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Part II, longest part, is on games with incomplete info, etc
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- Tradeoff method
- PT: data on probability weighting ; ambiguity seeking for losses ambiguity seeking for unlikely
| Part II, longest part, is on games with incomplete info, etc.
Seem to say that risk aversion and diminishing marginal utility are two factors that cannot be disentangled. %} Hirshleifer, Jack & John G. Riley (1992) “The Analytics of Uncertainty and Information.” Cambridge University Press, Cambridge. {% %} Hisdal, Ellen (1988) “Are Grades of Membership Probabilities?,” Fuzzy Sets and Systems 25, 325–348. {% Seem to demonstrate reference dependence when outcomes are combinations of money and time. %} Hjorth, Katrine & Mogens Fosgerau (2012) “Using Prospect Theory to Investigate the Low Marginal Value of Travel Time for Small Time Changes,” Transportation Research Part B: Methodological 46, 917–932. {% Managers are considered in cases where it is as bad to be above benchmark as below benchmark. They mostly preferred further investigation of a dept. with ambiguous performance than with unambiguous. The paper considers ambiguity about probabilities but also directly about outcomes. %} Ho, Joanna L.Y., L. Robin Keller, & Pamela Keltyka (2001) “Managers’ Variance Investigation Decisions: An Experimental Examination of Probabilistic and Outcome Ambiguity,” Journal of Behavioral Decision Making 14, 257–278. {% Hypothetical choice. The paper considers ambiguity about probabilities but also directly about outcomes. (ambiguous outcomes vs. ambiguous probabilities) ambiguity seeking for losses: find this indeed, and find ambiguity aversion for gains. The ambiguous probabilities are around 0.5, so not very small. For reference point, the benchmark is taken that is imposed on managers. reflection at individual level for ambiguity: Table 1 on p. 58 gives info on it. Subjects can choose ambiguous or unambiguous for gains and losses. This can happen for outcome ambiguity and for probability ambiguity. Outcome ambiguity: the subtable upper right shows that of the subjects ambiguity averse for gains about 2/3 was ambiguity seeking for losses, and for the subjects ambiguity seeking for gains it was about the same. So this suggests independence of ambiguity attitudes for gains and losses. Probability ambiguity: the subtable lower right shows that of the subjects ambiguity averse for gains about half was ambiguity seeking for losses, and for the 14 subjects ambiguity seeking for gains a majority was so for losses. So this provides some counter-evidence against reflection at the individual level, but weak given the small nr. of ambiguity seekers for gains. The percentages in the table do not correspond with integers (29% out of 40 is strange for instance, because 12 out of 40 is 30% and 11 of 40 is 27.5%), and there may be typos. The third experiment has only 20 subjects and only 2 ambiguity seekers for gains, and it gives no info on reflection at the individual level. correlation risk & ambiguity attitude: Section 5.5 reports relations between risk- and ambiguity attitudes. %} Ho, Joanna L.Y., L. Robin Keller, & Pamela Keltyka (2002) “Effects of Outcome and Probabilistic Ambiguity on Managerial Choices,” Journal of Risk and Uncertainty 24, 47–74. {% Use conjoint measurement to investigate how the perception of texture (“bumpiness”) and specularity (“glossiness”) affect each other. They say that they can capture interactions through a simple additive model, which I do not understand because I would say additivity means no interactions. %} Ho, Yun-Xian, Michael S. Landy, & Laurence T. Maloney (2008) “Conjoint Measurement of Gloss and Surface Texture,” Psychological Science 19, 196–204. {% According to Hammond idea of deriving subjective probabilities from willingness to bet (maybe even under linear utility, EV) is already here; free-will/determinism: seems that he has defended, here or elsewhere, “compatibilism,” meaning that free will and determinism can be combined. %} Hobbes, Thomas (1650) “Human Nature or the Fundamental Elements of Policy.” London. (New edn. 1994, with new introduction by G.A. John Rogers, Thoemmes, Bristol.) {% Behavioral responses in the Autonomic Nervous System are stronger for losses even whereas subjects do not exhibit loss aversion in decisions. %} Hochman, Guy & Eldad Yechiam (2011) “Loss Aversion in the Eye and in the Heart: The Autonomic Nervous System’s Responses to Losses,” Journal of Behavioral Decision Making 24, 140–156. {% revealed preference: using British household data, this paper tests some revealed preference conditions implied by weak order maximization, in particular negative semidefiniteness and symmetry of the Slutsky matrix. These conditions are not much violated. %} Hoderlein, Stefan (2011) “How Many Consumers Are Rational?,” Journal of Econometrics 164, 294–309. {% ordering of subsets: choice options are 0-1 functions defined on finite sets. Although the authors never even mention it, the most natural interpretation of such functions is subsets. The authors consider separability for such functions, which is the additivity condition of qualitative probability theory of de Finetti and others (not mentioned in the paper). They categorize the cases in which some sets are separable and others are not, so kinds of extensions of the Gorman (1968) results to discrete cases. P. 195 cites Gorman's theorem but forgets to mention that the sets S, T considered should not be nested. %} Hodge, Jonathan K. & Micah TerHaar (2008) “Classifying Interdependence in Multidimensional Binary Preferences,” Mathematical Social Sciences 55, 190–204. {% Seem to propose contamination. %} Hodges, Joseph L., Erich L. Lehmann (1952) “The Use of Previous Experience in Reaching Statistical Decisions,” Annals of Mathematical Statistics 23, 396–407. {% Find framing in experiment among senior managers %} Hodgkinson, Gerard P., Nicola J. Bown, A. John Maule, Keith W. Glaister, & Alan D. Pearman (1999) “Breaking the Frame: An Analysis of Strategic Cognition and Decision Making under Uncertainty,” Strategic Management Journal 10, 977–985. {% Seems to show that, with marginals given, correlation is maximal under comonotonicity. %} Hoeffding, Wassily (1940) “Masstabinvariante Korrelationstheorie,” Schriften des Mathematischen Instituts und des Instituts für Angewandte Mathematik der Universität Berlin 5, 179–233. {% What they call overconfidence is what is more often called unrealistic optimism, i.e., of 80% of people thinking that they belong to the best 10% of car drivers, etc., an alternative term that they also mention. The authors investigate the phenomenon with real incentives, which hasn’t been done much before. %} Hoelzl, Erik & Aldo Rustichini (2005) “Overconfident: Do You Put Your Money on It,” Economic Journal 115, 305–318. {% %} Hofstede, Geert (1982) “Culture's Consequences: International Differences in Work-Related Values.” Sage Publications, Beverly Hills, CA. {% %} Hölder, Otto (1901) “Die Axiome der Quantität und die Lehre vom Mass,” Berichte Verhand. König. Sächs. Gesell. Wiss. (Leipzig), Math. Phys., Classe 53, 1–64. Part I is translated into English by Joel Michell & Catherine Ernst (1996) “The Axioms of Quantity and the Theory of Measurement,” Journal of Mathematical Psychology 40, 235–252. Part II is translated into English by Joel Michell & Catherine Ernst (1997) “The Axioms of Quantity and the Theory of Measurement,” Journal of Mathematical Psychology 41, 345–356. {% Proposed Choquet integral for fuzzy measures on finite state space. %} Höhle, Ulrich (1982, January) “Integration with respect to Fuzzy Measures,” Proceedings IFAC Symposium on Theory and Application of Digital Control, New Delhi, 35–37. {% Suggests fuzzy measures as additive measures on nested sets. %} Höhle, Ulrich (1982) “A Mathematical Theory of Uncertainty.” In Ronald R. Yager (ed.) Fuzzy Sets and Possibility Theory, Pergamon Press, New York. {% %} Hoffman, Paul J. (1960) “The Paramorphic Representation of Clinical Judgment,” Psychological Bulletin 57, 116–131. {% %} Hofstee, Willem K.B. (1988) “De Empirische Discussie, Theorie van het Sociaal-Wetenschappelijk Onderzoek.” Boom, Meppel. {% %} Hofstee, Willem K.B. (1988) “Methodological Decision Rules as Research Policies: A Betting Reconstruction of Empirical Research.” In Katrin Borcherding, Berndt Brehmer, Charles A.J. Vlek, & Willem A. Wagenaar (eds.) Research Perspectives on Decision Making under Uncertainty: Basics Theory, Methodology, Risk and Applications. North-Holland, Amsterdam. {% %} Hofstee, Willem K.B. & Klaas Nevels (1981) “Do Not Take the Betting Model Literally,” Kwantitatieve Methoden 3, 70–72. {% %} Hogan, Andrew J., James G. Morris, & Howard E. Thompson (1981) “Decision Problems under Risk and Chance Constrained Programming: Dilemmas in the Transition,” Management Science 27, 698–716. {% probability elicitation Ch. 1, p. 3: indeed, it has been said that we are now living a second industrial revolution, but instead of steam, the new revolution is being propelled by information. More nice sentences %} Hogarth, Robin M. (1975) “Cognitive Processes and the Assessment of Subjective Probability Distributions,” Journal of the American Statistical Association 70, 271–289. {% %} Hogarth, Robin M. (1980) “Judgement and Choice: The Psychology of Decision.” Wiley, Chicester; 2nd edn. 1987. {% Beginning nicely points out that most models of ambiguity are normative, but the author wants to do a descriptive model. Tests Einhorn & Hogarth model of ambiguity using small probabilities; considers it in game situations, not clear on ambiguity seeking for unlikely; Camerer & Weber (1992) say they find that. reflection at individual level for ambiguity: no info on it: subjects faced only gains or only losses, or mixed. P. 32 last sentence: “; there are too many models chasing too few phenomena.” %} Hogarth, Robin M. (1989) “Ambiguity and Competitive Decision Making: Some Implications and Tests,” Annals of Operations Research 19, 31–50. {% blink decisions; gut feeling; think decisions; conscious deliberation; smink decisions; heuristic decision rule in sense of model-based decision; trink decisions; trust an expert %} Hogarth, Robin M. (2007) “Mapping the World of Decisions,” Presidential address, SPUDM 21, August 20, Warsaw, Poland. {% decreasing ARA/increasing RRA: use power utility; uncertainty amplifies risk: although I found no place where this was stated explicitly, it is throughout their model and theory. For inverse-S it is p. 786 middle, and Table 1 on p. 789 shows it. ambiguity seeking for losses?: they use only probabilities .10, .50, and .90, and don’t find very clear results for one thing because outcome curvature interferes. Their model has nonadditive probabilities depend on many things, e.g. sign and size of outcomes. risky utility u = strength of preference v (or other riskless cardinal utility, often called value): p. 780: “The view adopted here is that the value of an outcome received following a choice made under certainty does not differ intrinsically from the value of the same outcome received following a choice made under risk or uncertainty.” P. 780: “We therefore model the subjective evaluation of decision outcomes by psychophysical functions while the weights given to probabilities are conceptualized as the end result of mental processes that reflect both cognitive and motivational factors.” (cognitive ability related to likelihood insensitivity (= inverse-S)) reflection at individual level for ambiguity & reflection at individual level for risk: although they have the within-individual data for gains and losses to see it in all three experiments, they report it in none of their experiments. P. 791, Experiment 1: N = 96. Hypothetical choice. P. 791, Experiment 2: N = 146. Hypothetical choice. Experiment 3: N = 49. Real incentives; losses from prior endowment mechanism and RIS. P. 799: “However, it is important that future experimental work address the exact shape of the value function so that, without having to make a priori assumptions about either the value or the venture functions, it will be possible to attribute changes in risk attitudes to the value and venture functions as appropriate.” Well, the Tradeoff method of Wakker & Deneffe (1996) shows how to elicit value function properties! inverse-S; Risk averse for gains, risk seeking for losses: Table 2 on p. 792 suggests some more risk aversion for gains than risk seeking for losses. Table 4 on p. 795 suggests the same for large outcomes, but the opposite for small outcomes. risk seeking for symmetric fifty-fifty gambles: Table 4 suggests this strange risk seeking for fifty-fifty gambles. There is much risk seeking for small outcomes, probably because they were cents so that the Utility of gambling may have caused this. Real incentives: experiments 1 and 2 used hypothetical payments, experiment 3 used real incentives: random incentive system. losses from prior endowment mechanism: do this. real incentives/hypothetical choice: find small differences between real and hypothetical choices for gains, but large differences for losses. I guess that this may be because for losses they did (as always) from prior endowment mechanism. For real incentives they find more statistical power than for hypothetical choice. P. 800: the coexistence of gambling and insurance can be explained by the overweighting of small probabilities. P. 797: no clear relations between risk attitude and ambiguity attitude (correlation risk & ambiguity attitude). %} Hogarth, Robin M. & Hillel J. Einhorn (1990) “Venture Theory: A Model of Decision Weights,” Management Science 36, 780–803. {% Exactingness: the degree to which one is punished for suboptimal decisions %} Hogarth Robin M., Brian J. Gibbs BJ, Craig R.M. McKenzie, & Margareth A. Marquis (1991) “Learning from Feedback: Exactingness and Incentives,” Journal of Experimental Psychology, Learning, Memory and Cognition 17, 734–752. {% inverse-S: they find that for losses; i.e., ambiguity aversion for unlikely losses and seeking for likely losses. They find more inverse-S for ambiguity than for chance (uncertainty amplifies risk). So also: ambiguity seeking for losses; They study losses and there they find reflection, in accordance with what PT predicts, see above. reflection at individual level for ambiguity: they have only losses, so no results on this. They asked what is a reasonable premium for p-prob at losing $100,000, for various probabilities. They also cite market evidence (earth-quake insurance, flood-insurance, etc.) suggesting much ambiguity aversion for small-prob losses. %} Hogarth Robin M. & Howard C. Kunreuther (1985) “Ambiguity and Insurance Decisions,” American Economic Review, Papers and Proceedings 75, 386–390. {% PT: data on probability weighting; ambiguity seeking for losses & ambiguity seeking for unlikely: they consider losses and there the data confirm all the hypotheses of Tversky & Wakker (1995) perfectly well. reflection at individual level for ambiguity: does not speak to that because only losses. inverse-S: there is risk aversion for small probabilities and risk seeking for high (not stated explicitly in the paper I think, but visible in Table 2, Fig. 2, Tables 4 and 5) (Z&Z!). (uncertainty amplifies risk) These phenomena are amplified for ambiguity, by ambiguity aversion for small probabilities and ambiguity seeking for high. (Note that only the consumer data are relevant. The “firm” data consider selling of insurance which means both gains and losses, and loss aversion being relevant. As expected by PT, there more risk aversion etc. is indeed found.) Unfortunately, the data for ambiguous probabilities may be prone to distortion by regression to the mean, which can be an alternative explanation of the overestimation of small ambiguous probabilities and understimation of high ambiguous probabilities. I do not understand the analysis in §3.4, in particular why M(p) + M(1p) = 1 on page 18. If p and 1p are ambiguous and subject to second-order distributions, they may, as mentioned by the authors, differ from their “anchor values.” The participants, however, need not know that these referred to complementary events and may distort both downwards. real incentives/hypothetical choice: they use hypothetical choice, and discuss it nicely on p. 13 penultimate para. %} Hogarth, Robin M. & Howard C. Kunreuther (1989) “Risk, Ambiguity, and Insurance,” Journal of Risk and Uncertainty 2, 5–35. {% ambiguity seeking for losses; ambiguity seeking for unlikely: ambiguity aversion for unlikely losses: consider only small probability (.001, .01, .1) losses, and there they find risk aversion, the more so as the probabilities are smaller. The result is amplified under ambiguity (uncertainty amplifies risk), that may however have been biased by regression to the mean. For price setting of professional actuaries aspects other than ambiguity attitude, such as asymmetric information and avoidance of winner’s curse (p. 38) can play a role. reflection at individual level for ambiguity: only losses so do not speak to that. %} Hogarth, Robin M. & Howard C. Kunreuther (1992) “Pricing Insurance and Warranties: Ambiguity and Correlated Risks,” Geneva Papers on Risk and Insurance Theory 17, 35–60. {% Study cases in which not only probabilities but also outcomes are ambiguous/unknown. Ask subjects about heuristics used. Known/unknown firms that sell VCRs etc. enhances contrast effect. Only small probabilities. Nice (also done by Heath & Tversky 1991 and Zeckhauser 2006): p. 32 explains that they ask subjects to estimate unknown probabilities, and then later use objective known probabilities equal to those, so as to avoid the problem of ambiguity being confounded with belief effects, for which some earlier studies were criticized by Heath & Tversky (1991). reflection at individual level for ambiguity: only losses so do not speak to that. %} Hogarth, Robin M. & Howard C. Kunreuther (1995) “Decision Making under Ignorance: Arguing with Yourself,” Journal of Risk and Uncertainty 10, 15–36. {% Sent messages to students on arbitrary time points, asking them for risk perceptions. Mostly, it concerned loss of time or physical injuries. gender differences in risk attitudes: women did not assess losses of risk as bigger than men, but did consider them more probable. %} Hogarth, Robin M., Mariona Portell, & Anna Cuxart (2007) “What Risks Do People Perceive in Everyday Life? A Perspective Gained from the Experience Sampling Method (ESM),” Risk Analysis 27, 1427–1439. {% real incentives/hypothetical choice %} Hogarth, Robin M. & Melvin W. Reder (1987, eds.) “Rational Choice: The Contrast between Economics and Psychology.” University of Chicago Press. {% Seems that: real incentives/hypothetical choice: for time preferences; random incentive system; Delays of 1 day, 1 week, and 2 weeks; immediate reward was $5 or $17; interest rates of 1.5% a day or 3.0% a day for calculating the delayed reward. They find that stationarity is not violated, but increasing the interval between payments invites more subjects to choose the delayed payment. (decreasing/increasing impatience) %} Holcomb, James H., & Paul S. Nelson (1992) “Another Experimental Look at Individual Time Preference,” Rationality and Society 4, 199–220. {% probability elicitation. Measure beliefs using quadratic scoring rule, matching probabilities, and introspection. Matching probabilities is best, introspection a close second, and QSR is clearly last. For the QSR, subjects get tables with the many numbers indicating the various payments. I did not find how incentive compatibility was explained to the subjects and probably it was left to the subjects. They did not use the term probability when explaining the QSR to subjects. They measure belief in correctness of past guess but also use a perceptual task. %} Hollard, Guillaume, Sébastien Massoni, & Jean-Christophe Vergnaud (2016) “In Search of Good Probability Assessors: An Experimental Comparison of Elicitation Rules for Confidence Judgments,” Theory and Decision 80, 363–387. {% Gives arguments for random incentive system %} Holler, Manfred J. (1983) “Do Economics Students Choose Rationally? A Research Note,” Social Science Information 22, 623–630. {% Puts forward a potential theoretical problem for the random incentive system. Starmer & Sugden (1991, AER), Cubitt, Starmer, & Sugden (1998, ExEc), and others subsequently showed that these problems do not arise empirically. The random system is today (2004) the most popular and almost exclusively used system of real incentives for individual choice, mostly because it avoids income and house money effects. A strange text on p. 514: ”It is well known that many individuals make choices that are direct violations of the independence axiom in other contexts. Therefore any theory of rational choice in such contexts must be derived from a set of axioms that does not include or imply the independence axiom, at least not in its usual “strong” form.” [Italics from original] This seems to use descriptive evidence to argue for a normative model?? %} Holt, Charles A. (1986) “Preference Reversals and the Independence Axiom,” American Economic Review 76, 508–513. {% §30.5: for event A with unknown probability, determines the “matching probability” p (without using this term), i.e., the probability p such that (A:x) ~ (p:x), through the BDM (Becker-DeGroot-Marschak) mechanism as follows. The subject chooses a number p for A. So as to give an incentive for truly giving the p satisfying the equivalence just mentioned, a BDM mechanism is used: first a prospect (j/100:x) is chosen randomly, by randomly choosing a number 1 j 100. Then the subject gets this lottery if j/100 > p, and (A:x) if j/100 p. %} Holt, Charles A. (2007) “Markets, Games, & Strategic Behavior.” Addison-Wesley, London. {% %} Holt’s 2000 annotated bibliography {% Throughout equate risk aversion with utility curvature, as commonly done in economics, which assumes expected utility. This I regret. For stakes below two month’s salary, utility is close to linear, and any risk aversion found is better explained by other factors such as loss aversion and probability weighting. This paper has often been mis-cited (e.g., by Harrison & List 2004 p. 1031) as refuting the argument against real incentives that big stakes cannot be implemented, by interpreting the stakes of this experiment as big. This is not so. Stakes of some hundreds of dollars are small. No-one would do a decision analysis for those. For such amounts, below two month’s salary, utility is close to linear. Whatever risk aversion is found there is due to probability weighting, loss aversion, numerical sensitivity, and other factors, but it does not reflect changes of marginal utility. Big stakes are when buying a house, a car, deciding on mastectomy to avoid risk of breast cancer, etc. decreasing ARA/increasing RRA: is found. The paper points out that literature on auctions commonly assumes log/power utility. Choosing between lotteries (p, 2.00; 1.60) and (p, 3.85; 0.10) for p = 1/10, 2/10, ..., 1. These were low payoffs. Also for 20 times higher payoffs, the high payoffs. So real payments up to $77. (Also 50 and 90 times higher for 19 and 18 participants, respectively.) So main group has 20 x 3.85 = $77 as highest possible prize, and the 19/18 participants have 50 x 3.85 = $192.50 and 90 x 3.85 = $346.50 as maximum outcomes. 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