américaine,” Colloques Internationaux du Centre National de la Recherche Scientifique. XL. Econométrie, Paris (1953), 257–332.
Allais, Maurice. (1979). “The So-called Allais Paradox and Rational Decisions under Uncertainty.” In Maurice Allais and Ole Hagen (eds.). Expected Utility Hypotheses and the Allais Paradox. Dordrecht: Reidel, pp. 437–681.
Allais, Maurice. (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. Dordrecht: Reidel, pp. 231–289.
Allais Maurice and Ole Hagen (eds.). (1979). Expected Utility Hypotheses and the Allais Paradox. Dordrecht: Reidel.
Alt, Franz. (1936). “Uber die Messbarkeit des Nutzens,” Zeitschrift für Nationaloekonomie 7, 161–169. English translation by Siegfried Schach in John S. Chipman et al. (eds.). (1971). Preferences, Utility, and Demand. New York: Harcourt Brace Jovanovich. pp. 424–431.
Arrow, Kenneth J. (1951). “Alternative Approaches to the Theory of Choice in Risk-Taking Situations,” Econometrica 19, 404–437.
Arrow, Kenneth J. (1958). “Bernoulli Utility Indicators for Distributions over Arbitrary Spaces,” Technical Report 57, Department of Economics, Stanford University, Stanford.
Aumann, Robert J. (1962). “Utility Theory without the Completeness Axiom,” Econometrica 30, 445–462; 32 (1964), 210–212.
Baumol, William J. (1958). “The Cardinal Utility which is Ordinal,” Economic Journal 68, 665–672.
Bentham, Jeremy. (1823). An Introduction to the Principles of Morals and Legislation. Oxford: Clarendon Press. (Original edition dated 1789.)
Bernard, Georges. (1986) “The Present State of Utility Theory.” In L. Daboni, A. Montesano, and M. Lines (eds.). Recent Developments in the Foundations of Utility and Risk Theory. Dordrecht: Reidel. pp. 121–138.
Bernoulli, Daniel. (1738). “Specimen Theoriae Novae de Mensura Sortis,” Commentarii Academiae Scientiarum Imperialis Petropolitanae 5, 175–192. Translated by Louise Sommer. (1954). “Exposition of a New Theory on the Measurement of Risk.” Econometrica 22, 23–36. Translation reprinted in Alfred N. Page. (1968). Utility Theory: A Book of Readings. New York: Wiley, pp. 199–214.
Blackwell, David and M. A. Girshick. (1954). Theory of Games and Statistical Decisions. New York: Wiley.
Cantor, G. (1895). “Beiträge zur Begründung der Transfiniten Mengenlehre,” Mathematische Annalen 46, 481–512; 49 (1897), 207–246. Translation: Contributions to the Founding of the Theory of Transfinite Numbers. New York: Dover, n.d.
Chipman, John S. (1960). “The Foundations of Utility,” Econometrica 28, 193–224.
Cramer, Gabriel. (1728). Letter from Cramer to Nicholas Bernoulli. Translated by Louise Sommer in Bernoulli, Daniel. (1954). “Exposition of a New Theory on the Measurement of Risk,” Econometrica 22, 23–36.
Cramer, Harald. (1956). “A Theorem on Ordered Sets of Probability Distributions,” Theory of Probability and Its Applications 1, 16–21.
Daboni, L., A. Montesano, and M. Lines (eds.). (1986). Recent Developments in the Foundations of Utility and Risk Theory. Dordrecht: Reidel.
Debreu, Gerard. (1960). “Topological Methods in Cardinal Utility Theory,” In Kenneth J. Arrow, Samuel Karlin, and Patrick Suppes (eds.), Mathematical Methods in the Social Sciences, 1959. Stanford: Stanford University Press, pp. 16–26.
Edgeworth, F. Y. (1881). Mathematical Psychics. London: Kegan Paul.
Ellsberg, Daniel. (1954). “Classic and Current Notions of ‘Measurable Utility’,” Economic Journal 64, 528–556. Reprinted in Alfred N. Page. (1968). Utility Theory: A Book of Readings. New York: Wiley, pp. 269–296.
Fishburn, Peter C. (1964). Decision and Value Theory. New York: Wiley.
Fishburn, Peter C. (1970). Utility Theory for Decision Making. New York: Wiley.
Fishburn, Peter C. (1979). “On the Nature of Expected Utility.” In Maurice Allais and Ole Hagen (eds.) Expected Utility Hypotheses and the Allais Paradox. Dordrecht: Reidel, pp. 243–257.
Fishburn, Peter C. (1982). The Foundations of Expected Utility. Dordrecht: Reidel.
Fishburn, Peter C. (1988a). Nonlinear Preference and Utility Theory. Baltimore: Johns Hopkins University Press.
Fishburn, Peter C. (1988b). “Expected Utility: An Anniversary and a New Era,” Journal of Risk and Uncertainty 1, 267–283.
Fisher, Irving. (1892). “Mathematical Investigations in the Theory of Values and Prices,” Transactions of Connecticut Academy of Arts and Sciences 9, 1–124. Reprinted. New York: Augustus M. Kelley, 1965.
Fisher, Irving. (1918). “Is ‘Utility’ the Most Suitable Term for the Concept it is Used to Denote?,” American Economic Review 8, 335–337. Reprinted in Alfred N. Page. (1968). Utility Theory: A Book of Readings. New York: Wiley, pp. 49–51.
Friedman Milton and L. J. Savage. (1948). “The Utility Analysis of Choices Involving Risk,” Journal of Political Economy 56. 279–304. Reprinted in Alfred N. Page. (1968). Utility Theory: A Book of Readings. New York: Wiley, pp. 234–268.
Friedman Milton and L. J. Savage. (1952). “The Expected-Utility Hypothesis and the Measurability of Utility,” Journal of Political Economy 60, 463–474.
Frisch, Ragnar. (1926). “Sur un problème d'économie pure,” Norsk Matematisk Forenings Skrifter 16, 1–40. English translation by J. S. Chipman in John S. Chipman et al. (eds.) (1971). Preferences, Utility, and Demand. New York: Harcourt Brace Jovanovich, pp. 386–423.
Hagen, Ole. (1979). “Towards a Positive Theory of Preferences under Risk.” In Maurice Allais and Ole Hagen (eds.), Expected Utility Hypotheses and the Allais Paradox. Dordrecht: Reidel, pp. 271–302.
Hausner, Melvin. (1954). “Multidimensional Utilities.” In Robert M. Thrall, Clyde H. Coombs, and Robert L. Davis (eds.), Decision Processes. New York: Wiley, pp. 167–180.
Herstein, I. N. and John, Milnor. (1953). “An Axiomatic Approach to Measurable Utility,” Econometrica 21, 291–297.
Hicks, J. R. and R. G. D. Allen. (1934). “A Reconsideration of the Theory of Value: I; II,” Econometrica 1, 52–75; 196–219.
Houthakker, H. S. (1961). “The Present State of Consumption Theory,” Econometrica 29, 704–740.
Jensen, Niels Erik. (1967a). “An Introduction to Bernoullian Utility Theory. I. Utility Functions,” Swedish Journal of Economics 69, 163–183.
Jensen, Niels Erik. (1967b). “An Introduction to Bernoullian Utility Theory. II. Interpretation, Evaluation and Application; a Critical Survey,” Swedish Journal of Economics 69, 229–247.
Jevons, W. Stanley. (1871). The Theory of Political Economy. London: Macmillan.
Johnson, W. E. (1913). “The Pure Theory of Utility Curves,” Economic Journal 23, 483–513.
Kahneman Daniel and Amos Tversky. (1979). “Prospect Theory: An Analysis of Decision under Risk,” Econometrica 47, 263–291.
Kauder Emil. (1965). A History of Marginal Utility Theory. Princeton: Princeton University Press.
Klein, Felix. (1872). Verleichende Betrachtungen über Neuere Geometrische Forschungen. Erlangen.
Krantz, David H. et al. (1971). Foundations of Measurement. Volume I. New York: Academic Press.
Lange, O. (1934). “The Determinateness of the Utility Function,” Review of Economic Studies 1, 218–224.
Luce, R. Duncan and Louis, Narens. (1987). “Measurement Scales on the Continuum,” Science 236, 1527–1532.
Luce, R. Duncan and Howard, Raiffa. (1957). Games and Decisions. New York: Wiley.
MacCrimmon, Kenneth R. and Stig, Larsson. (1979). “Utility Theory: Axioms versus ‘Paradoxes’.” In Maurice Allais and Ole Hagen (eds.), Expected Utility Hypotheses and the Allais Paradox. Dordrecht: Reidel, pp. 333–409.
Machina, Mark J. (1987a). “Decision-Making in the Presence of Risk,” Science 236, 537–543.
Machina, Mark J. (1987b). “Choice under Uncertainty: Problems Solved and Unsolved,” Economic Perspectives 1, 121–154.
Malinvaud, E. (1952). “Note on von Neumann-Morgenstern's Strong Independence Axiom,” Econometrica 20, 679.
Marschak Jacob. (1950). “Rational Behavior, Uncertain Prospects, and Measurable Utility,” Econometrica 18, 111–141. Errata, 1950. p. 312.
Marschak, J. (1979). “Utilities, Psychological Values, and Decision Makers.” In Maurice Allais and Ole Hagen (eds.), Expected Utility Hypotheses and the Allais Paradox. Dordrecht: Reidel, pp. 163–174.
Marshall, Alfred. (1890). Principles of Economics. London: Macmillan.
Morgenstern, Oskar. (1976). “The Collaboration Between Oskar Morgenstern and John von Neumann on the Theory of Games,” Journal of Economic Literature 14, 805–816.
Morgenstern, Oskar. (1979). “Some Reflections on Utility,” In Maurice Allais and Ole Hagen (eds.), Expected Utility Hypotheses and the Allais Paradox. Dordrecht: Reidel, pp. 175–183.
Page, Alfred N. (1968) Utility Theory: A Book of Readings. New York: Wiley.
Pareto, Vilfredo. (1906). Manuale di Economia Politica. Milan: Società Editrice Libraria. Parts of the second edition (1927) are reprinted in Alfred N. Page. (1968). Utility Theory: A Book of Readings. New York: Wiley, pp. 108–181: translated by Ann Stranquist Schwier.
Pfanzagl, J. (1967). “Subjective Probability Derived from the Morgenstern-von Neumann Utility Concept.” In Martin Shubik (ed.), Essays in Mathematical Economics in Honor of Oskar Morgenstern. Princeton: Princeton University Press, pp. 237–251.
Pfanzagl, J. (1968). Theory of Measurement. New York: Wiley.
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. Dordrecht: Reidel, pp. 215–229.
Ramsey, Frank P. (1931). “Truth and Probability.” In R.B. Braithwaite (ed.), The Foundations of Mathematics and Other Logical Essays. London: Routledge and Kegan Paul, pp. 156–198. Reprinted in H. E. Kyburg and H. E. Smokler (eds.), Studies in Subjective Probablity. New York: Wiley, 1964, pp. 61–92.
Reichenbach, H. (1949). The Theory of Probability. Berkeley: University of California Press. English translation by Ernest H. Hutton and Maria Reichenbach of the 2nd edition of Wahrscheinlichkeitslehre (Leiden, 1935).
Roberts, Fred S. (1979). Measurement Theory with Applications to Decisionmaking, Utility, and the Social Sciences. Reading, MA: Addison-Wesley.
Robertson, D. H. (1954). “Utility and All What?,” Economic Journal 64, 665–678.
Samuelson, Paul A. (1952). “Probability, Utility, and the Independence Axiom,” Econometrica 20, 670–678.
Samuelson, Paul A. (1966). “Utility, Preference, and Probability.” In J. E. Stiglitz (ed.), The Collected Scientific Papers of Paul A. Samuelson. Volume 1. Cambridge, MA: M.I.T. Press, pp. 127–136. (From a paper delivered in May, 1952.)
Savage, Leonard J. (1954). The Foundations of Statistics. New York: Wiley.
Slutsky, Eugenio. (1915). “Sulla Teoria del Bilancio del Consumatore,” Giornale degli Economisti e Rivista di Statistica 51, 1–26.
Stigler, George J. (1950). “The Development of Utility Theory: I: II,” Journal of Political Economy 58, 307–327; 373–396 Reprinted in Alfred N. Page. (1968). Utility Theory: A Book of Readings. New York: Wiley, pp. 55–119.
Strotz, Robert H. (1953). “Cardinal Utility,” American Economic Review 43, 384–397.
Venn, J. (1962). Logic of Chance. Fourth edition. New York: Chelsea. First edition, 1886.
von Mises, Richard. (1957). Probability, Statistics and Truth. New York, Macmillan Second revised English edition of the original edition of 1928.
von Neumann, John and Oskar Morgenstern. (1944). Theory of Games and Economic Behavior. Princeton: Princeton University Press. Second edition, 1947; third edition, 1953. Section 3, chapter I. reprinted in Alfred N. Page. (1968). Utility Theory: A Book of Readings. New York: Wiley, pp. 215–233.
Weldon, J. C. (1950). “A Note on Measures of Utility,” Canadian Journal of Economics and Political Science 16, 227–233.
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The author wishes to thank Princeton University Press for permission to quote extensively from Theory of Games and Economic Behavior by John von Neumann and Oskar Morgenstern.
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Fishburn, P.C. Retrospective on the utility theory of von Neumann and Morgenstern. J Risk Uncertainty 2, 127–157 (1989). https://doi.org/10.1007/BF00056134
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DOI: https://doi.org/10.1007/BF00056134