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risky utility u = transform of strength of preference v, latter doesn
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risky utility u = transform of strength of preference v, latter doesn’t exist. P. 406, middle: “It is not at all clear to me what the outside source of information about marginal utility is, ” P. 406, last para: “a concept used in the interpretation of observable phenomena has no meaning independently of the operations specified for measuring it.” P. 409: “Science is science and ethics is ethics; it takes both to make a whole man;” %} Friedman, Milton (1955) “What All Is Utility?,” Economic Journal 65, 405–409. {% A classic paper. Posit utility function that has convex regions, so that EU can explain the simultaneous existence of gambling and insurance. Markowitz (1952) discussed that their utility curve makes many wrong empirical predictions. F&S themselves also pointed out such predictions, not yet knowing they are wrong but saying they are things to be tested. See the comments on their pages 282/301 below. The authors argue that the common thinking has been that marginal riskless utility is meaningful, that it is diminishing, and that the expectation of this utility is to be maximized under risk (EU), which implies universal risk aversion. They argue that this reasoning is incorrect because, first, marginal riskless utility is not meaningful anyhow and, second, if it were, it need not be vNM utility. Therefore, their partly convex vNM utility does not violate the intuition of diminishing riskless marginal utility. P. 282 says about their conjectured utility function that it has predictions beyond the phenomena considered and then, very appropriately, “Further empirical work should make it possible to determine whether or not these implications conform to reality.” P. 282 seems to write (utility = representational?) “asserts that individuals behave as if they calculated and compared expected utility and as if they knew the odds...the validity of this assertion does not depend on whether individuals know the precise odds, much less on whether they say that they calculate and compare expected utilities or think that they do, or whether psychologists can uncover any evidence that they do, but solely on whether it yields sufficiently accurate predictions about the class of decisions with which the hypothesis deals” P. 301 indicates, correctly, that their curve predicts risk seeking for small gambles at specific levels of wealth. That this does not hold has later been taken as empirical refutation of their utility function. So, F&S themselves very correctly pointed out a critical test of their theory. P. 283 cites Vickrey who identifies marginal utility with vNM utility in a critical manner. P. 298 gives nice description of EU as an as-if model. !not! risky utility u = strength of preference v (or other riskless cardinal utility, often called value) because they assume that riskless utility is only ordinal and not cardinal; the famous paper; one of the early papers to state that risk aversion iff u concave, referring to Marshall for it. %} Friedman, Milton & Leonard J. Savage (1948) “The Utility Analysis of Choices Involving Risk,” Journal of Political Economy 56, 279–304. {% A verbose discussion of Baumol’s (1951) reaction, and a correction of a mathematical mistake in the EU derivation in their 1948 paper (I think that they only used betweenness and not full-force vNM independence there). This paper seems to have been the first to formulate the sure-thing principle. About it, p. 468: “practically unique among maxims for wise action in the face of uncertainty, in the strength of its intuitive appeal. The principle is universally known and recognized; and the Greeks must surely have had a name for it, though current English seems not to”. At a young age I was puzzled by this claim, until Peter Fishburn pointed out to me that they wrote this tongue-in-cheek. %} Friedman, Milton & Leonard J. Savage (1952) “The Expected Utility Hypothesis and the Measurability of Utility,” Journal of Political Economy 60, 463–474. {% utility elicitation?; decreasing ARA/increasing RRA: seem to criticize, on p. 901, Arrow’s conjecture of increasing RRA. Seem to estimate, based upon portfolio holdings of individuals, that the index of RRA is about 2, so power 1. %} Friend, Irwin & Marshall E. Blume (1975) “The Demand for Risky Assets,” American Economic Review 65, 900–922. {% anonymity protection %} Frigg, Roman (2004) “In What Sense is the Kolmogorov-Sinai Entropy a Measure for Chaotic Behaviour? - Bridging the Gap between Dynamical Systems Theory and Communication Theory,” British Journal for the Philosophy of Science 55, 411–434. {% suspicion under ambiguity: p. 153 seems to say that people need ambiguity aversion because that’s rational in game situations. People transfer a heuristic which is helpful in many natural situations --- to other situations in which their fears are unfounded. Sometimes called the hostile nature hypothesis (Curley, Yates, & Abrams 1986). Seem to have been first to conjecture that ambiguity avoidance is driven by the salience of missing information. %} Frisch, Deborah & Jonathan Baron (1988) “Ambiguity and Rationality,” Journal of Behavioral Decision Making 1, 149–157. {% P. 47: SEU as an as if model versus SEU as a process model. %} Frisch, Deborah & Robert T. Clemen (1994) “Beyond Expected Utility: Rethinking Behavioral Decision Research,” Psychological Bulletin 116, 46–54. {% strength-of-preference representation; May have been first, together with Pareto, to define strength of preference. %} Frisch, Ragnar (1926) “Sur un Problème d’Economie Pure,” Norsk Matematisk Forenings Skrifter Serie 1 16, 1–40. Translated into English by John S. Chipman, “On a Problem in Pure Economics.” In John S. Chipman, Leonid Hurwicz, Marcel K. Richter, & Hugo F. Sonnenschein (1971, eds.) Preferences, Utility, and Demand, Ch. 19, Hartcourt, New York. {% Obtains cardinal utility by imposing additive decomposability %} Frisch, Ragnar (1932) “New Methods of Measuring Marginal Utility,” Beiträge zur Ökonomischen Theorie 3 (Tübingen 1932); Henri Schultz, The Theory and Measurement of Demand, pp. 111–117. {% %} Frisch, Ragnar (1937) “General Choice-Field Theory.” In Report of Third Annual Research Conference on Economics and Statistics, Cowles Commision for Research in Economics, 64–69. {% Law invariance means decision under risk (acts are completely determined by their generated probability distribution over outcomes). They take the representing functional as primitive, as this is common in the theory of risk measures, and derive some results for convexity. %} Frittel, Marco & Emanuela Rosazza Gianin (2005) “Law Invariance Convex Risk Measures,” Advances in Mathematical Economics 7, 33–46. {% risky utility u = strength of preference v (or other riskless cardinal utility, often called value).: seems to open with: “In this paper, preferences or utilities refer to levels of subjective satisfaction, distress, or desirability that people associate with a particular health state.” %} Frohberg, Debra G. & Robert L. Kane (1989) “Methodology for Measuring Health State Preferences,” Journal of Clininal Epidemiology 42, 345–354, 459–471, 585–592, 675–685. {% Conservation of influence: below follows a famous poem. One can recognize decision theory principles. The choice of the less trodden road can be taken as a plea for ambiguity seeking (: why not?). The one taken having the better claim but still being essentially equivalent in every respect can be taken as lexicographic preference. The justification of the choice in retrospect (if the last line can be interpreted this way, which is debatable) can be taken as cognitive dissonance. The last sentence can also be taken as definition of influence (conservation of influence), with “all the difference” taken as identifying the decision maker with his actions. Nice is that “sigh” and “all the difference” can equally well be positive as negative. The title refers to the essential role of counterfactuals in analyzing preferences, decisions, and free will, which distinguishes social sciences from natural sciences. The Road Not Taken TWO roads diverged in a yellow wood
Then took the other, as just as fair And having perhaps the better claim Because it was grassy and wanted wear Though as for that the passing there Had worn them really about the same; And both that morning equally lay In leaves no step had trodden black. Oh, I kept the first for another day! Yet knowing how way leads on to way I doubted if I should ever come back. I shall be telling this with a sigh Somewhere ages and ages hence: Two roads diverged in a wood, and I— I took the one less traveled by And that has made all the difference. %} Robert Frost (1920) “The Road Not Taken” {% The more risk dependence, the higher in the convex ordering. Probably something like second-order risk aversion. Mrl (mean residual life) ordering seems to generalize it. Refer to Dhaene & Goovaerts and others. %} Frostig, Esther (2006) “On Risk Dependence and Mrl Ordering,” Statistics and Probability Letters 76, 231–243. {% %} Fryback, Dennis G. (1993) “QALYs, HYEs, and the Loss of Innocence,” Medical Decision Making 13, 271–272. {% nice survey of QALY history %} Fryback, Dennis G. (1999) “The QALY Model: Utilities for Cost-Utility Analysis in Health Care.” In James C. Shanteau, Barbara A. Mellers, & David A. Schum (eds.) Decision Science and Technology: Reflections on the Contributions of Ward Edwards, 331–351, Kluwer, Dordrecht. {% Is function of percentage of body burnt to what degree. Is MAUT on subsets of product sets. %} Fryback, Dennis G. & Ralph L. Keeney (1983) “Constructing a Complex Judgmental Model: An Index of Trauma Severity,” Management Science 29, 869–883. {% questionnaire versus choice utility %} Fryback, Dennis G., William F. Lawrence, Patricia A. Martin, Ronald Klein, & Barbara E.K. Klein (1997) “Predicting Quality of Well-Being Scores from the SF-36,” Medical Decision Making 17, 1–9. {% Has Hahn’s embedding theorem, which says that every linearly ordered Abelian group can be represented as a subgrou[p of endowed with the lexicographic ordering, with linearly ordered. %} Fuchs, László (1963) “Partially Ordered Algebraic Systems.” Pergamon Press, Oxford. {% %} Fuchs, Victor R. (1974) “Who Shall Live? Health, Economics, and Social Choice.” Basic Books, New York. {% %} Fuchs, Victor R. & Richard Zeckhauser (1987) “Valuing Health—A “Priceless” Commodity,” American Economic Review, Papers and Proceedings 77, 263–268. {% Dutch book; ordered vector space; gezien in boekenkast van Alain Chateauneuf december 1994 %} Fuchssteiner, Benno & Wolfgang Lusky (1981) “Convex Cones.” Mathematical Studies, 82. North-Holland, Amsterdam. {% %} Fudenberg, Drew (2006) “Advancing Beyond Advances in Behavioral Economics,” Journal of Economic Literature 44, 694–711. {% %} Fudenberg, Drew & Dorothy Hodges (1997) “Manual for Eonometrica Authors, Revised,” Econometrica 65, 965–975. {% quasi-concave so deliberate randomization: axiomatize many probabilistic error models for choices over menus. State space can be subjective. %} Fudenberg, Drew, Ryota Lijima, & Tomasz Strzalecki (2015) “Stochastic Choice and Revealed Perturbed Utility,” Econometrica 83, 2371–2409. {% Superstitions two or more steps off the equilibrium path are more likely to survive. %} Fudenberg, Drew & David K. Levine (2006) “Superstition and Rational Learning,” American Economic Review 96, 630–651. {% %} Fudenberg, Drew & David K. Levine (2006) “A Dual Self Model of Impulse Control,” American Economic Review 96, 1449–1476. {% Use the dual model of their 2006 AER paper, where for decisions within a day the emotional self plays the biggest role, and cognitive load does so too; with the cost function of self-control convex. Increasing stakes and probability of winning reduces the importance of cognitive load and enhances rational choice, and reduction of paradoxes such as Allais’. This model suggests that in the usual Allais paradox the irrational emotional choosing occurs with the small-probability choices and, hence, that the certainty effect plays less of a role as irrationality. In their model, discount rates ranging 1-7% and relative risk aversion (they assume EU) of 2 fit some existing data sets well. They also predict that violations of stationarity will reduce if the intertemporal choices are risky, which has been confirmed by Keren & Roelofsma (1995) and later papers. In the conclusion they argue that their model may be better in explaining a wide range of phenomena across different contexts with a limited number of parameters than, for instance, prospect theory. But they, nicely, also mention problems for their theory. %} Fudenberg, Drew & David K. Levine (2011) “Risk, Delay, and Convex Self-Control Costs,” American Economic Journal: Microeconomics 3, 34–68. {% Preferences not only over present menus but also for how they affect future menus (conservation of influence: this is a bit about future influence). %} Fudenberg, Drew & Tomasz Strzalecki (2015) “Dynamic Logit with Choice Aversion,” Econometrica 83, 651–691. {% strength-of-preference representation %} Fuhrken, Gebhard & Marcel K. Richter (1988) “Algebra and Topology in Cardinal Utility Theory.” In Wolfgang Eichhorn (ed.) “Measurement in Economics (Theory and Applications of Economic Indices),” 239–252, Physica-Verlag, Heidelberg. {% cancellation axioms: do additive representations like Debreu (1960) but impose all cancellation axioms. This is of course not at all general in a mathematical sense. The nice thing is that it makes continuity purely technical. That is, under additive representation with all cancellation axioms states continuity becomes only technical in the sense of adding no empirical content to the other axioms. P. 94, on continuity in Debreu (1960): “Thus his Theorem 1 lacks a clear separation of proper and [A]rchimedean axioms.” %} Fuhrken, Gebhard & Marcel K. Richter (1991) “Additive Utility,” Economic Theory 1, 83–105. {% %} Fuhrken, Gebhard & Marcel K. Richter (1991) “Polynomial Utility,” Economic Theory 1, 231–249. {% %} Fuhrken, Gebhard & Marcel K. Richter (1987) “Additive Measurement Theory,” Department of Economics, University of Minnesota. {% %} Füllbrunn, Sascha, Holger A. Rau, & Utz Weitzel (2014) “Does Ambiguity Aversion Survive in Experimental Asset Markets?,” Journal of Economic Behavior and Organization 107, 810–816. {% Criticizes relevance of neurostudies for economics, as title indicates. %} Fumagalli, Roberto (2014) “Neural Findings and Economic Models: Why Brains Have Limited Relevance for Economics,” Philosophy of the Social Sciences 44, 606–629. {% questionnaire versus choice utility: use the nice term “transfer to utility.” From the abstract: Quality of life mapping methods such as “Transfer to Utility” can be used to translate scores on disease-specific measures to utility values, when traditional utility measurement methods (e.g. standard gamble, time trade-off, preference-based multi-attribute instruments) have not been used. The aim of this study was to generate preliminary ordinary least squares (OLS) regression-based algorithms to transform scores from the Strengths and Difficulties Questionnaires (SDQ), a widely used measure of mental health in children and adolescents, to utility values obtained using the preference-based Child Health Utility (CHU9D) instrument. %} Furber, Gareth, Leonie Segal, Matthew Leach, & Jane Cocks (2014) “Mapping Scores from the Strengths and Difficulties Questionnaire (SDQ) to Preference-Based Utility Values,” Quality of Life Research 23, 403–411. {% %} Furlong William J., David H. Feeny, George W. Torrance, & Ronald D. Barr (2001) “The Health Utilities Index (HUI) System for Assessing Health-Related Quality of Life in Clinical Studies,” Annals of Medicine 33, 375–384. {% %} Furnham, Adrian & Michael Argyle (1998) “The Psychology of Money.” Routledge, London. {% natural-language-ambiguity: seem to argue that tolerance of ambiguity, in general natural-language sense, as a unitary model has been operationalized using quantitative assessments, but assessing qualitatively multi-dimensional attitudes toward ambiguity is a more realistic and attractive approach. %} Furnham, Adrian, & Joseph Marks (2013) “Tolerance of Ambiguity: A Review of the Recent Literature,” Psychology 4, 717–728. {% natural-language-ambiguity: seem to argue that tolerance of ambiguity, in general natural-language sense, as a unitary model has been operationalized using quantitative assessments, but assessing qualitatively multi-dimensional attitudes toward ambiguity is a more realistic and attractive approach. %} Furnham, Adrian, & Ribchester, Tracy (1995) “Tolerance of Ambiguity: A Review of the Concept, Its Measurement and Applications,” Current Psychology 14, 179–199. {% Relative to Baucells & Shapley (2008) and Dubra, Maccheroni, & Ok (2004), they treat strict preferences differently. %} Galaabaatar, Tsogbadral & Edi Karni (2012) “Expected Multi-Utility Representations,” Mathematical Social Sciences 64, 242–246. {% completeness-criticisms: Relax completeness in SEU (in the AA framework). They require unanimous agreement over sets of pairs {(P,U)} of subjective probability measures and utility functions. They also characterize special cases where the set is a product set of a probability-measure set and a utility-function set, and then where one or the other is a singleton. P. 268 derives from : f g if h f h g. This def. allows separating indifference from noncomparability. %} Galaabaatar, Tsogbadral & Edi Karni (2013) “Subjective Expected Utility Theory with Incomplete Preferences,” Econometrica 81, 255–284. {% %} Gabaix, Xavier (2012) “Variable Rare Disasters: An Exactly Solved Framework for Ten Puzzles in Macro-Finance,” Quarterly Journal of Economics 127, 645–700. {% For ESA conference 2006 subscription, for half the participants they formulated early registration as a discount, and for the other half late registration as a penalty. Among old participants they found no difference, but among the young they found more early subscriptions in the penalty treatment. Nice illustration of framing with real field data and experimental economists as subjects! Nice paper. %} Gächter, Simon, Henrik Orzen, Elke Renner, & Chris Starmer (2009) “Are Experimental Economists Prone to Framing Effects? A Natural Field Experiment,” Journal of Economic Behavior and Organization 70, 443–446. {% Very impressive data on loss aversion. %} Gächter, Simon, Andreas Herrmann, & Eric J. Johnson (2007) “Individual-Level Loss Aversion in Riskless and Risky Choice.” Working Paper, University of Nottingham. {% questionnaire versus choice utility: derive CRRA (logpower) utility from introspective well-being using big surveys. Find that ln utility fits well (power 0, CRRA index 1). Marginal utility of money decreases with increasing health, contrary to what other studies find. %} Gandelman, Néstor & Rubén Hernández-Murillo (2013) “What Do Happiness and Health Satisfaction Data Tell Us about Relative Risk Aversion?,” Journal of Economic Psychology 39, 301–312. {% ordering of subsets: Definition 3 lists properties for set ordering, useful to avoid manipulation in social choice, that are satisfied under average utility and not under additive utility over subsets. %} Gärdenfors, Peter (1976) “Manipulation of Social Choice Functions,” Journal of Economic Theory 13, 217–228. {% second-order probabilities to model ambiguity: in his §6. §5 has probability intervals. There he proposes maxmin EU w.r.t probability intervals. %} Gärdenfors, Peter (1979) “Forecasts, Decisions and Uncertain Probabilities,” Erkenntnis 14, 159–181. {% second-order probabilities to model ambiguity; ambiguity seeking for unlikely: not really. P. 363, citing (then unpublished) experiments by Goldsmith & Sahlin: “for probabilities other than fairly low ones, lottery tickets involving more reliable probability estimates tend to be preferred.” P. 366 2nd para explains that set of priors is more general than assigning probability interval to each event. P. 371: paper proposes to take a set of 1st order probability distributions, assign a degree of epistemic reliability to each, take only the set of 1st order probability distributions that exceed a threshold, and then do maxmin EU with respect to this set, displayed in the middle of p. 371. So, it essentially has the maxmin EU version of multiple priors. The paper is a theoretical discussion. %} Gärdenfors, Peter & Nils-Eric Sahlin (1982) “Unreliable Probabilities, Risk Taking, and Decision Making,” Synthese 53, 361–386. {% second-order probabilities to model ambiguity: p. 244 bottom argues that subjects in Yates & Zukowski (1976), being psychology students who must have had some statistical training, will reduce 2nd order distributions to 1st, so that 2nd order distribution was no good way to implement ambiguity there. §5 p. 247 does consider it with the wave effect, which amounts to overweighting of extreme 2nd order probabilities, meaning violation of RCLA. %} Gärdenfors, Peter & Nils-Eric Sahlin (1983) “Decision Making with Unreliable Probabilities,” British Journal of Mathematical and Statistical Psychology 36, 240–251. {% Maybe in US?; second-order probabilities to model ambiguity %} Gärdenfors, Peter & Nils-Eric Sahlin (1987, eds.) “Decision, Probability, and Utility; Selected Readings.” Cambridge University Press, Cambridge. {% utility elicitation %} Gafni, Amiram (1991) “Measuring the Adverse Effects of Unnecessary Hypertension Drug Therapy: QALYs vs HYE,” Clin. Invest. Med. 14, 266–270. {% utility elicitation %} Gafni, Amiram (1991) “Willingness-to-Pay as a Measure of Benefits,” Medical Care 29, 1246–1252. {% utility elicitation %} Gafni, Amiram (1989) “The Quality of QALYs (Quality-Adjusted Life-Years): Do QALYs Measure What They at Least Intend to Measure?,” Health Policy 13, 81–83. {% utility elicitation %} Gafni, Amiram & Stephen Birch (1991) “Equity Considerations in Utility-Based Measures of Health Outcomes in Economic Appraisals: An Adjustment Algorithm,” Journal of Health Economics 10, 329–342. {% utility elicitation %} Gafni, Amiram & Stephen Birch (1997) “QALYs and HYEs; Spotting the Differences,” Journal of Health Economics 16, 601–608. {% utility elicitation %} Gafni, Amiram, Stephen Birch, & Abraham Mehrez (1993) “Economics, Health and Health Economics: HYEs versus QALYs,” Journal of Health Economics 11, 325–339. {% %} Gafni, Amiram & Abraham Mehrez (1993) Reply, Medical Decision Making 13, 168–169. {% utility elicitation; Take exponential function as utility function, with exponent sum of Gamble Effect parameter, time preference effect, and Quantity Effect; They are not aware that this is all empirically indistinguishable. %} Gafni, Amiram & George W. Torrance (1984) “Risk Attitude and Time Preference in Health,” Management Science 30, 440–451. {% %} Gafni, Amiram & Carl J. Zylak (1990) “Ionic versus Nonionic Contrast Media: A Burden or a Bargain?,” Can Med Assoc J 143, 475–481. {% %} Gafni, Amiram & Carl J. Zylak (1991) Reply (to Kalant, “Ionic versus Nonionic Contrast Media: A Burden or a Bargain?”), Can. Med. Assoc. J. 144, 123–124. {% %} Gahvari, Firouz (1984) “Incidence and Efficiency Aspects of Differential Taxation of Residential and Industrial Capital in a Growing Economy,” Journal of Public Economics 25, 211–234. {% %} Gahvari, Firouz (1986) “A Note on Additivity and Diminishing Marginal Utility,” Oxford Economic Papers 38, 185–186. {% %} Gaifman, Haim & Yang Liu (2015) “Context-Dependent Utilities: A Solution to the Problem of Constant Acts in Savage.” In Wiebe van der Hoek, Wesley H. Holliday, & Wen-Fang Wang (eds.) Proceedings of the Fifth International Workshop on Logic, Rationality, and Interaction, vol. LNCS 9394, 90–101, Springer, Berlin. {% %} Gaines, Brian R. (1983) “Precise Past, Fuzzy Future,” International Journal of Man-Machine Studies 19, 117–134. {% Math. Reviews 86d:03-023; relates probability theory and fuzzy sets. %} Gaines, Brian R. (1984) “Fundamentals of Decision: Probabilistic, Possibilistic and other Forms of Uncertainty in Decision Analysis,” Fuzzy Sets and Decision Analysis 47–65, Stud. Management Sci., 20, North-Holland, Amsterdam. {% SWF is weighted sum of values of all coalitions in society. These use RDU-transformation with linear utility with transformation function the k-th power and all coalitions with more than k members contributing nothing. %} Gajdos, Thibault (2002) “Measuring Inequalities without Linearity in Envy: Choquet Integrals for Symmetric Capacities,” Journal of Economic Theory 106, 190–200. {% Preferences between (x,C) and (x´,C´) where x and x´ are acts and C, C´ are sets of priors. C and C´ can be different and are exogenously given. Thus the data set is very rich. The decision maker evaluates each (x,C) using the multiple priors model where the set of priors is a subset of C. C reflects state of information and its subset reflects decision attitude. The paper generalizes some preceding papers on similar models by (subsets of) these authors. Section 4 has a convenient subfamily of multiple priors: to define the subjective family of priors, we start from an objective set of priors denoted P, which is assumed given as it is assumed throughout this paper. s(P) is its midpoint (center of gravity; Steiner point), and 0 1 is a subjective parameter reflecting perceived ambiguity. The subjective family of priors to be used then consists of all convex combinations (1)s(P) + Q for any Q from P. This theory can be called contraction EU. A generalization would consist of allowing s(P) to be different than the midpoint of P. Download 7.23 Mb. Share with your friends:
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