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PT: data on probability weighting
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PT: data on probability weighting; This paper was the first to introduce the basic ideas of source dependence (a term not yet used in this paper) into ambiguity. It is great to see these valuable ideas expressed. Unfortunately, the experiments are not good, having too many confounds, and not being incentive compatible. Tversky & Kahneman (1992) mention the concept source and do use the term, but do not elaborate much on it. Hence I usually cite Tversky & Fox (1995) for it. This paper still keeps things narrow by having source dependence driven by competence. There can be many other factors. P. 6 ll. 6-7: point out that ambiguity had better be called vagueness. P. 6: cites Raiffa (1961) affirmatively on the irrationality of ambiguity: “Several authors, notably Ellsberg (1963), maintain that aversion to ambiguity can be justified on normative grounds, although Raiffa (1961) has shown that it leads to incoherence.” It shows that Tversky considered expected utility to be rational. One can discuss Raiffa’s arguments, primarily because it implicitly assumes dynamic decision priniciples à la Hammond(1988) that are known to imply EU, and that are questioned by nonEUers (although not by me Bayesian). P. 6 penultimate para points out that comparing known to unknown probabilities is limited, and that comparisons beyond objective probabilities have not been found in the literature. It pleas for studying natural events rather than Ellsberg urns. P. 7 bottom explains competence effect as an irrational carrying-over from other situations. Suggests that it is more motivational than cognitive. Then suggests that experts can augment credit after good decision, and reduce blame, suggesting that judgments by others (or other part of the self) is what drives these things. P. 9 first full para suggests that Ellsberg might be due to difference between pre- and post-diction. Throughout Tversky’s writings one sees he does not believe that the Ellsberg paradox says something substantial about uncertainty/ambiguity attitude. Experiment 1 asks for judged probabilities and than matches those with objective probabilities, which is a way to control for beliefs when studying ambiguity. (It is not manipulation-proof if known ahead.) Subjects betted both on events and on their complements (source-preference directly tested). Part of the subjects were paid for real. They use the term regression hypothesis, referring to Einhorn & Hogarth, for what I now call likelihood insensitivity or inverse-S. For high probability judgments subjects prefer to bet on the ambiguous events, which is explained by competence. Experiment 5 also considers bets on events and on their complements, but does so between subjects. P. 22 near bottom: points 1 and 2 are similar to the separation between probabilistic sophistication and expectation maximization. P. 23 l. 8 ff. has a nice sentence: under the standard interpretation of the Bayesian theory, the two concepts coincide. As we go beyond this theory, however, it is essential to distinguish between the two. Section 2.1 criticizes Einhorn & Hogarth studies for not properly controlling for belief when studying ambiguity (p. 26 l. 3: “a regressive shift in the perception of probability”. %} Heath, Chip & Amos Tversky (1991) “Preference and Belief: Ambiguity and Competence in Choice under Uncertainty,” Journal of Risk and Uncertainty 4, 5–28. {% Dutch book etc. %} Heath, David, David A. Lane, & William D. Sudderth (1972, 1978, 1985, 1989, JRSSB (1980). {% %} Heaton, John & Deborah Lucas (1997) “Market Frictions, Savings Behavior, and Portfolio Choice,” Macroeconomic Dynamics 1, 76–101. {% Takes some journal on risk and insurance, and gives tables of authors who published most there. In the list of the three elite journals (JRU, Geneva Risk and Insurance Review, and Journal of Risk and Insurance) 1984 – 2013 I have a 7th place. %} Heck, Jean (2013) “The Most Prolific Contributing Authors to the Leading Risk Management and Insurance Journals: 1984-2013,” working paper. {% Empirical tests of bargaining solutions %} Heckathorn, Douglas D. (1978) “A Paradigm for Bargaining and a Test of Two Bargaining Models,” Behavioral Science 23, 73–85. {% Empirical tests of bargaining solutions %} Heckathorn, Douglas D. (1980) “A Unified Model for Bargaining and Conflict,” Behavioral Science 25, 261–284. {% %} Heckerling, Paul S., Marion S. Verp, & Teresa A. Hadro (1994) “Preferences of Pregnant Women for Amniocentesis or Chronic Villus Sampling for Prenatal Testing: Comparison of Patients’ Choices and Those of a Decision-Analytic Model,” Journal of Clinical Epidemiology 47, 1215–1228. {% intuitive versus analytical decisions; Test whether intuitive choices of women for a prenatal test agree more with decision analysis based on their own value assessments or on physicians’ value assessments, and to what extent that provides arguments for desirability yes-or-no of more autonomy. I disagree with their main discussions and conclusions because they assume that decision rules should agree as much as possible with intuitive natural choice. The latter is the case only for descriptive purposes but not at all for prescriptive purposes, as already Raiffa (1961, p. 690/691) explained nicely. %} Heckerling, Paul S., Marion S. Verp, & Nancy Albert (1999) “Patient or Physician Preferences for Decision Analyis: The Prenatal Genetic Testing Decision,” Medical Decision Making 19, 66–77. {% expert systems, medical, using Bayesian methods; compare Hanson; contains discussion of certainty-factor, belief functions, etc. %} Heckerman, David E., Eric J. Horvitz, & Bharat N. Nathwani (1992) “Toward Normative Expert Systems: Part I The Pathfinder Project,” Methods of Information in Medicin 31, 90–105. {% Argue against representative-agent assumption, and for importance of heterogeneity. %} Heckman, James J. (2001) “Micro Data, Heterogeneity, and the Evaluation of Public Policy: Nobel Lecture,” Journal of Political Economy 109, 673–748. {% Dutch book: discusses relations between beliefs and decision making. End of §3 discusses Schmexpected utility, which is expected utility minus any assumption on the probability numbers. %} Hedden, Brian (2013 “Incoherence without Exploitability,” Noûs 47, 482–495. {% %} Hedrich, Reiner (2007) “The Internal and External Problems of String Theory: A Philosophical View,” Journal for General Philosophy of Science 38, 261–278. {% First saw this presented at the ZIF-Bielefeld on May 18, 2000. Assumes that society starts with subjective probabilities for each individual. At each next time point, people update their probabilities by mixing with subjective probabilities of others. People with similar subjective probabilities are incorporated, those with probabilities more different than some -distance, are ignored as too different. Then simulations demonstrate how the viewpoints of society develop. Depending on the weights assigned to others’ subjective probabilities, and , society converges to one common viewpoint, or to two extreme viewpoints, or to other things. Nice graphs illustrate this development. This nice work could be in prominent general-public journals, on tv, etc. %} Hegselmann, Rainer & A Flache (1998) “Understanding Complex Social Dynamics—A Plea for Cellular Automata Based Modelling,” Journal of Artificial Societies and Social Simulation 1, no. 3. {% %} Heidhues, Paul & Koszegi Botond (2010) “Exploiting Naivite about Self-Control in the Credit Market,” American Economic Review 100, 2279–2303. {% common knowledge; readable version of Mertens & Zamir (1985) %} Heifetz, Aviad (1993) “The Bayesian Formulation to Incomplete Information - The Non-Compact Case,” International Journal of Game Theory 21, 329–338. {% %} Heil, Sara H., Jennifer W. Tidey, Heather W. Holmes, & Stephen T. Higgins (2003) “A Contingent Payment Model of Smoking Cessation: Effects of Abstinence and Withdrawal,” Nicotine and Tobacco Research 5, 205–213. {% Dutch book; nice refs. P. 337 gives an example of !two! book makers for a boat race in 1971 who offered different odds so that a clever client could make book against these two book makers. %} Heilig, Klaus (1978) “Carnap and de Finetti on Bets and the Probability of Singular Events: The Dutch Book Argument Reconsidered,” British Journal for the Philosophy of Science 29, 325–346. {% %} Heilman, Conrad & Peter P. Wakker (2017) Interview, The Reasoner 11, 26–29. {% %} Heinemann, Frank, Rosemarie Nagel, & Peter Ockenfels (2004) “The Theory of Global Games on Test: Experimental Analysis of Coordination Games with Public and Private information,” Econometrica 72, 1583–1600. {% probability elicitation: applied to experimental economics. Imagine the 2-player game where each can choose safe (A) or risky (B), with payoffs, for some parameter 0 < x < 15 A B A xx x0 B 0x 1515 The notation A, B is used in the paper. It is a coordination game. If both go risky, they gain. There are two pure NE (Nash equilibria), (A,A) and (B,B). The randomized NE is ((15x)/15: A, x/15: B) for both players. Note that it has the counterintuitive property of decreasing probability of choosing the safe x as x increases. It is symmetric but not stable. All NE are symmetric, so conceivable if both players are chosen randomly from one “uniform/symmetric” population. The authors measure for several values of x whether players prefer A or B. Unsurprisingly, increasing the safe x decreases willingness to choose the risky B. The authors consider variations with N > 2 players and a minimum of k B choices needed to get the reward 15 for all who entered (and 0 for the enterers if too few entered), but default below is that I consider only the two-player version. For each player, the switching value x is called the certainty equivalent (CE) of the player for the game. This is an unconventional interpretation because x itself is part of the definition of the game. With increasing x the probability of sufficiently many others choosing B will decrease, affecting the optimal strategy in the game, as the authors point out in some places (e.g. p. 213 just above the displayed formula “when the alternative safe payoff from A is Xc”). The authors also measure CEs, conventional now, of lotteries (p:15, 1p:0), for various parameters p. If a lottery (p:15, 1p:0) and a game with parameter x have the same CE, and if (subjective) expected utility is assumed (also for the game, and with the same utility function U always (U player-dependent)), then it does follow that p is the subjective probability of an opponent choosing B in the game with x, even if x is not a CE in a conventional manner. So, p is a matching probability in this sense. This method of measuring CEs and matching probabilities cannot be applied very generally because of the unconventional nature of CE x (contrary to the authors’ suggestion of generality in the final para on p. 219), but here it works. One restriction is, for instance, that the authors can derive the CE only for games that have a sure constant as option, where that constant furthermore has to be exactly the CE. I just derived the matching probability from a kind of transitivity which, in fact, could do without the assumption of EU. The authors, instead, assume EU and derive a utility function U from the risky CEs, which they then use to derive matching probabilities and so on for the game. P. 189 penultimate para discusses this, mentioning that they want to measure risk attitude also. Unlike my transitivity reasoning, the authors’ derivation will be distorted by violations of EU. I would interpret the matching probability as capturing ambiguity attitude + beliefs, rather than only beliefs. Working with SEU, the authors suggest, following some other economists, that, the moment subjective probabilities have been assigned, the case is (like) decision under risk. In the source method for ambiguity that I like to work with, this is not so, and there can be different ambiguity attitudes in the game for instance than for the risky lotteries (where it is ambiguity neutrality), even though there are subjective probabilities describing beliefs in the game. Pp. 189-190 argues that a separate measurement of belief (with an extraneous parameter not part of the (definition of) the game) has the problem of income effect and even influencing the game. P. 213 l. 4/5 reiterates the point. But, procedures have been developed to avoid this, involving that randomly only the game or the belief measurement is implemented. Belief only concerns what the opponent will do, something a player cannot influence. P. 191 4th para writes that, in sessions where beliefs were measured with proper scoring rules, the authors payed both for one randomly chosen game and for one randomly chosen belief measurement. The authors find plausible results when x, k, or N are varied. Page 182 3rd para (& p. 213 3rd para from below) describe how small probabilities are overestimated and high ones are underestimated (comparing derived subjective probabilities to percentages of subjects choosing B). This confirms likelihood insensitivity (ambiguity seeking for unlikely). Pp. 182-183 discuss the application of individual risk theory to game theory. (game theory can/cannot be seen as decision under uncertainty). They take strategic uncertainty as a case of ambiguity (they call it endogenous uncertainty), relating it to Knight (1921). P. 213, the derivation in §7.1 could be simplified by normalizing U(0) = 0, U(15) = 1. Some steps in the analysis I did not understand, where I conjecture typos. P. 216 3rd para points out that altruism/social preferences could lead to more willingness to play B, and overestimation of probabilities. %} Heinemann, Frank, Rosemarie Nagel, & Peter Ockenfels (2009) “Measuring Strategic Uncertainty in Coordination Games,” Review of Economic Studies 76, 181–221. {% Don’t come all the way to preference axiomatizations, but list many qualitative criteria that come close. %} Heink, Ulrich & Ingo Kowarik (2010) “What Criteria Should Be Used to Select Biodiversity Indicators?,” Biodiversity and Conservation 19, 3769–3797. {% The smaller the subjective life expectancy of subjects relative to the long-time-duration offered in TTO, the more willing they are to trade off life years to gain health quality. %} Heintz, Emelie, Marieke Krol, & Lars-Ake Levin (2013) “The Impact of Patients’ Subjective Life Expectancy on Time Tradeoff Valuations,” Medical Decision Making 33, 261–270. {% %} Heisenberg, Werner (1930) “The Physical Principles of the Quantum Theory,” (Translated into English by Carl Eckart & Frank C. Hoyt). Dover Publications, New York. {% P. 158 about indeterminacy of location/momentum of particle (Heisenberg’s uncertainty principle). Related is Bohr’s principle of complementarity: two quantities are complementary if measurement of one excludes measurement of the other. %} Heisenberg, Werner (1959) “Physics and Philosophy,” London. {% %} Hek, Paul de & Santanu Roy (2001) “On Sustained Growth under Uncertainty,” International Economic Review 42, 801–813. {% conditional probability; foundations of statistics; about theorem of Birnbaum %} Helland, Inge S. (1995) “Simple Counterexamples against the Conditionality Principle,” American Statistician 49, 351–356. {% For brightness, heat, etc., people are more sensitive towards changes from adapted levels than to absolute levels. %} Helson, Harry (1964) “Adaptation Level Theory: An Experimental and Systematic Approach to Behavior.” Harper and Row, New York. {% %} Hellman, Ziv (2007) “An Imprecise Day at the Races,” in preparation; the Shalem Center, Jerusalem, Israel. {% Z&Z; propitious selection is opposite of adverse selection %} Hemenway, David (1990) “Propitious Selection,” Quarterly Journal of Economics 105, 1063–1069. {% Seems to distinguish between fundamental and derived measurement. %} Hempel, Carl G. (1952) “Fundamentals of Concept Formation in Empirical Science.” University of Chicago Press, Chicago. {% Describes Semmelweis’ famous empirical investigation into childbed fever, done in the 1840s in Vienna. %} Hempel, Carl G. (1966) “Philosophy of Natural Science.” Prentice-Hall, Englewood Cliffs, NJ. {% Finds that PT can well accommodate the disposition effect. %} Henderson, Vicky (2012) “Prospect Theory, Liquidation, and the Disposition Effect,” Management Science 58, 445–460. {% dynamic consistency: Ebert & Strack (2015 AER) presented a model in which prospect theory maximizers always continue gambling. This paper adds the possibility to randomize, defines everything formally, and then shows that verything changes, where agents can stop. %} Henderson, Vicky, David Hobson, & Alex S.L. Tse (2017) “Randomized Strategies and Prospect Theory in a Dynamic Context,” Journal of Economic Theory 168, 287–300. {% Did things similar to Jaffray (1989). %} Hendon, Ebbe, Hans-Jörgen Jacobsen, Birgitte Sloth, & Torben Tranaes (1994) “Expected Utility with Lower Probabilities,” Journal of Risk and Uncertainty 8, 197–216. {% %} Hendon, Ebbe, Hans-Jörgen Jacobsen, Birgitte Sloth, & Torben Tranaes (1996) “The Product of Capacities and Belief Functions,” Mathematical Social Sciences 32, 95–108. {% %} Hendon, Ebbe, Hans-Jörgen Jacobsen, & Birgitte Sloth (1996) “The One-Shot-Deviation Principle for Sequential Rationality,” Games and Economic Behavior 12, 274–282. {% Opens with describing societies where it is believed that young boys should fellate and drink semon so as to achieve manhood. Weird means Western educated, industrialized, rich, and democratic. The authors give many examples where the weird subjects are very different than other people. The authors exaggarate negatively: “are among the least representative populations one could find” (abstract). End of §61: except for students, most people punish/reject hyper-fair offers in the ultimatum game. Pp. 83-135 provide comments by others. The weird subjects may, even if not very representative, be very interesting. Thus I agree with Rozin’s reply on p. 108 ff. They are in the presently dominant society in the world, disseminating its culture through tv and so on more than any other culture. P. 93, answer by Gaertner et al., is the silly thing of researchers saying that all is wrong that does not study their particular small topic of specialization. Commentary by Maryanski on p 103 ff. rightly points out that the authors exaggarate. %} Henrich, Joseph, Steven J. Heine, & Ara Norenzayan (2010) “The Weirdest People in the World?,” Behavioral and Brain Sciences 33, 61–135. {% Let farmers in rural areas in Chili, and UCLA undergrads, choose between risky prospects (one nonzero outcome) and their expected values. Expectations of prospects were about 1/3 day’s salary. Probabilities were 0.05, .020, .050, 0.80. The farmers were very risk seeking. real incentives/hypothetical choice: all choices were first administered, and then ALL were played out for real. Hence, there will have been income effects and, in view of law of large numbers, all prospects will have been about indifferent. For these reasons, the data are not very interesting other than for an explicit study of repeated choice. The undergrads were risk averse for 0.05 and 0.20, risk neutral for 0.80, and very risk seeking for 0.50 [risk seeking for symmetric fifty-fifty gambles]. When asked about latter, undergrads said things such as “It’s a good chance” or “it’s fair.” These data go against the fourfold pattern of inverse-S. %} Henrich, Joseph & Richard Mcelreat (2002) “Are Peasants Risk-Averse Decision Makers?,” Current Anthropology 43, 172–181. {% %} Henrion, Max, Ross D. Shachter, Laveen N. Kanal, & John F. Lemmer (1990, eds.) “Uncertainty in Artificial Intelligence 5’,” North-Holland, Amsterdam. {% %} Hens, Thorsten (1992) “A Note on Savage’s Theorem with a Finite Number of States,” Journal of Risk and Uncertainty 5, 63–71. {% one-dimensional utility %} Herden, Gerhard (1995) “On Some Equivalent Approaches to Mathematical Utility Theory,” Mathematical Social Sciences 29, 19–31. {% one-dimensional utility; Generalize Debreu topological-separability conditions. %} Herden, Gerhard & Vladimir L. Levin (2012) “Utility Representation Theorems for Debreu Separable Preorders,” Journal of Mathematical Economics 48, 148–154. {% equity-versus-efficiency: seems to be on it %} Herne, Kaisa & Maria Suojanen (2004) “The Role of Information in Choices over Income Distributions,” The Journal of Conflict Resolution 48, 173–193. {% conservation of influence: citation from Keynes (1921, p. 307): “There is nothing more profitable for a man than to take good counsil with himself; for even if the event turns out contrary to one’s hope, still one’s decision was right, even though fortune has made it of no effect.: whereas if a man acts contrary to good council, although by luck he gets what he had no right to expect, his decision was not any the less foolish.” %} Herodotus vii. 10. {% %} Herrmann, Andreas, Rüdiger von Nitzsch, & Frank Huber (1998) “Referenzpunktbezogenheit, Verlustaversion und Abnehmende Sensitivität bei Kundenzufriedenheitsurteilen,” Zeitschrift für Betriebswirtschaft 11, 1225–1243. {% cognitive ability related to risk/ambiguity aversion: Test Allais paradox (common ratio) in poor rural area, in North-East Thailand. Find 54% doing violation of EU, which is some more than usually found. This between-study comparison suggests that poor people commit Allais more. Within-study comparisons: Allais violation of EU is enhanced by: lack of ability (poor education, unemployment, little financial education), general instrospective-questionnaire risk seeking, general instrospective-questionnaire optimism, violation of Tversky-Kahneman-Birnbaum type of stochastic dominance. Not affected by gender or age. math-related cognitive ability and memory-verbal cognitive ability have 0.37 correlation (p. 145).. %} Herrmann, Tabea, Olaf Hübler, Lukas Menkhoff, & Ulrich Schmidt (2017) “Allais for the Poor: Relations to Ability, Information Processing, and Risk Attitudes,” Journal of Risk and Uncertainty 54, 129–156. {% %} Herrnstein, Richard J. (1961) “Relative and Absolute Strength of Response as a Function of Frequency of Reinforcement,” Journal of the Experimental Analysis of Behavior 4, 267–272. {% information aversion, w.r.t. AIDS testing or Huntington’s disease (I don’t know which) %} Herrnstein, Richard J. (1990) “Rational Choice Theory: Necessary, but Not Sufficient,” American Psychologist 45, 356–367. {% %} Herrnstein, Richard J., George F. Loewenstein, Drazen Prelec, & William Vaughan, Jr. (1993) “Utility Maximization and Melioration: Internalities in Individual Choice,” Journal of Behavioral Decision Making 6, 149–185. {% %} Herrnstein, Richard J. & Drazen Prelec (1991) “Melioration: A Theory of Distributed Choice,” Journal of Economic Perspectives 5 no. 3, 137–156. {% Use the well known Ellstein et al. (1986, AJM, on estrogen) to, nicely, illustrate current issues in decision theory. Download 7.23 Mb. Share with your friends:
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