PSU ACCTG 597E - Risk Ambiguity and the Savage Axioms

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Risk, Ambiguity, and the Savage AxiomsDaniel EllsbergThe Quarterly Journal of Economics, Vol. 75, No. 4. (Nov., 1961), pp. 643-669.Stable URL:http://links.jstor.org/sici?sici=0033-5533%28196111%2975%3A4%3C643%3ARAATSA%3E2.0.CO%3B2-EThe Quarterly Journal of Economics is currently published by The MIT Press.Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available athttp://www.jstor.org/about/terms.html. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtainedprior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content inthe JSTOR archive only for your personal, non-commercial use.Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained athttp://www.jstor.org/journals/mitpress.html.Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printedpage of such transmission.The JSTOR Archive is a trusted digital repository providing for long-term preservation and access to leading academicjournals and scholarly literature from around the world. The Archive is supported by libraries, scholarly societies, publishers,and foundations. It is an initiative of JSTOR, a not-for-profit organization with a mission to help the scholarly community takeadvantage of advances in technology. For more information regarding JSTOR, please contact [email protected]://www.jstor.orgMon Mar 10 11:54:44 2008RISK, AMBIGUITY, AND THE SAVAGE AXIOMS* I. Are there uncertainties that are not risks? 643.-11. Uncertainties that are not risks, 647. -111. Why are some uncertainties not risks? -656. There has always been a good deal of skepticism about the behavioral significance of Frank Knight's distinction between "meas- urable uncertainty" or "risk," which may be represented by numeri- cal probabilities, and "unmeasurable uncertainty" which cannot. Knight maintained that the latter "uncertainty" prevailed -and hence t,hat numerical probabilities were inapplicable -in situations when the decision-maker was ignorant of the statistical frequencies of events relevant to his decision; or when a priori calculations were impossible; or when the relevant events were in some sense unique; or when an important, once-and-for-all decision was concerned.' Yet the feeling has persisted that, even in these situations, people tend to behave "as though" they assigned numerical probabilities, or "degrees of belief," to the events impinging on their actions. How-ever, it is hard either to confirm or to deny such a proposition in the absence of precisely-defined procedures for measuring these alleged "degrees of belief." What might it mean operationally, in terms of refutable predic- tions about observable phenomena, to say that someone behaves "as if" he assigned quantitative likelihoods to events: or to say that he does not? An intuitive answer may emerge if we consider an example proposed by Shackle, who takes an extreme form of the Knightian * Research for this paper was done as a member of the Society of Fellows, Haward University, 1957. It was delivered in essentially its present form, except for Section 111, at the December meetings of the Econometric Society, St. Louis, 1960. In the recent revision of Section 111, I have been particularly stim- ulated by discussions with A. Madansky, T. Schelling, L. Shapley and S. Winter. 1. F. H. Knight, Rzsk, Uncertaznty and Profit (Boston: Houghton hlifflin, 1921). But see Arrow's comment: "In brief, Knight's uncertainties seem to have surprisingly many of the properties of ordinary probabilities, and it is not clear how much is gained by the distinction. . . Actually, his uncertainties produce about the same reactions in individuals as other writers ascribe to risks." K. J. Arrow, "Alternative Apprbaches to the Theory of Choice in Risk-taking Situa- tions," Ewnometrzca, Vol. 19 (Oct. 1951), pp. 417, 426.644 QUARTERLY JOURNAL OF ECONOMICS position that statistical information on frequencies within a large, repetitive class of events is strictly irrelevant to a decision whose outcome depends on a single trial. Shackle not only rejects numerical probabilities for representing the uncertainty in this situation; he maintains that in situations where all the potential outcomes seem "perfectly possible" in the sense that they would not violate accepted laws and thus cause "surprise," it is impossible to distinguish mean- ingfully (i.e., in terms of a person's behavior, or any other observa- tions) between the relative "likelihoods" of these outcomes. In throw- ing a die, for instance, it would not surprise us at all if an ace came up on a single trial, nor if, on the other hand, some other number came up. So Shackle concludes: Suppose the captains in a Test Match have agreed that instead of tossing a coin for a choice of innings they will decide the matter by this next throw of a die, and that if it shows an ace Australia shall bat first, if any other number, then England shall bat first. Can we now give any meaningful answer whatever to the ques- tion, "Who will bat first?" except "We do not know?"* Most of us might think we could give better answers than that. We could say, "England will bat first," or more cautiously: "I think England will probably bat first." And if Shackle challenges us as to what we "mean" by that statement, it is quite natural to reply: "We'll bet on England; and we'll give you good odds." It so happens that in this case statistical information (on the behavior of dice) is available and does seem relevant even to a "single shot" decision, our bet; it will affect the odds we offer. As Damon Runyon once said, "The race is not always to the swift nor the battle to the strong, but that's the way to bet." However, it is our bet itself, and not the reasoning and evidence that lies behind it, that gives operational meaning to our statement that we find one outcome "more likely" than another. And we may be willing to place bets -thus revealing "degrees of belief" in a quantitative form -about events for which there is no statistical information at all, or regarding which statistical information seems in principle


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PSU ACCTG 597E - Risk Ambiguity and the Savage Axioms

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