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- Harsanyi’s aggregation
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- PT: data on probability weighting ; natural sources of ambiguity
| §II.IV.8, p. 89, already stated concisely and perfectly, ordinalism (note the premise that puts it all in the right perspective!!!!). It is the whole Part II, Ch. IVC, §8.
“Thus if we seek only the causation of the objective facts of prices and commodity distributions four attributes of utility as a quantity are entirely unessential, (1) that one man’s utility can be compared to another’s, (2) that for the same individual the marginal utilities at one consumption-combination can be compared with those at another, or at one time with another, (3) even if they could, total utility and gain might not be integratable, (4) even if they were, there would be no need of determining the constants of integration.” %} Fisher, Irving (1892) “Mathematical Investigations in the Theory of Values and Prices,” Transactions of Connecticut Academy of Arts and Sciences 9, 1–124. Reprinted as book in 1965 (1st edn. 1925), Yale University Press, New Haven. {% %} Fisher, Irving (1916) “Is ‘Utility’ the Most Suitable Term for the Concept It Is Used to Denote?,” American Economic Review 8, 335–337. Reprinted in Alfred N. Page (1968), Utility Theory: A Book of Readings, Wiley, New York, 49–51. {% On the possibility to use interpersonal comparisons of utility he seems to have written, p. 179-180: “To all these questions I would answer ‘yes’—approximately at least. But the only, or only important, reason I can give for this answer is that, in actual practice human life, we do proceed on just such assumptions.” And then some later comes the, beautiful: “Philosophical doubt is right and proper, but the problems of life cannot, and do not, wait.” P. 159 cites J. Willard Gibbs: “The whole is simpler than its parts.” Obtains cardinal utility by imposing additive decomposability. Assume oddland and evenland, with different prizes and budget for two families with identical pref. rels. Assume two commodities, one and two. Assume (y1,x2) is what a family in evenland buys. The marginal utility of money spent on first commodity must bne equal to that spent on second, there; it is the marginal utility of money there. In oddland we have two observations for different prize/budget combinations, leading to (x1,x2) and (y1,y2), respectively. Comparing the prize ratios of the 2nd commodity at (x1,x2) in oddland and (y1,x2) in evenland shows the ratio of marginal utility of money in those two cases, comparing the prize ratios of the 1st commodity at (y1,y2) in oddland and (y1,x2) in evenland shows the ratio of marginal utility of money in those two cases. So, we obtain the ratio of marginal utility of money at (x1,x2) and (y1,y2) in oddland, so at two different levels of wealth, having used evenland as a measuring rod/yardstick. P. 187 says that these observations can be extended to more levels: give the family in evenland budget/prices so that it buys (z1,y2), in oddland so that it buys (z1,z2), and the marginal utility of money at (z1,z2) can be related to the others; etc. Discussion on pp. 179-181 is in fact a nice discussion of the many assumptions underlying a preference relation. Seems to assume also comparability of utilities for different persons, in order to achieve concrete results applicable to income taxation. P. 181 seems to argue that individual data on utility contains too much noise. P. 180, about people who doubt about cardinal utility: “Philosophic doubt is right and proper, but the problems of life cannot, and do not, wait.” P. 181: “Even the philosophic doubter, if himself taxed unfairly, would be apt to know it!” %} Fisher, Irving (1927) “A Statistical Method for Measuring “Marginal Utility” and Testing the Justice of a Progressive Income Tax.” In Jacob H. Hollander (ed.) Economic Essays Contributed in Honor of John Bates Clark, 157–193, MacMillan, New York. {% %} Fisher, Irving (1927) “The Making of Index Numbers.” Houghton-Mifflin, Boston. (3rd edn. 1967, Augustus M. Kelley, New York.) {% %} Fisher, Irving (1928) “The Money Illustion.” Adelphi, New York. {% Seems that this book introduced discounted utility; I doubt. Nonconstant discounting has surely been known before, constant discounted utility did Fisher impose it, or was Samuelson the first? Benzion, Rappoport, & Yagill (1989) and the Nobel committee (2017) suggest this book. On time preference and discounting normative: p. 67: “It seems preferabe ... first to find the principles which fix the terms on which present and future goods exchange, without restricting ourselves in advance to the thesis that, always and necessarily, present goods command a premium over future goods.” (citation taken from Weibull, 1985). Seems that Fisher also makes clear that in a perfect free market present money can be equated completely with market-discounted future money, which can serve as a serious confound in experiments to measure intertemporal preference. %} Fisher, Irving (1930) “The Theory of Interest.” MacMillan, New York. {% Seems to stress likelihood and sufficiency. %} Fisher, Ronald A. (1922) “On the Mathematical Foundations of Theoretical Statistics,” Philosophical Transactions of the Royal Society of London, Part A, 222, 309–368. {% Seems to be a major paper introducing ancillarity, in an informal manner just by examples. Seems that ’34 and ’35 he also wrote on ancillarity. %} Fisher, Ronald A. (1925) “Theory of Statistical Estimation,” Proceedings of the Cambridge Philosophical Society 22, 200–225. {% conservation of influence: seems to have proposed expected nr. of offspring as %} Fisher, Ronald A. (1930) “The Genetic Theory of Natural Selection.” Oxford University Press, New York. {% %} Fisher, Ronald A. (1935) “The Design of Experiments.” Oliver and Boyd, Edinburgh. {% foundations of statistics: argues against Neyman’s classical statistics. %} Fisher, Ronald A. (1955) “Statistical Methods and Scientific Induction,” Journal of the Royal Statistical Society, Series B (Methodological) 17, 69–78. {% Discussed in Zabell (1992). In this book Fisher thought to justify his fiducial approach by “recognizable subsets.” Seems to write (p. 77; p. 81 in 3rd, 1973, edn.): “the only populations that can be referred to in a test of significance have no objective reality, being exclusively the product of the statistician’s imagination through the hypotheses he has decided to test.” Seems to have proposed the likelihood principle (earlier by Barnard 1947, 1949). %} Fisher, Ronald A. (1956) “Statistical Methods and Scientific Inference.” Oliver and Boyd, Edinburgh. (3rd edn. 1973, Hafner Press, New York.) {% %} Fiske, Alan P. & Tetlock, Philip E. (1997) “Taboo Trade-Offs: Reactions to Transactions that Transgress Spheres of Justice,” Political Psychology 18, 255–297. {% %} Fleischer, Isidore (1961) “Numerical Representation of Utility,” Journal of the Society of Industrial and Applied Mathematics 9, 48–50. {% Show how error theory can be introduced to test a Varian (1983) condition for consumer demand functions necessary and sufficient for concave additive decomposable utility. %} Fleissig, Adrian R. & Gerald A. Whitney (2007) “Testing Additive Separability,” Economics Letters 96, 215–220. {% Test weak separability from econometric data and find that any violations are probably just errors in data. %} Fleissig, Adrian R. & Gerald A. Whitney (2008) “A Nonparametric Test of Weak Separability and Consumer Preferences,” Journal of Econometrics 147, 275–281. {% %} Fleming, J. Marcus (1952) “A Cardinal Concept of Welfare,” Quarterly Journal of Economics 66, 366–384. {% %} Fleming, J. Marcus (1957) “Cardinal Welfare and Individualistic Ethics: A Comment,” Journal of Political Economy 65, 355–357. {% %} Fleurbaey, Marc (2010) “Assessing Risky Social Situations?,” Journal of Political Economy 118, 649–680. {% Harsanyi’s aggregation: ex post welfare can depend on ex ante prospects and counterfactuals. %} Fleurbaey, Marc, Thibault Gajdos, Stéphane Zuber (2015) “Social Rationality, Separability, and Equity under Uncertainty,” Mathematical Social Sciences 73, 13–22. {% They assume given for riskless alternatives, a social utility function that is a sum of individual functions. Then they show that under some reasonable axioms, in Harsanyi’s (1955) setup, the vNM social utility function must be that same sum and, thus, a linear combination of individual vNM utilities. %} Fleurbaey, Marc & Philippe Mongin (2016) “The Utilitarian Relevance of the Aggregation Theorem,” American Economic Journal: Microeconomics 8, 289–306. {% Use the Bernheim-Rangel approach, extending it to incomplete prererences and distributive issues. %} Fleurbaey, Marc & Erik Schokkaert (2013) “Behavioral Welfare Economics and Redistribution,” American Economic Journal: Microeconomics 5, 180–205. {% Consider a weakening of Arrow’s independence of irrelevant alternatives (in its social-choice meaning, and not its revealed-preference meaning) to independence only of alternatives not actually available. Still get some impossibility results. Give economic interpretations. %} Fleurbaey, Marc & Koichi Tadenuma (2007) “Do Irrelevant Commodities Matter?,” Econometrica 75, 1143–1174. {% %} Flom, Merton C., Frank W. Weynouth, & Daniel Kahneman (1963) “Visual Resolution and Contour Interaction,” Journal of the Optical Society of America 53, 1026–1032. {% %} Florens, Jean-Pierre & Michel Mouchart (1988) “Bayesian Specification Tests,” CORE discussion paper 8831. {% foundations of statistics; contains many useful references. %} Florens, Jean-Pierre & Michel Mouchart (1993) “Bayesian Testing and Testing Bayesians.” In Gangadharrao S. Maddala, C. Radhakrishna Rao, & Hriskikesh D. Vinod (eds.) Handbook of Statistics 11, Elsevier Science Publishers, Amsterdam. {% Derive quality of life (for multiattribute health states) not from trading it off against life duration, but by letting people choose repeatedly and using an error theory, where the probability of choosing a health state is led into a cardinal value scale. They cite two papers that introduced this method and use it to do something about health states worse than death. %} Flynn, Terry N., Jordan J. Louviere, Anthony A.J. Marley, Joanna Coast & Tim J. Peters (2008) “Rescaling Quality of Life Values from Discrete Choice Experiments for Use as QALYs: A Cautionary Tale,” Population Health Metrics 6/1/6. {% Cetuximab gave patients with lung cancer and metastases on average 1.2 months more life duration, with serious decrease in quality of life, but costs $80,000 per patient. Nevertheless it was accepted as treatment in the US (based on a study that did not measure or incorporate quality of life). The authors argue that this is too expensive. They propose $129,000 as maximum price per QALY (healthy year). The UK seems to take 30,000 pound per year. %} Fojo, Tito & Christine Grady (2009) “How Much Is Life Worth: Cetuximab, Non–Small Cell Lung Cancer, and the $440 Billion Question,” Journal of the National Cancer Institute 101, 1044–1048. {% %} Fokkema, Sipke D. & Arie Dirkzwager (1960) “A Comparison of Subjective and Objective Methods for Observation of Discussion Groups in Personnel Selection,” Acta Psychologica 17, 55–79. {% Seems to have nice comments on continuity conditions for preferences. %} Foldes, Lucien (1972) “Expected Utility and Continuity,” Review of Economic Studies 39, 407–421. {% %} Foltz, Gregory S., Steven E. Poltrock, & George R. Potts (1984) “Mental Comparison of Size and Magnitude: Size Congruity Effects,” Journal of Experimental Psychology: Learning, Memory and Cognition 10, 442–453. {% Discusses a number of indexes of risk aversion that are relevant in different decision situations, such as when considering small absolute stakes (Pratt-Arrow), a small chance of a great gain, or a small chance of ruin. The latter is U(x)/U´(x), a measure introduced by Aumann & Kurz (1977). %} Foncel, Jérôme & Nicolas Treich (2005) “Fear of Ruin,” Journal of Risk and Uncertainty 31, 289–300. {% Seems to argue that any theory of choice under uncertainty should encompass risk. %} Ford, James L. (1987) “Economic Choice under Uncertainty: A Prespective Theory Approach.” Edward Elgar, Aldershot. {% P. 688, last paragraph: majority of Shackle’s work concerns presence of uncertainty in economics; replace expected utility by Shackle’s original concepts, “potential surprise” and focus-outcomes of competing action-choices. Refs are given %} Ford, James L. (1993) “G.L.S. Shackle (1903-1992): A Life with Uncertainty,” Economic Journal 103, 683–697. {% %} Ford, James L. & Sudip Ghose (1995) “Shackle’s Theory of Decision-Making under Uncertainty: The Findings of a Laboratory Experiment,” Discussion Paper (University of Birmingham, Department of Economics) {% Study implications of neo-additive capacities in financial markets. %} Ford, Jim L., David Kelsey, & Wei Pang (2013) “Information and Ambiguity: Herd and Contrarian Behaviour in Financial Markets,” Theory and Decision 75, 1–15. {% Counterexample to footnote 14 of Aumann (1987), Econometrica 55, 1–18 %} Forges, Françoise (1990) “Correlated Equilibrium in Two-Person Zero-Sum Games,” Econometrica 58, 515. {% %} Forges, Françoise (1993) “Five Legitimate Definitions of Correlated Equilibrium in Games with Incomplete Information,” Theory and Decision 35, 277–310. {% AHP; Paper mostly seems to propagates the software develpoped by the author, and to defend against criticisms, rather than to give a didactical exposition. %} Forman, Ernest H. & Saul I. Gass (2001) “The Analytical Hierarchy Process—An Exposition,” Operations Research 49, 469–486. {% Christiane, Veronika & I: p. 542 seems to pay subjects in francs/pesos iso dollars or cents so as to encourage better decisions, apparently through the higher numbers. %} Forsythe, Robert, Thomas R. Palfrey, & Charles R. Plott (1982) “Asset Valuation in an Experimental Market,” Econometrica 50, 537–568. {% DOI 10.1007/s00186-015-0493-1 Take utility linear for gains but quadratic for losses, to model a kind of loss aversion where extreme losses are disliked much. They explain nicely in the intro that there is much interest in measures for downside risks, with VaR most well-known. They relate to mean-variance analysis, and analyze optimization problems. %} Fortin, Ines & Jaroslava Hlouskova (2015) “Downside Loss Aversion: Winner or Loser?,” Mathematical Methods of Operations Research 81, 181–233. {% Seems to be a paradox essentially different than Cox’ conditioning paradox. Estimating mean of normal distribution with known variance, then conditions on observed variance. %} Foster, Dean P. & Edward I. George (1996) “A Simple Ancillarity Paradox,” Scandinavian Journal of Statistics 23, 233–242. {% Aumann & Serrano (2008, JPE) define a measure of riskiness of a prospect (lottery) g that has both positive and negative outcomes as the risk tolerance (reciproke of measure of absolute risk aversion, which has the nice property of having monetary unit as its unit; in other words, of being a money amount) at which the person is indifferent between taking the prospect or the 0 prospect. That is, with U(x) = 1exp(x), EU(x) = EU(0) = 0. This paper does the same thing but with a different utility family, being the logarithmic family defined by U(x) = log( + x), where is the parameter. The authors show this definition of their measure only in Section VI.B, following Eq. 5. Their defining Eq. 1 is equivalent, as readily follows from substitution. They denote the measure by R(g). They interpret as wealth level, as this is often done. Beause log(0) is (we approximate for x to 0 from above), this should always be avoided and dominates all else, and R(g) should exceed the minimal outcome. If I understand right, this simply means that R(g) is the liminf of the support of g. Thus, if there is a minimal outcome and it has positive probability, then R(g) is this outcome. The authors put this interpretation, of avoiding bankruptcy, central in many discussions in the first part of the paper. They derive many properties in Section V Proposition 1, such as homogeneity, which follows from CRRA, subadditivity, and so on. P. 800 3rd para criticizes Rabin (2000) on the ground that the extreme risk aversion that Rabin derives agrees with the authors’ criterion of R(g). R(g) is indeed the most pessimistic and risk averse one can think of. The authors judge R(g) and its extreme risk aversion to be plausible. Hence, they disagree with the implausibility claim that Rabin assigns to extreme risk aversion. %} Foster, Dean P. & Sergiu Hart (2009) “An Operational Measure of Riskiness,” Journal of Political Economy 117, 785–814. {% Axiomatize the measures of riskiness of Aumann & Serrano (2008) and Foster & Hart (2009). %} Foster, Dean P. & Sergiu Hart (2013) “A Wealth-Requirement Axiomatization of Riskiness,” Theoretical Economics 8, 591–620. {% Seems that they introduced calibration into game theory. %} Foster, Dean P. & Rakesh V. Vohra (1997) “Calibrated Learning and Correlated Equilibrium,” Games and Economic Behavior 21, 40–55. {% Seems to be a classic in the sense that it was first to show that charlatan can pass calibration tests as soon as experts can. %} Foster, Dean P. & Rakesh V. Vohra (1998) “Asymptotic Calibration,” Biometrica 85, 379–390. {% Gekregen van Moulin op 18 mei 1990 %} Foster, James E. (1985) “Inequality Measurement.” In H. Peyton Young (eds.) Fair Allocation, Proceedings of Symposia in Applied Mathematics, American Mathematical Society, Providence. {% %} Foster, James E. & Efe A. Ok (1999) “Lorenz Dominance and the Variance of Logarithms,” Econometrica 67, 901–907. {% Debreu’s (1960) additive decomposability theorem with some interpretations added %} Foster, James E. & Anthony F. Shorrocks (1991) “Subgroup Consistent Poverty Indices,” Econometrica 59, 687–709. {% %} Fountain, John (2002) “Eliciting Beliefs from Risk Averse Forecasters Using a Log Scoring Rule,” University of Canterbury, Christchurch, New Zealand. {% %} Fountain, John & Michael McCosker (1993) “Fans, Frames and Risk Aversion: How Robust is the Common Consequence Effect ?”- University of Canterbury; Department of Economics and Operations Research. {% Treatment variation: for a group of patients, 93% of urologists consider radical prostatectomy to be the optimal treatment, 72% of radiation oncologists consider surgery and external beam radiotherapy as equivalent. The authors conclude: “specialists overwhelmingly recommend the therapy that they themselves deliver.” %} Fowler, Floyd J., Jr., Mary McNaughton Collins, Peter C. Albertsen, Anthony Zietman, Diana B. Elliot, & Michael J. Barry (2000) “Comparison of Recommendations by Urologists and Radiation Oncologists for Treatment of Clinically Localized Prostate Cancer,” JAMA (Journal of the American Medical Association) 283, 3217–3222. {% %} Fox, Craig R. (1990) “From Risk to Uncertainty: Exploring the Effects of Ambiguity and Source Preference on Decision Weights,” Stanford University, Dept. of Psychology. {% %} Fox, Craig R. (1999) “Strength of Evidence, Judged Probability, and Choice under Uncertainty,” Cognitive Psychology 38, 167–189. {% %} Fox, Craig R. (2006) “The Availability Heuristic in the Classroom: How Soliciting More Criticism Can Boost Your Course Ratings,” Judgment and Decision Making 1, 86–90. {% %} Fox, Craig R. & Richard Birke (2002) “Forecasting Trial Outcomes: Lawyers Assign Higher Probabilities to Scenarios That Are Described in Greater Detail,” Law and Human Behavior 26, 159–173. {% They demonstrate clear bias of probability estimations towards the neutral distribution with respect to the partition chosen. %} Fox, Craig R. & Robert T. Clemen (2005) “Subjective Probability Assessment in Decision Analysis: Partition Dependence and Bias toward the Ignorance Prior,” Management Science 51, 1417–1432. {% survey on nonEU: Focuses on decision under risk with a bit on ambiguity. Not primarily a complete survey but rather a didactical account giving the main ideas, with some nicely written sentences. For example, p. 51, on Rabin’s paradox: “by way of analogy, if one could perceive the curvature of the earth by walking the length of a football field, then the earth must be implausibly small.” loss aversion: erroneously thinking it is reflection: this paper of course does NOT make this mistake. It usefully lists it as the first of some misunderstandings (top p. 55): “A few points of common confusion are worth highlighting at this juncture. First, loss aversion is not the same as risk seeking for losses. …Second, decision weights are not generally interpreted as a measure of belief. … Third, the concavity (convexity) of the value function is not the same as risk aversion (risk seeking), and overweighting low-probability gains (losses) is not the same as risk seeking (risk aversion).” P. 58 brings up the two-stage model of PT for ambiguity, in the spirit of Tversky that I know well, having discussed it so much with him: there is belief and risk-probability weighting in the first para, with no space for the typical Ellsberg source preference. The latter is considered a relatively unimportant phenomenon much driven by contrast effects beyond individual choice, and reluctantly showing up in the 2nd para. Tversky convinced me of this and it underlied my work on ambiguity ever after. Tversky mostly discussed these things with Craig and me. PT falsified: P. 59-63 lists violations. The 2nd part of this paper is on external validity from lab to field, giving procedures to work on this. P. 79 (conclusion): “Despite its limitations, we find that prospect theory is the most successful general purpose model currently available for predicting, describing, and interpreting decisions under risk; to our reading alternative models that we reviewed outperform prospect theory only under specific conditions. %} Fox, Craig R., Carsten Erner, & Daniel J. Walters (2015) “Decision under Risk: From the Field to the Laboratory and back.” In Gideon Keren & George Wu (eds.), The Wiley Blackwell Handbook of Judgment and Decision Making, 43–88, Blackwell, Oxford, UK. {% %} Fox, Craig R. & Liat Hadar (2006) “Decisions from Experience = Sampling Error + Prospect Theory: Reconsidering Hertwig, Barron, Weber & Erev (2004),” Judgment and Decision Making 1, 159–161. {% %} Fox, Craig R. & Julie R. Irwin (1998) “The Role of Context in the Communication of Uncertain Beliefs,” Basic and Applied Social Psychology 20, 57–70. {% %} Fox, Craig R. & Daniel Kahneman (1992) “Correlations, Causes and Heuristics in Surveys of Life Satisfaction,” Social Indicators Research 27, 221–234. {% Does belief reversals analogously to preference reversals, with choices revealing different orderings of likelihood than matching judgments. A greater proportion of subjects rate the more familiar event as more likely than assigning a higher probability to that event. %} Fox, Craig R. & Jonathan Levav (2000) “Familiarity Bias and Belief Reversal in Relative Likelihood Judgment,” Organizational Behavior and Human Decision Processes 82, 268–292. {% %} Fox, Craig R. & Jonathan Levav (2004) “Partition-Edit-Count: Naïve Extensional Reasoning in Conditional Probability Judgment,” Journal of Experimental Psychology: General 133, 626–642. {% %} Fox, Craig R. & Jonathan Levav (2012) “Absolute versus Relative Likelihood Judgment,” working paper. {% %} Fox, Craig R. & Russell A. Poldrack (2008) “Prospect Theory on the Brain: Studies on the Neuroeconomics of Decision under Risk.” In Paul W. Glimcher, Colin F. Camerer, Ernst Fehr, & Russell A. Poldrack (eds.), Handbook of Neuroeconomics, 145–173, Elsevier, New York. {% %} Fox, Craig R., Rebecca K. Ratner, & Daniel Lieb (2005) “How Subjective Grouping of Options Influences Choice and Allocation: Diversification Bias and the Phenomenon of Partition Dependence,” Journal of Experimental Psychology: General 134, 538–551. {% PT: data on probability weighting; natural sources of ambiguity: Download 7.23 Mb. Share with your friends:
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