Hostname: page-component-8448b6f56d-cfpbc Total loading time: 0 Render date: 2024-04-23T10:09:16.464Z Has data issue: false hasContentIssue false
  • English
  • Français

The Allais paradox: what it became, what it really was, what it now suggests to us

Published online by Cambridge University Press:  30 January 2019

Philippe Mongin
Philippe Mongin*
Affiliation:
GREGHEC, 1 rue de la Libération, F-78350 Jouy-en-Josas, France
*
Email: mongin@greg-hec.com
Get access Rights & Permissions [Opens in a new window]

Abstract

Whereas many others have scrutinized the Allais paradox from a theoretical angle, we study the paradox from an historical perspective and link our findings to a suggestion as to how decision theory could make use of it today. We emphasize that Allais proposed the paradox as a normative argument, concerned with ‘the rational man’ and not the ‘real man’, to use his words. Moreover, and more subtly, we argue that Allais had an unusual sense of the normative, being concerned not so much with the rationality of choices as with the rationality of the agent as a person. These two claims are buttressed by a detailed investigation – the first of its kind – of the 1952 Paris conference on risk, which set the context for the invention of the paradox, and a detailed reconstruction – also the first of its kind – of Allais’s specific normative argument from his numerous but allusive writings. The paper contrasts these interpretations of what the paradox historically represented, with how it generally came to function within decision theory from the late 1970s onwards: that is, as an empirical refutation of the expected utility hypothesis, and more specifically of the condition of von Neumann–Morgenstern independence that underlies that hypothesis. While not denying that this use of the paradox was fruitful in many ways, we propose another use that turns out also to be compatible with an experimental perspective. Following Allais’s hints on ‘the experimental definition of rationality’, this new use consists in letting the experiment itself speak of the rationality or otherwise of the subjects. In the 1970s, a short sequence of papers inspired by Allais implemented original ways of eliciting the reasons guiding the subjects’ choices, and claimed to be able to draw relevant normative consequences from this information. We end by reviewing this forgotten experimental avenue not simply historically, but with a view to recommending it for possible use by decision theorists today.

Keywords

Allais paradoxdecision theoryexpected utility theoryexperimental economicspositive vs normativerationality1952 Paris conferenceAllaisvon Neumann and MorgensternSamuelsonSavageB21B31B41C91D8
Type
Article
Information
Economics & Philosophy , Volume 35 , Issue 3 , November 2019 , pp. 423 - 459
Check for updates
Copyright
© Cambridge University Press 2019 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Allais, M. 1952. Fondements d’une théorie positive des choix comportant un risque et critique des postulats et axiomes de l’école américaine. Econométrie 257–331.Google Scholar
Allais, M. 1953a. La psychologie de l’homme rationnel devant le risque. La théorie et l’expérience. Journal de la Société de Statistique de Paris 94, 47–73.Google Scholar
Allais, M. 1953b. Le comportement de l’homme rationnel devant le risque. Econometrica 21, 503–546.CrossRefGoogle Scholar
Allais, M. 1979. The so-called Allais paradox and rational decisions under uncertainty. In Allais, M. and Hagen, O. (eds), Expected Utility and the Allais Paradox, Dordrecht: D. Reidel, pp. 437–683.CrossRefGoogle Scholar
Allais, M. 1987. Allais’s paradox. In The New Palgrave. A Dictionary of Economics. London: Macmillan.Google Scholar
Allais, M. 1994. An outline of my main contributions to Risk and Utility Theory: theory, experience, and applications: general overview. In Munier, B. and Machina, M. J. (eds), Models and Experiments in Risk and Rationality. Dordrecht: Kluwer, pp. 173–221.CrossRefGoogle Scholar
Allais, M. and Hagen, O. eds. 1979. Expected Utility and the Allais Paradox. Dordrecht: D. Reidel.CrossRefGoogle Scholar
Andreoni, J. and Sprenger, C. 2009. Certain and Uncertain Utility: The Allais Paradox and Five Decision Theory Phenomena. Manuscript, University of California, San Diego.Google Scholar
Bierman, H. 1989. The Allais paradox: a framing perspective. Behavioral Science 34, 46–52.CrossRefGoogle Scholar
Birnbaum, M. H. 1998. The paradoxes of Allais, stochastic dominance, and decision weights. In Shanteau, J. C., Mellers, B. A. and Schum, D. (eds), Decision Research from Bayesian Approaches to Normative Systems: Reflections on the Contributions of Ward Edwards. Norwell: Kluwer, pp. 27–52.Google Scholar
Birnbaum, M. H. 2004. Causes of Allais common consequence paradoxes: an experimental dissection. Journal of Mathematical Psychology 48, 87–106.CrossRefGoogle Scholar
Birnbaum, M. H., Coffey, G., Mellers, B. A. and Weiss, R. 1992. Utility measurement: configural weight theory and the judge’s point of view. Journal of Experimental Psychology: Human Perception and Performance 18, 331–346.Google Scholar
Borch, K. and Mossin, J. eds. 1968. Risk and Uncertainty. London: Macmillan.Google Scholar
Bourgeois-Gironde, S. and Giraud, R. 2008. Le tournant cognitif en économie de la décision et des comportements. In Walliser, B. (ed.), Economie et Cognition. Paris: Ophrys, pp. 55–91.CrossRefGoogle Scholar
Bouyssou, D. and Vansnick, J. C. 1990. Utilité cardinale’ dans le certain et choix dans le risque. Revue économique 41, 979–1000.Google Scholar
Camerer, C. 1995. Individual decision making. In Roth, A. E. and Kagel, J. H. (eds), Handbook of Experimental Economics. Princeton, NJ: Princeton University Press, pp. 587–703.Google Scholar
Cerreia-Vioglio, S., Dillenberger, D. and Ortoleva, P. 2015. Cautious expected utility and the certainty effect. Econometrica 83, 693–728.CrossRefGoogle Scholar
Cohen, M. 1992. Security level, potential level, expected utility: a three-criteria decision model under risk. Theory and Decision 33, 101–134.CrossRefGoogle Scholar
Conlisk, J. 1989. Three variants on the Allais example. American Economic Review 79, 392–407.Google Scholar
Cubitt, R. P., Starmer, C. and Sugden, R. 1991. Dynamic choice and the common ratio effect: an experimental investigation. Economic Journal 108, 1362–1380.CrossRefGoogle Scholar
Diemer, A., Lallement, J. and Munier, B. 2010. Maurice Allais et la science économique. Paris: Clément Juglar.Google Scholar
Drèze, J. H. 1989. Maurice Allais and the French Marginalist School. Scandinavian Journal of Economics 91, 5–16.CrossRefGoogle Scholar
Edwards, W. 1954. The theory of decision making. Psychological Bulletin 51, 380–417.CrossRefGoogle ScholarPubMed
Edwards, W. 1962. Subjective probabilities inferred from decisions. Psychological Review 69, 109–135.CrossRefGoogle ScholarPubMed
Eli, V. 2017. Essays in Normative and Descriptive Decision Theory. Doctoral thesis, Université Paris-Saclay and HEC Paris.Google Scholar
Fishburn, P. C. 1989. Retrospective on the utility theory of von Neumann and Morgenstern. Journal of Risk and Uncertainty 2, 127–158.CrossRefGoogle Scholar
Fishburn, P. C. and Wakker, P. 1995. The invention of the independence condition for preferences. Management Science 41, 1130–1144.CrossRefGoogle Scholar
Friedman, M. and Savage, L. J. 1948. The utility analysis of choices involving risk. Journal of Political Economy 56, 278–304.CrossRefGoogle Scholar
Friedman, M. and Savage, L. J. 1952. The expected-utility hypothesis and the measurability of utility. Journal of Political Economy 60, 463–474.CrossRefGoogle Scholar
Gilboa, I. 1988. A combination of expected utility and maxmin decision criteria. Journal of Mathematical Economics 32, 405–420.Google Scholar
Gilboa, I. 2011. Questions in decision theory. In Apt, K. R. (ed.), Proceedings of Tark XIII. ACM Publications, pp. 17–27.CrossRefGoogle Scholar
Gilboa, I. and Schmeidler, D. 2001. A Theory of Case-Based Decisions. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Gilboa, I., Maccheroni, F., Marinacci, M. and Schmeidler, D. 2010. Objective and subjective rationality in a multiple prior model. Econometrica 78, 755–770.Google Scholar
Grandmont, J. M. 1989. Report on Maurice Allais’s scientific work. Scandinavian Journal of Economics 91, 17–28.CrossRefGoogle Scholar
Guala, F. 2000. The logic of normative falsification: rationality and experiments in decision theory. Journal of Economic Methodology 7, 59–93.CrossRefGoogle Scholar
Hagen, O. 1972. A new axiomatization of utility under risk. Teorie e Metoda 4, 55–80.Google Scholar
Hands, D. W. 2015. Normative Rational Choice Theory: Past, Present and Future. University of Puget Sound Working Paper.Google Scholar
Herstein, I. N. and Milnor, J. 1953. An axiomatic approach to measurable utility. Econometrica 21, 291–297.CrossRefGoogle Scholar
Heukelom, F. 2014. Behavioral Economics. A History. New York, NY: Cambridge University Press.CrossRefGoogle Scholar
Heukelom, F. 2015. A history of the Allais paradox. British Journal for the History of Science 48, 147–169.CrossRefGoogle ScholarPubMed
Hey, J. D. 1991. Experiments in Economics. Oxford: Blackwell.Google Scholar
Hey, J. D. and Orme, C. 1994. Investigating generalizations of expected utility theory using experimental data. Journal of Risk and Uncertainty 62, 1291–1326.Google Scholar
Jaffray, J. Y. 1988. Choice under risk and the security factor. Theory and Decision 24, 169–200.CrossRefGoogle Scholar
Jallais, S. and Pradier, P. C. 2005. The Allais paradox and its immediate consequences for expected utility theory. In Fontaine, P. and Leonard, R. (eds), The ‘Experiment’ in the History of Economics. London: Routledge, pp. 25–49.Google Scholar
Jallais, S., Pradier, P. C. and Teira, D. 2008. Facts, norms and expected utility functions. History of the Human Sciences 21, 45–62.CrossRefGoogle Scholar
Kahneman, D. and Tversky, A. 1979. Prospect theory: an analysis of decision under risk. Econometrica 47, 263–291.CrossRefGoogle Scholar
Karmakar, U. S. 1978. Subjectively weighted utility: a descriptive extension of the expected utility model. Organization Behavior and Human Performance 21, 61–72.CrossRefGoogle Scholar
Karmakar, U. S. 1979. Subjectively weighted utility and the Allais paradox. Organization Behavior and Human Performance 24, 67–72.CrossRefGoogle Scholar
Karni, E. and Schmeidler, D. 1991. Atemporal dynamic consistency and expected utility theory. Journal of Economic Theory 54, 401–408.CrossRefGoogle Scholar
Leonard, R. 1995. From parlor games to social science: von Neumann, Morgenstern and the creation of game theory, 1928–1944. Journal of Economic Literature 33, 730–761.Google Scholar
Luce, R. D. and Raiffa, H. 1957. Games and Decisions. New York, NY: Wiley.Google Scholar
MacCrimmon, K. R. 1965. An Experimental Study of the Decision-Making Behavior of Business Executives. Ph.D. dissertation, University of California, Los Angeles.Google Scholar
MacCrimmon, K. R. 1968. Descriptive and normative implications of the decision-theory postulates. In Borch, K. and Mossin, J. (eds), Risk and Uncertainty. London: Macmillan, pp. 3–23.Google Scholar
MacCrimmon, K. R. and Larsson, S. 1979. Utility theory: axioms versus ‘paradoxes’. In Allais, M. and Hagen, O. (eds), Expected Utility and the Allais Paradox. Dordrecht: D. Reidel, pp 333–409.CrossRefGoogle Scholar
Machina, M. J. 1983. Generalized expected utility analysis and the nature of observed violations of the independence axiom. In Stigum, B. and Wenstop, F. (eds), Foundations of Utility and Risk theory with Applications. Dordrecht: Reidel, pp. 263–293.CrossRefGoogle Scholar
Machina, M. J. 1987. Choices under uncertainty: problems solved and unsolved. Journal of Economic Perspectives 1, 121–154.CrossRefGoogle Scholar
Machina, M. J. 1989. Dynamic consistency and non-expected utility models of choice under uncertainty. Journal of Economic Literature 27, 1622–1668.Google Scholar
Machina, M. J. 1991. Dynamic consistency and non-expected utility. In Bacharach, M. and Hurley, S. (eds), Foundations of Decision Theory. Oxford: Blackwell, pp. 39–91.Google Scholar
Marschak, J. 1950. Rational behavior, uncertain prospects and measurable utility. Econometrica 18, 111–141.CrossRefGoogle Scholar
Mongin, P. 1988. Problèmes de Duhem en théorie de l’utilité espérée. Fundamenta Scientiae 9, 289–317.Google Scholar
Mongin, P. 2009. Duhemian themes in expected utility theory. In Brenner, A. and Gayon, J. (eds), French Studies in the Philosophy of Science. New York, NY: Springer, pp. 303–357.CrossRefGoogle Scholar
Mongin, P. 2012. Une source méconnue de la théorie de l’agrégation des jugements. Revue économique 63, 645–657.CrossRefGoogle Scholar
Morrison, D. G. 1967. On the consistency of preferences in Allais’ paradox. Behavioral Science 12, 373–383.CrossRefGoogle ScholarPubMed
Moscati, I. 2013. How cardinal utility entered economic analysis. European Journal 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.CrossRefGoogle Scholar
Moscati, I. (Forthcoming). Measuring Utility: From the Marginal Revolution to Neuroeconomics. Oxford: Oxford University Press.Google Scholar
Moskowitz, H. 1974. Effects of problem representation and feedback on rational behavior in Allais and Morlat-type problems. Decision Sciences 5, 225–241.CrossRefGoogle Scholar
Mosteller, F. and Nogee, P. 1951. An experimental measurement of utility. Journal of Political Economy 59, 371–404.CrossRefGoogle Scholar
Munier, B. 1991. The many other Allais paradoxes. Journal of Economic Perspectives 5, 179–189.CrossRefGoogle Scholar
Munier, B. 1995. Fifty years of Maurice Allais’ economic writings: seeds for renewal in contemporary economic thought. In Munier, B. (ed.), Markets, Risk and Money. Essays in Honor of Maurice Allais. Dordrecht: Kluwer, pp. 1–50.CrossRefGoogle Scholar
Munier, B. 2011. Maurice Allais, précurseur et devancier de l’analyse du risque contemporain. In Diemer, A., Lallement, J. and Munier, B. (eds), Maurice Allais et la science économique. Paris: Clément Juglar, pp. 75–94.Google Scholar
Preston, M. G. and Barratta, P. 1948. An experimental study of the auction-value of an uncertain outcome. American Journal of Psychology 61, 183–193.CrossRefGoogle ScholarPubMed
Raiffa, H. 1968. Decision analysis. In Introductory Lectures on Choices under Uncertainty. Reading, MA: Addison-Wesley.Google Scholar
Roth, A. E. 1995. Introduction to experimental economics. In Roth, A. E. and Kagel, J. H. (eds), Handbook of Experimental Economics. Princeton, NJ: Princeton University Press, pp. 3–109.Google Scholar
Rubin, H. 1949. The existence of measurable utility and psychological probability. Cowles Commission Discussion Paper: Statistics 332.Google Scholar
Rubinstein, A. 1988. Similarity and decision-making under risk (is there a utility theory resolution to the Allais paradox?). Journal of Economic Theory 46, 145–153.CrossRefGoogle Scholar
Samuelson, P. A. 1952a. Utilité, préférence et probabilité. Econométrie, 141–150. English version: Utility, preference, and probability. In Collected Economic Papers, I, 127–136. Cambridge, MA: MIT Press, 1966.Google Scholar
Samuelson, P. A. 1952b. Probability, utility, and the independence axiom. Econometrica 20, 670–678.CrossRefGoogle Scholar
Savage, L. J. 1951. The theory of statistical decision. Journal of the American Statistical Association 46, 55–67.CrossRefGoogle Scholar
Savage, L. J. 1952. Une axiomatisation du comportement raisonnable face à l’incertitude. Econométrie, 29–33.Google Scholar
Savage, L. J. 1954. The Foundations of Statistics. New York, NY: Dover (2nd edn, 1972).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. 1990. Two-stage lotteries without the reduction axiom. Econometrica 58, 349–377.CrossRefGoogle Scholar
Slovic, P. and Tversky, A. 1974. Who accepts Savage’s axioms? Behavioral Science 19, 368–378.CrossRefGoogle Scholar
Starmer, C. 2000. Developments in non-expected utility theory: the hunt for a descriptive theory of choice under risk. Journal of Economic Literature 38, 332–382.CrossRefGoogle Scholar
Tversky, A. 1975. A critique of expected utility theory: descriptive and normative considerations. Erkenntnis 9, 163–173.Google Scholar
Tversky, A. and Kahneman, D. 1986. Rational choice and the framing of decisions. Journal of Business 59, S251–S278.CrossRefGoogle Scholar
Tversky, A. and Kahneman, D. 1992. Advances in prospect theory: cumulative representation of uncertainty. Journal of Risk and Uncertainty 5, 297–323.CrossRefGoogle Scholar
van de Kuilen, G. and Wakker, P. 2006. Learning in the Allais paradox. Journal of Risk and Uncertainty 33, 155–164.CrossRefGoogle Scholar
von Neumann, J. and Morgenstern, O. 1944. The Theory of Games and Economic Behavior. Princeton, NJ: Princeton University Press (2nd edn, 1947).Google Scholar
Wakker, P. 1999. Justifying Bayesianism by Dynamic Principles. Mimeo: Leiden University Medical Center.Google Scholar
Wakker, P. 2010. Prospect Theory. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Weber, B. J. 2008. The effects of payout and probability magnitude on the Allais paradox. Memory and Cognition 5, 1013–1023.CrossRefGoogle Scholar