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| §§I and II write that Marshall (Principles of Economics) and Jevons thought that a person could find out about his strength of preference through introspection (p. 530 5th para); this str. of pr. then could as well serve as vNM utility, certainly in a normative sense. E.g. W. Stanley Jevons (1911) “The Theory of Political Economy.” London, p. 36.
P. 537: ascribes vNM theorem to von Neumann solely Nowhere Ellsberg says that vNM explicitly deny that risky=riskless utility. He only says, correctly, that vNM say they did not claim risky=riskless P. 544: Ellsberg ascribes independence to Samuelson. He says, kind of, that independence is indisputable, and that the problems of EU lie elsewhere. Whole Ch. V of Ellsberg’s paper is on risky versus riskless utility %} Ellsberg, Daniel (1954) “Classic and Current Notions of ‘Measurable Utility’,” Economic Journal 62, 528–556. {% Seems that pp. 1010-1011 alludes to it being reasonable to violate SEU. %} Ellsberg, Daniel (1958) Book Review of: Donald Davidson, Patrick Suppes, & Sidney Siegel (1957) “Decision Making: An Experimental Approach.” Stanford University Press, Stanford, CA; American Economic Review 48, 1009–1011. {% In the two-color urn the colors are Red and Black, in the three-color urn the known color is Red, and Black and Yellow are the unknown colors. I hope that everyone in the field will consistently use these colors! Is a convenient convention. The common payment for ambiguity is on Yellow and not on black (suspicion under ambiguity: just like that it will give the confound of suspicion). About the works of Savage/Ramsey: “the implication that—for a “rational” man—all uncertainties can be reduced to risks” (p. 645). This may have contributed to the unfortunate terminology where SEU for unknown probabilities is called risk. P. 75 of Keynes (1921) presents the Ellsberg 2-color urns, says there is more probability error (meaning probability being more unknown) in the unknown than the known, but does not relate it to decision making. I feel, therefore, that the priority goes to Ellsberg. P. 645 points out that a problem arises in the distinction between beliefs (called relative expectations by Ellsberg, context shows it’s beliefs) and utilities (called relative preferences for outcomes by Ellsberg) in revelations from choices: the Tradeoff method of Wakker & Deneffe (1996) can do it! P. 646 middle writes that Ellsberg is less interested in normative than in reflective (sort of prescriptive; decisions after reflection) P. 649, footnote 5, points out that the sure-thing principle, in the presence of known probabilities, reduces to the independence condition. P. 651-652: Ellsberg's analysis of the two-urn example is not natural. He does not take the product space as state space, as most do and as is most natural, but he takes an urn that contains the union of the separate urns. Pfff! Here is a different way of showing that the two-urn example violates the sure-thing principle, which I hope is clearer. P. 657b says that in addition to utility and probability there is a third dimension (ambiguity). P. 659: an individual … can always assign relative likelihoods to the states of nature. But how does he act in the presence of uncertainty? The answer to that may depend on another judgment, about the reliability, credibility, or adequacy of his information. P. 664 L. 2: EU+a*sup+b*inf P. 667 uses, for common Ellsberg behavior, the term “pessimism” to refer to belief and “conservatism” to refer to decision attitude. P. 667 bottom suggests a rank-dependent idea: “He “distorts” his best estimates of likelihood, in the direction of increased emphasis on the less favorable outcomes.” He then elaborates on an example with this. %} Ellsberg, Daniel (1961) “Risk, Ambiguity and the Savage Axioms,” Quarterly Journal of Economics 75, 643–669. {% Is a reply to Roberts’ comment. Essentially both agree that many emotional factors besides ambiguity attitude (he used the term vagueness which is actually better than ambiguity) play a role, and only disagree somewhat on the extent. P. 342: “This is not to say that vagueness, as defined, is typically the sole factor underlying deliberate choices in conflict with the Savage postulates, even in the situations that I described, or that such choices reflect mainly a simple aversion to vagueness (though my article may have given those impressions). My own thinking has moved recently toward recognizing the influence of various dimensions of the decision problem under uncertainty that are strongly associated with vagueness but distinct from it;” %} Ellsberg, Daniel (1963) “Risk, Ambiguity and the Savage Axioms: Reply,” Quarterly Journal of Economics 77, 336–342. {% With an introduction by Isaac Levi and an updated bibliography by Mark Machina. ambiguity seeking for unlikely: in 1962 version, pp. 268–270 and onwards, clearly and explicitly describes ambiguity seeking. ambiguity seeking for unlikely: in 2001 version, p. 203 l. 12-14: "… whereas a preference influenced significantly by extreme favorable possibilities is easily stigmatized as "wishful." … Nevertheless, the deliberated preferences in this example of some individuals—including myself—seem to reflect in a systematic way both favorable and unfavorable positions in an ambiguous situation." It is about a known urn K with 100 balls of 10 colors, each 10-fold present, and an unknown urn A with 100 balls of 10 colors in unknown proportion, where Ellsberg prefers to gamble on not-Green from known to that from unknown, but prefers to gamble on Green-from-unknown to Green-from-known, so that he exhibits ambiguity preference regarding 1/10 probability. Ellsberg repeats his sympathy in footnote 1 on p. 206. He discusses at length in pp. 205-206 that not only the worst conceivable probability distribution receive extra weight, but also the best one. P. 206 2nd para: “…; in their own decision-making they wish to take some account also of favorable possibilities in ambiguous situations. These individuals will not exhibit a uniform tendency to "avoid ambiguity." ” %} Ellsberg, Daniel (2001) “Risk, Ambiguity and Decision.” Garland Publishers, New York. Original Ph.D. dissertation: Ellsberg, Daniel (1962) “Risk, Ambiguity and Decision.” Harvard University, Cambridge, MA. {% DOI http://dx.doi.org/10.1007/s00199-011-0653-3 Ellsberg very explicitly considers the usual Ellsberg paradox behavior to be rational, and the sure-thing principle not to be rational. P. 222 says that 2-color paradox came first to him, before 3-color. P. 223 writes that he discovered Keynes (1921) only in 1962, before his Ph.D.. But obviously after his 1961 paper. (P. 224: he did not know Allais paradox in 1961, but did in 1962 before thesis.) P. 223 writes, to my joy, what I interpret as a plea for investigating natural events and not to overstudy the Ellsberg urns as the field now (2013) does, with square brackets from the original: “[Hint: it is long overdue to perform experiments that test for other forms of ambiguity. That shouldn’t be hard; and they may well turn out to have interestingly differential effects.]” P. 223 writes that Savage and Raiffa (two Bayesians) are the most clever people he ever met. P. 225 does what many do today: ambiguity is automatically equated with the multiple priors model where there are more than one possible probability measures: “ambiguity (where, one might say, more than one probability distribution over events seems reasonable).” I find this unsatisfactory, because there can be situations where there is nothing like a probability distribution in the mind of the decision maker, and the whole concept of “true” but unknown objective probability is questionable. ambiguity seeking: p. 225 mentions that ambiguity seeking is to him as rational and normative as ambiguity aversion, also in his own urn examples, and that he has thought so from the beginning. He discusses it much for unlikely events (ambiguity seeking for unlikely), but not for losses. ambiguity seeking: p. 226 gives a long plea against universal ambiguity aversion (italics added): “I should have emphasized the last clause in the QJE article, but my failure to do so doesn’t fully explain to me why nearly all later research has focused only on “ambiguity aversion,” nor why most expositions have wrongly attributed the same preoccupation to me. It is as if the comments noted above—noting the occurrence of patterns of choice that clearly contradict “ambiguity aversion” even in these particular, frequently-replicated examples—had never appeared in the article. My long-term complaint is not about the mischaracterization of my own exposition but about the general failure to explore this phenomenon in subsequent experiments and analysis. That is especially frustrating to me, because I happen to believe that this latter pattern will be much more frequent than the reverse in certain circumstances of payoffs and events other than the ones that were addressed explicitly in the QJE article and almost exclusively investigated later. Because these other circumstances (discussed in RAD, especially pp. 199–209) often characterize high-stakes political or economic decisions, I see it as being at least as significant empirically as “ambiguity aversion,” if not more so; hence, certainly deserving of much more experimental and theoretical investigation than it has received.” [Italics added here] For reasons unclear to me, Ellsberg does not like the term ambiguity seeking for what I call ambiguity seeking for unlikely, but prefers something like hope, which may be something like optimism (he does not use this term). I will probably be imposing my views on his thinking if I conjecture that he is searching there for Tversky’s concept of insensitivity, but does not grasp it. Here is his text that I am now referring to: P. 225 (italics added): “What to call this pattern? “Ambiguity seeking” would be misleading; it doesn’t relate to the subjective considerations of the decision makers, who reasonably don’t see themselves as “preferring ambiguity” but simply as giving special weight in situations of ambiguity to more hopeful possibilities. Some would criticize this as “wishful,” which may be why it has received less or no attention in discussions of normative criteria (though that doesn’t excuse the neglect of it as an empirical phenomenon).” [Italics added here] He goes on to argue for something like -maxmin, which he calls restricted Bayes-Hurwicz criterion. P. 227 very clearly argues for ambiguity seeking for unlikely, which he already expects with one of 10 colors, and expects more strongly with 1 of 100 or more colors. uncertainty amplifies risk: I did not see this idea in his paper. %} Ellsberg, Daniel (2011) “Notes on the Origins of the Ellsberg Urns (Introduction to the Symposium Issue),” Economic Theory 48, 221–227. {% normal/extensive form %} Elmes, Susan & Philip J. Reny (1994) “On the Strategic Equivalence of Extensive Form Games,” Journal of Economic Theory 62, 1–23. {% %} Elstein, Arthur S. (1996) “The Normative Status of Expected Utility Theory,” Medical Decision Making 16, 7. {% simple decision analysis cases using EU: bit complex. Suggest that an irrational decision not to prescribe estrogen may be caused by the overestimation of small probability of endometrial cancer. %} Elstein, Arthur S., Gerald B. Holzman, Michael M. Ratvick, et al. (1986) “Comparison of Physicians’ Decisions Regarding Oestrogen Replacement Therapy for Menopausal Women and Decisions Derived from a Decision Analytic Model,” American Journal of Medicine 80, 246–258. {% %} Elster, John (1978, ed.) “Logic and Society.” Wiley, New York. {% %} Elster, John (1979, ed.) “Ulysses and the Syrens.” Cambridge University Press, New York; revised 1984. {% %} Elster, John (1983, ed.) “Sour Grapes.” Cambridge University Press, New York. {% discounting normative: seems to argue for 0 discounting. %} Elster, John (1986) “Introduction.” In John Elster (ed.) The Multiple Self, 1–34, Cambridge University Press, New York. {% %} Elster, John (1986, ed.) “The Multiple Self.” Cambridge University Press, New York. {% %} Elster, John (1998) “Emotions and Economic Theory,” Journal of Economic Literature 36, 47–74. {% P. 11 seems to claim that ambiguity aversion is normative and seems to write: “Farmers deciding on a crop mix or doctors deciding whether to operate act under risk. They can rely on well-defined probabilities derived from past frequencies. Stock market speculators, soldiers and others who have to act in novel situations cannot rely on frequencies. If they have sufficient information and good judgement, they may be able to make good probability estimates to feed into the expected utility calculus. If they have little information or poor judgement, rationality requires them to abstain from forming and acting upon such estimates. To attempt to do so would, for them, be a form of hyperrationality.” Same page: “Here is a case in which objective probabilities and judgemental, subjective probabilities are equally out of reach.” Again on page 16; P. 22 (footnote 51)/23, is negative on idea that one can choose one’s beliefs so as to maximize utility (as in Brunnermeier & Parker 2005): “the pleasure of wishful thinking is of brief duration, like the warmth provided by pissing in one's pants.'' P. 26, on elicitation, seems to write: “It is always possible to devise questions that will force a person to reveal his preferences or subjective probabilities, but often there is no reason to believe in the robustness of the results. If the outcome depends on the procedures of elicitation, there is nothing “out there” which is captured by the questions.” P. 58 seems to write: “Bayesian decision theory itself is an expression of the desire to have reasons for everything; P. 90: desire to have decisions based on reasons;” %} Elster, John (1989) “Solomonic Judgements.” Cambridge University Press, New York. {% %} Elster, John & George F. Loewenstein (1992) “Utility from Memory and Anticipation.” In George F. Loewenstein & John Elster (1992) Choice over Time, 213–234, Russell Sage Foundation, New York. {% free-will/determinism: not precisely this, but rather combining chance with determinism (foundations of probability). %} Emery, Nina (2015) “Chance, Possibility, and Explanation,” British Journal for the Philosophy of Science 41, 141–142. {% %} Engel, Yagil & Michael P. Wellman (2010) “Multiattribute Auctions Based on Generalized Additive Independence,” Journal of Artificial Intelligence Research 37, 479–525. {% %} Engelbrecht-Wiggans, Richard & Elena Katok (2008) “Regret and Feedback Information in First-Price Sealed-Bid Auctions,” Management Science 53, 808–819. {% PT, applications, loss aversion: dependency of household mobility on house prices is hard to explain by classical models. Equity cannot explain it very well, but loss aversion can. %} Engelhardt, Gary V. (2003) “Nominal Loss Aversion, Housing Equity Constraints, and Household Mobility: Evidence from the United States,” Journal of Urban Economics 53, 171–195. {% %} Engelmann, Dirk & Guillaume Hollard (2010) “Reconsidering the Effect of Market Experience on the ‘Endowment Effect’,” Econometrica 78, 2005–2019. {% equity-versus-efficiency: let subjects choose between (x,y,z), where y is their own payment, and x and z are payments for two anonymous others. P. 862 last para: the Fehr & Schmidt model performs poorly regarding its predictions of Pareto-dominance violations. Efficiency (I think this is the sum total x+y+z) and maximin, as in a model by Charness & Rabin (2002) explain much of the data. What Fehr-Schmidt contributes in addition is not significant. A model by Bolton & Ockenfels (2000) performs poorly. %} Engelmann, Dirk & Martin Strobel (2004) “Inequality Aversion, Efficiency, and Maximin Preferences in Simple Distribution Experiments,” American Economic Review 94, 857–869. {% %} Engers, Maxim, Joshua S. Gans, Simon Grant, & Stephen P. King (1999) “Articles - First-Author Conditions,” Journal of Political Economy 107, 859–883. {% In a first experiment, risk and ambiguity aversion are measured. For the risk attitude, consider lotteries Lj = (0.5:(13j 3), 0.5:(13+j 4.5)), j = 0,…,4. Choice situation j gives a choice between Lj1 and Lj, j = 1,…,4. Note that, under EU, a subject with utility function U() = (13)r has the same preference in all four situations, exhibiting constant relative risk aversion w.r.t. outcomes 13. For the ambiguity attitude, subjects chose five times, each time between Lj and an ambiguous version of it, where the probability 0.5 is replaced by an unknown two-color Ellsberg urn. Subjects could choose the winning color (p. 77 1st para; suspicion under ambiguity). The authors seem to suggest that subjects only once switch from risky to safe, and from ambiguous to risky, or vice versa, as j increases, but I do not understand why, and neither which direction of switch the authors have in mind. But this point is not important for the rest of the paper. P. 78, §2.6: The authors took the number safe vs. risky choices as index of risk aversion, and number of risky vs ambiguous choices as index of ambiguity aversion. These are atheoretical indexes, with all the pros and cons of those. (E.g., no need to commit to a theory, but no direct comparability with other experiments or existing indexes.) It is not clear to me why the authors restrict to expected utility for risk, or the smooth model for ambiguity, in the first part of their paper, because their indexes are atheoretical. For the smooth model they assume that the second-order distribution is uniform over all probability compositions. In a second experiment done a month later, the same subjects could play a game with ambiguous choices where they could pay to receive extra info, I think a drawing from the unknown distribution. Ambiguity averse subjects are willing to pay more. I would of course be interesting in a relation between a(mbiguity)-generated insensivitity and willingness to pay for extra info, but the experiment, with only 05-05 uncertainties, does not give the data to investigate this. It would accrdingly have interested me much if ambiguity attitudes had also been measured with a(mbiguity)-neutral probabilities 0.1 and 0.9. %} Engle-Warnick, Jim & Sonia Laszlo (2017) “Learning-by-Doing in an Ambiguous Environment,” Journal of Risk and Uncertainty 55, 71–94. {% foundations of statistics: discusses it for sociology, arguing against classical statistics. %} Engman, Athena (2013) “Is there Life after P<0.05? Statistical Significance and Quantitative Sociology,” Quality and Quantity 47, 257–270. {% Quick surveys based on telephonic interviews. %} EOS Gallup Europe (2002) “Euro Attitudes—Euro Zone,” Flash Eurobarometer no. 121/3, June 2002. {% Andereoni & Sprenger (2012 AER “Risk Preferences Are not Time Preferences”) consider a case of both risk and time. They first aggregate over risk, which amounts to a kind of separability of singel timepoints. This paper points out that one may as well first aggregate over time (which in a way amounts to taking states of nature as separable). Then counterevidence against RDU claimed by A&S disappears. The authors write in the closing para: “Overall, RDU can explain all of the major findings in CTB experiments and provides the most convincing explanation of the evidence. The model respects first-order stochastic dominance, it can handle general boundary effects aside from the certainty effect, and correctly predicts behavior under different correlation structures. Thus, RDU and its cousins are an attractive modeling choice not only in atemporal, but also in intertemporal situations.” %} Epper, Thomas & Helga Fehr-Duda (2015) “Risk Preferences Are not Time Preferences: Balancing on a Budget Line: comment (#12)” American Economic Review 105, 2261–2271. {% real incentives/hypothetical choice: for time preferences: RIS with one risky choice, but also one intertemporal choice, paid for real (p. 174). So, a bit of income effect. Subjects got a voucher to collect their money either next day, or in two months, or in four months. P. 177 points out that not paying every subject may interfere with purpose of no risk perception in intertemporal choice. Use relative risk premium: (EVCE)/EV (p. 181). P. 181: risk seeking for small-probability gains: they find this (supports also inverse-S although they did not try to fit other curves than inverse-S). risky utility u = strength of preference v (or other riskless cardinal utility, often called value): use risky utility to calculate discounting, as did Andersen, Harrison, Lau, & Rutstrom (2008), but use the more realistic prospect theory rather than EU (the latter, using EU, was done by Andersen et al.). Wakker (1994, Theory and Decision) argued for such use of one utility for all fields, coppled with nonEU to be descriptively realistic. P. 182, §3.1: 17% of subjects reveal increasing impatience, and 54% reveal decreasing impatience. P. 184: show that, if future consumption is always endowed with uncertainty as is reasonable, then hyperbolic discounting can be generated by probability weighting. Find strong correlations between inverse-S probability weighting and hyperbolic discounting, confirming their relation. Find no relation between degree of convexity of probability weighting and discounting, or between utility curvature and discounting. Discounting correlated in fact with nothing else, not with demographic variables and not with Frederick’s (2005) cognitive ability score. (cognitive ability related to discounting) linear utility for small stakes: find it because they capture much of risk attitude through probability weighting. Argue that decreasing impatience may be generated by uncertainty. P. 193: “Arguably, the future is uncertain by definition.” %} Epper, Thomas, Helga Fehr-Duda, & Adrian Bruhin (2011) “Viewing the Future through a Warped Lens: Why Uncertainty Generates Hyperbolic Discounting,” Journal of Risk and Uncertainty 43, 163–203. {% Seems to considers EU where consequences are streams of outcomes. In this framework, gives conditions implying that the utility function over outcomes is constant discounting. %} Epstein, Larry G. (1983) “Stationary Cardinal Utility and Optimal Growth under Uncertainty,” Journal of Economic Theory 31, 133–152. {% Nice survey of the recursive betweenness literature; dynamic consistency (= constant tastes). P. 1 defines risk in the traditional way where probabilities should be known: “…individual behavior under risk where, following Knight (1921), risk is defined as randomness with a known probability distribution.” Expresses a strong preference for betweenness theories over other nonexpected utility models such as rank-dependent theories, prospect theory, etc. for normative and tractability reasons. See, for example, (1) P. 6: “There are a number of alternative axiomatically based generalizations of expected utility theory that have been developed, but the one which seems to me to strike the optimal balance between generality and tractability, at least for the applications that I will consider, is the betweenness theory due to …” and references follow [italics from original]. §4 considers applications to consumption and asset returns, §5 to sequential choice and game theory. Endnote 2, concerning the text just cited and given on p. 52, writes: “rank-dependent expected or anticipated utility …, the nontransitive regret theory … these alternative models are not particularly useful for the applications in §§4 and 5. The same comment applies to prospect theory (Kahneman & Tversky, 1979). The latter also suffers, in comparison with expected utility and the other models mentioned, from more ambiguous predictions because of the lack of a precise theory of the framing and editing processes.” (2) §3.4 on normative considerations on p. 24 2nd paragraph suggests normative appeal and also tractability. (3) End of §5.1 also for sequential choice (no physical time) P. 21 defines stationarity. (4) p. 48 for applications to game theory. On dynamic decision principles, this paper strongly favors the approach that keeps forgone-event independence (mostly called consequentialism) and update-consistency (mostly called dynamic consistency) and abandons RCLA, in the context of “intertemporal utility” where intertemporal means that there can be consumptions at intermediate nodes so there is physical time: (a) P. 19, l. 10-13: “The route corresponding to the middle branch … has been by far the most productive to date and will be the focus of the remaining discussion of intertemporal utility and applications.” Here the middle branch designates what I described above. (b) dynamic consistency: favors abandoning RCLA when time is physical: “Introspection suggests that one might care about the temporal resolution of risk even in the absence of any implications for planning.” In sequential choice where there is no physical time, the paper considers RCLA to be natural (p. 43). Download 7.23 Mb. Share with your friends:
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