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biseparable utility %} Gajdos, Thibault, Takashi Hayashi, Jean-Marc Tallon, & Jean-Christophe Vergnaud (2008) “Attitude towards Imprecise Information,” Journal of Economic Theory 140, 27–65. {% Do something like -maxmin but for social choice. Maintain anonymity and conclude that, therefore, anonymity alone does not distinguish Harsany's welfarism from Rawls. %} Gajdos, Thibault & Feriel Kandil (2008) “The Ignorant Observer,” Social Choice and Welfare 31, 193–232. {% Model with welfare and uncertainty, so two-fold aggregation. For example, weighted average of ex post and ex ante optimum. %} Gajdos, Thibault & Eric Maurin (2004) “Unequal Uncertainties and Uncertain Inequalities: An Axiomatic Approach,” Journal of Economic Theory 116, 93–118. {% If two sets of beliefs have one Pareto optimal two-period allocation in common, and it is interior solution, then the two sets of PO-optimal allocations must actually coincide, because the first-order conditions imply same marginal rates of substitutions across different states. multiattribute CEU (Choquet expected utility) %} Gajdos, Thibault & Jean-Marc Tallon (2002) “Beliefs and Pareto Efficient Sets: A Remark,” Journal of Economic Theory 106, 467–471. {% Show that allocations may exist that are both ex ante efficient and ex post envy-free. %} Gajdos, Thibault & Jean-Marc Tallon (2002) “Fairness under Uncertainty,” Economic Bulletin 4, 1–7. {% Imagine DUU with three colors, Red, Black, and Yellow. Consider choices with multiple priors between f when set of priors is F, and g when set of priors is G. F and G refer to DIFFERENT unrelated urns. For each urn, there is a rich set of acts, and in addition there are many urns. In addition, each set of priors has a so-called anchor, being the one to be chosen if only one measure can be chosen. %} Gajdos, Thibault, Jean-Marc Tallon, & Jean-Christophe Vergnaud (2004) “Decision Making with Imprecise Probabilistic Information,” Journal of Mathematical Economics 40, 647–681. {% Belief aggregation in Anscombe-Aumann model and then nonEU at first stage, much like Schmeidler (1989). They consider a state-dependent version of RDU (rank-dependent utility for uncertainty; is Choquet expected utility = CEU) as axiomatized by Chew & Wakker (1996) for instance, but restricted to acts with only two outcomes (outcome is probability distribution over prizes in Anscombe-Aumann). Show that aggregation, if existing, must be linear, and that nonEU models such as RDU and multiple priors cannot deliver belief aggregation. %} Gajdos, Thibault, Jean-Marc Tallon, & Jean-Christophe Vergnaud (2008) “Representation and Aggregation of Preferences under Uncertainty,” Journal of Economic Theory 141, 68–99. {% Relative to the JME-2004 paper of the same authors, they drop the anchor. %} Gajdos, Thibault, Jean-Marc Tallon, & Jean-Christophe Vergnaud (2004) “Coping with Imprecise Information: A Decision Theoretic Approach,” {% The authors consider expert aggregation, comparing disagreement between precise predictions (one says 1/3, and the other says 2/3) with agreement between vague predictions (both say that it is either 1/3 or 2/3). Motivtion is on pp. 420-421: “Therefore, the first step for making policy decisions in complex situations (such as, for instance, climate changes) is to elicit experts beliefs.” They introduce a theoretical decision model for it, building on ambiguity models of these authors (Gajdos, Hayashi, Tallon, & Vergnaud 2008 JET). Novelties in modeling are described on p. 431. Agents can choose between options that have different informations: for instance, they can choose between [a with experts saying A and B] or [b with experts saying C and D]. This cannot readily be modeled through Savage’s state space, but the authors solve this problem by giving up on any interpretation of the state space, and they write: “state space … It is for us a mere coding device, without any substantial existence.” (p. 421). The provide results on more averse to imprecision (Proposition 2, p. 437). Because now info provided by two experts is considered, and this can be different for different acts considered, the model is very general. %} Gajdos, Thibault & Jean-Christophe Vergnaud (2013) “Decisions with Conflicting and Imprecise Information,” Social Choice and Welfare 41, 427–452. {% multiattribute CEU (Choquet expected utility) %} Gajdos, Thibault & John A. Weymark (2004) “Multidimensional Generalized Gini Indices,” Economic Theory 26, 471–496. {% Apply Choquet integral in multiattribute optimization. %} Galand, Lucie, Patrice Perny, & Olivier Spanjaard (2010) “Choquet-Based Optimisation in Multiobjective Shortest Path and Spanning Tree Problems,” European Journal of Operational Research 204, 303–315. {% value of information: under unawareness, which is a form of mistaken belief, info can have negative value (also under usual EU). But the agent cannot know this. %} Galanis, Spyros (2015) “The Value of Information under Unawareness,” Journal of Economic Theory 157, 384–396. {% utility elicitation: asked for direct assessment of utility of money. Found that x to the power 0.43 fitted well for gains. Seems to find that subjects find it very difficult for losses. %} Galanter, Eugene (1962) “The Direct Measurement of Utility and Subjective Probability,” American Journal of Psychology 75, 208–220. {% Seems simple. %} Galanter, Eugene (1990) “Utility Functions for Nonmonetary Events,” American Journal of Psychology 103, 449–470. {% utility elicitation, p. 65: “But all of the data are sketchy, and the field is more populated with theory and derivations of a variety of models than it is with a wealth of empirical information” P. 75: “The remarkable consistency of the power function as a representation of data that show how people judge events that have a quantitative character is once again supported in these studies.” P. 75 suggests loss aversion using nice words: “On the basis of intuition and anecdote, one would expect the negative limb of the utility function to decrease more sharply than the positive limb increases.” concave utility for gains, convex utility for losses: power for gains is 0.45 (Experiment 1, p. 68), for losses it is 0.59 (Experiment 2, p. 70). So, utility is concave for gains and (less) convex for losses. Cross-modality matching means comparing subjective evaluations of different continua with each other. This paper does it with money and loudness. For example, is the value of this amount of money the same as the loudness of this tone? Power transformations seem to fit the data well. The method can be compared to the VAS which asks to relate lengths of lines to value of money/lifeduration, be it that length of a line is objective. More pessimistically, it can be argued that this kind of research demonstrates that participants answer to all questions no matter what the questions are. One may be measuring stable response modes without anything underlying it. I haven’t yet made up my mind on the validity of this viewpoint. Christiane, Veronika & I: Cross-modality matching seems to measure numerical sensitivity more than intrinsic value. %} Galanter, Eugene & Patricia Pliner (1974) “Cross-Modality Matching of Money against Other Continua.” In Herbert Moskowitz, Bertram Sharf, & Joseph C. Stevens (eds.) Sensation and Measurement: Papers in Honor of S.S. Stevens, 65–76, Reidel, Dordrecht. {% foundations of probability: %} Galavotti, Maria Carla (2005) “Philosophical Introduction to Probability.” University of Chicago Press, Chicago. {% foundations of probability: DOI: HTTP://DX.DOI.ORG/10.1177/0149206314532951 %} Galavotti, Maria Carla (2014) “Probability Theories and Organization Science: The Nature and Usefulness of Different Ways of Treating Uncertainty” Journal of Management 41, 744–760. Galaxy NGC 3783. {% revealed preference %} Gale, David (1960) “A Note on Revealed Preference,” Economica, N.S. 27, 348–354. {% cancellation axioms: seems to show that solving linear inequalities as relevant to additive conjoint measurement is equivalent to solving an integer optimization problem. %} Gale, David (1960) “The Theory of Linear Economic Models.” McGraw-Hill, New York. {% Shows existence of policies optimal w.r.t. overtaking criterion in certain context. %} Gale, David (1967) “An Optimal Development in a Multi-Sector Economy,” Review of Economic Studies 34, 1–18. {% Primary/secondary quality distinction: “I think that tastes, odors, colors, and so on are no more than mere names so far as the object in which we locate them are concerned, and that they reside in consciousness. Hence if the living creature were removed, all these qualities would be wiped away and annihilated.” John Locke discussed it extensively. Leibniz argued that it is gradual. Berkeley argued that only secondary (subjective) we can know for sure. %} Galilei, Galileo (1623) The Assayer. {% Seems that the character Sagredo says, on the water-diamond paradox: What greater stupidity can be imagined than that of calling jewels, silver and gold “precious,” and earth and soil “base”? People who do this ought to remember that if there were as great a scarcity of soil as jewels or precious metals, there would not be a prince who would not spend a bushel of diamonds and rubies and a cartload of gold just to have enough earth to plant a jasmine in a little pot, or to sow an orange seed and watch it sprout, grow, and produce its handsome leaves, its fragrant flowers and fine fruit. It is scarcity and plenty that make the vulgar take things to be precious or worthless; they call a diamond very beautiful because it is like pure water, and then would not exchange one for ten barrels of water. This is apparently in Dava Sobel (1999) “Galileo’s Daughter: A Historical Memoir of Science, Faith, and Love.” Fourth Estate, London, p. 152. %} Galilei, Galileo (1638) Dialogues. {% %} Galizzi, Matteo M. & Daniel Navarro-Martínez (2017) “On the External Validity of Social Preference Games: A Systematic Lab-Field Study,” Management Science, forthcoming. {% %} Gallant, A. Ronald, Mohammad R. Jahan-Parvar, & Hening Liu (2015) “Measuring Ambiguity Aversion,” working paper. {% Use Hofstede’s (1991) index of long-term orientation to proxy time preference. Analyze many countries and regions and pre-industrial agro-climatic characteristics. Find that higher return to agricultural investment triggered long-term orientation and impacted technological adoption, education, saving, and smoking. %} Galor, Oded & Ömer Özak (2016) “The Agricultural Origins of Time Preference,” American Economic Review 106, 3064–3103. {% Paper was written in 1907. Crowd should guess weight of an ox. Their average was incredibly close. %} Galton, F. (1949) “Vox Populi,” Nature 75, 450–451. {% %} Gambetta, Diego (2000) “Can We Trust Trust,” Trust: Making and Breaking Cooperative Relations, electronic edn., University of Oxford, 213–237. {% Christiane, Veronika & I; no clear results are found. If not only prices but also income are expressed in a low-value unit (high numbers) then sometimes a reversed euro illusion may be expected. This paper finds different effects for cheap than for expensive products. %} Gamble, Amelie (2006) “Euro Illusion or the Reverse? Effects of Currency and Income on Evaluations of Prices of Consumer Products,” Journal of Economic Psychology 27, 531–542. {% Christiane, Veronika & I %} Gamble, Amelie, Tommy Gärling, John P. Charlton, & Rob Ranyard (2002) “Euro Illusion: Psychological insights into Price Evaluations with a Unitary Currency,” European Psychologist 7, 302–311. {% Christiane, Veronika & I %} Gamble, Amelie & Tommy Gärling (2003) “Violations of Invariance of Perceived Value of Money,” {% Good book on proposition-logic, recommended to me by Monika. %} Gamut, L.T.F. (1991) Logic, Language, and Meaning (Vol. 1. Introduction to Logic, Vol. 2. Intensional Logic and Logical Grammar). The University of Chicago Press, Chicago. Gamut = Johan F.A.K. van Benthem, Jeroen Groenendijk, Dick de Jongh, Martin Stokhof, & Henk Verkuyl {% Mehrez & Gafni, end 1980s, introduced their so-called healthy years equivalent (HYE) as an alternative to QALYs in health economics. Unfortunately, their papers have many logical errors, and many have criticized it, including Johannesson, Pliskin, & Weinstein (1993, MDM), Loomes (1995, JHE), and myself (Wakker 2008 MDM). This paper is a follow-up, worthy of the traditions, because again it is full of logical errors. The basic new model, Eq, 2 p. 1210, is not well defined because a utility function of (x,x2) (wiggle above x and arrow above x2 I do not write here) he lets depend on other things than just (x,x2), being a distribution L(u2(x)) of x of which it has never been specified formally where it comes from. L should by the rules of logic have been expressed as an argument of the utility function then. But then the theory becomes very different from traditional QALY models that first take utility of outcomes without regarding any distribution and only then look at distribution and see how the utilities are to be aggregated, using a probability-weighted mean as in EU or some other aggregation formula. In particular, it loses the tractability of QALYs where evaluation of outcomes is separated from the aggregation of distribution. It now also is unclear if the utility as the author defines should be maximized using an EU aggregation, or otherwise. The author sometimes (p. 1211 top and also 2nd para) explicitly writes that he is deviating from EU. So in what theory is this function to be used? There he seems to take his model as just taking certainty equivalents without even EU, so that his model is not much more than continuituy and transitivity, leaving almost no predictive power. Many positive claims about HYE are based on nothing other than that HYE is, here, apparently, taken as nothing other than a certainty equivalent (with health assumed perfect) under general EU. Then little wonder that no empirical violations (other than general EU), but problem that little predictive power (mentioned on .p. 1210 4th para but not properly incorporated in the rest of the text). Then little wonder that the particular case of SSUF and HYE coincide whenever the model of SSUF holds (pp. 1209-1210). P. 1211 surprises us with the claim that the risk theory of EU imply the intertemporal restriction of time consistency. New to me! The second para seems to present, as a positive feature of the theory, that we don’t “need to” elicit its separate parameters. I would put this more negatively: these parameters are not identifiable because the theory if of almost total generality. P. 1211 end of 2nd -to last para writes that the only assumption is monotonicity in life years in full health. (Let us give the author continuity and weak ordering free of charge.) equate risk aversion with concave utility under nonEU: p. 1211 penultimate para then equates risk aversion with concave utility, which only holds true under EU, a theory explicitly abandoned here. One thing the author and I share is admiration for the appealing idea (SSUF) of Guerrero & Herrero (2005). %} Gandjour, Afschin (2008) “Incorporating Feelings Related to the Uncertainty about Future Health in Utility Measurement,” Health Economics 17, 1207–1213. {% Argues for higher relevance of patient preferences than community preferences in C/E (cost-effectiveness) analyses. Apparently sees a theoretical justification in Harsanyi’s 1955 welfare theorem using veil of ignorance. %} Gandjour, Afschin (2010) “Theoretical Foundation of Patient v. Population Preferences in Calculating QALYs,” Medical Decision Making 30, E57–E63. {% %} Gandjour, Afschin & Amiram Gafni (2010) “The Additive Utility Assumption of the QALY Model Revisited,” Journal of Health Economics 29, 325–328. {% Points out that Keeler-Cretin argument for constant discounting of money and health requires fungibility between money and health with constant exchange rate between them. %} Ganiats, Theodore G. (1994) “Discounting in Cost-Effectiveness Research,” Medical Decision Making 14, 298–300. {% Configurality is very similar to rank-dependence; disjunctive is similar to optimism, overweighting of high values; conjunctive is similar to pessimism, overweighting of low values. For judgment of intervention for cases of child abuse, based on aggregation of some pieces of information, laypersons were more disjunctive than experts. %} Ganzach, Yoah (1994) “Theory and Configurality in Expert and Layperson Judgment,” Journal of Applied Probability 79, 439–448. {% P. 170: normative regressions should be regressive for most bivariate distributions. Representativeness heuristic leads people to give overly extreme answers, so that variation in dependent variable resembles true variation and variation in predictor. These things are moderated by weak regressiveness. Leniency is like the positivity bias from social research, where under uncertainty people tend to judge overly positive about others (“the benefit of the doubt”). %} Ganzach, Yoah & David H. Krantz (1991) “The Psychology of Moderate Prediction II. Leniency and Uncertainty,” Organizational Behavior and Human Decision Processes 48, 169–192. {% Intro to the special issue on Liu’s uncertainty theory. %} Gao, Jinwu, Jin Peng, & Baoding Liu (2013) “Uncertainty Theory with Applications,” Fuzzy Optimization and Decision Making 12, 12. {% Let subjects choose from three risky prospects, so that their choice shows their risk tolerance à la Binswanger (1981). Show that people with a higher ratio of the length of their second and fourth finger take more risks. %} Garbarino, Ellen, Robert Slonim, & Justin Sydnor (2011) “Digit Ratios (2D:4D) as Predictors of Risky Decision Making for Both Sexes,” Journal of Risk and Uncertainty 42, 1–26. {% Tradeoffs involving small-probability health hazards are difficult to make for subjects because small probabilities are hard to process as is well known. This paper proposes to translate those tradeoffs into a threshoods of mortality. %} Garcia-Hernandez, Alberto (2014) “Quality-of-Life—Adjusted Hazard of Death: A Formulation of the Quality-Adjusted Life-Years Model of Use in Benefit- Risk Assessment,” Value in Health 17, 275–279. {% Seems to be: decision under stress; Ch. 9 deals with risks, catastrophes and “protection-motivation theory,” comparing external threats and internal coping %} Gardner, Gerald T. & Paul C. Stern (1996) “Environmental Problems and Human Behavior.” Allyn and Bacon, Boston. {% Gives an account of the cognitive revolution. %} Gardner, Howard (1985) “The Mind’s New Science: A History of the Cognitive Revolution.” Basic Books, new York. {% three-prisoners problem %} Gardner, Martin (1961) “Second Scientific American Book of Mathematical Puzzles and Diversions.” Simon and Schuster, New York NY. {% %} Gardner, Martin (1973) “Free Will Revisited, with a Mind-Bending Prediction Paradox by William Newcomb,” Scientific American 229, No. 1 (July), 104–108. {% 652 readers of Scientific American wrote their choices; 70% would take only one box. %} Gardner, Martin (1974) “Reflections on Newcomb’s Problem: A Prediction and Free-Will Dilemma,” Scientific American 230, No. 3 (March), 102–109. {% %} Gardner, Martin (1974) “Mathematical Games,” Scientific American 230, March 1974, 108–113. {% This seems to be part of a serious called “Mathematical Games” by Gardner. P. 120 2nd column gives “juicy” reference to Samuelson who relates Arrow’s theorem to democracy. John Conway found a simple formula for calculating the probability that player A wins. This formula is described by Gardner. %} Gardner, Martin (1974) “On the Paradoxical Situations that Arise from Nontransitive Relations,” Scientific American 123 no. 4 (Oct.), 120–125.
Gardner, Martin J. & David G. Altman (1986) “Confidence Intervals rather than P Values: Estimation rather than Hypothesis Testing,” Br. Med. J. (Clin. Res. ed.) 292, 746–750. {% finite additivity %} Gardner, Roy J. (1981) “The Regularity of Borel Measures.” In Dietrich Kölzow & Dorothy Mahararn-Stone (eds.) Proceedings of Measure Theory, Oberwolfach, Lecture notes 945, Springer, Berlin. {% %} Garey, Michael R. & David S. Johnson (1979) “Computers and Intractability: A Guide to the Theory of NP-Completeness.” Freeman, San Francisco. {% anonymity protection %} Garfinkel, Robert, Ram Gopal, & Paulo Goes (2002) “Privacy Protection of Binary Confidential Data against Deterministic, Stochastic, and Insider Threat,” Management Science 48, 749–764. {% A 2011 study on this interesting decision problem. %} Garrouste, Clémentine, Jérôme Le, & Eric Maurin (2011) “The Choice of Detecting Down Syndrome: Does Money Matter?,” Health Economics 20, 1073–1089. {% probability elicitation; Compares eliciting all j/4 quantiles to another similar procedure and sees which performs best. %} Garthwaite, Paul H. & James M. Dickey (1985) “Double- and Single-Bisection Methods for Subjective Probability Assessments in a Location-Scale Family, Journal of Econometrics 29, 149–163. {% survey on belief measurement. %} Garthwaite, Paul H., Joseph B. Kadane, & Anthony O’Hagan (2005) “Statistical Methods for Eliciting Probability Distributions,” Journal of the American Statistical Association 100, 680–701. {% real incentives/hypothetical choice: for time preferences: finds annual discount rate exceeding 26% at purchases of individual refrigerators. %} Gately, Dermot (1980) “Individual Discount Rates and the Purchase and Utilization of Energy-Using Durables: Comment,” Bell Journal of Economics 11, 373–374. {% P. 330: relative curvature %} Gati, Itamar & Amos Tversky (1982) “Representations of Qualitative and Quantitative Dimensions,” Journal of Experimental Psychology: Human Perception and Performance 8, 325–340. {% %} Gattig, Alexander (2002) “Intertemporal Decision Making,” Ph.D. dissertation, ICS, Groningen, the Netherlands. {% Made pictures of RDU on p. 9 %} Gayant, Jean-Pascal (1991) “Un Diagramme Représentatif de l’Utilité “Anticipée” ,” W.P. 9109, June 1991, Center of Mathematics, Economics, and Computer Science, University of Paris I, Paris, France. {% Made nice pictures of RDU; p. 1056: estimate of w(.5) for 20 participants, yielding w(.5) = .42 (hurray!); the estimation is, however, based on some linearity assumptions P. 1054 writes (translated from French original): “the dissociation of the two effects is difficult because they interact jointly without it being possible to isolate one from the other” It then assumes, and will later verify, linear utility to estimate transformation of p=.5. Well, by the Tradeoff method it is easy! P. 1056: participants do not distinguish between close probabilities, which reminds a bit of low sensitivity à la Tversky & I. %} Gayant, Jean-Pascal (1995) “Généralisation de l’Espérance d’utilité en univers risqué: Représentation en Estimation,” Revue Economique 46, 1047–1061. {% CBDT; inverse-S; cognitive ability related to likelihood insensitivity (= inverse-S): develops a case-based, cognitive, justification for inverse-S shaped probability transformation. Has probability 0.5 undistorted, as Quiggin (1982). It also supports my claim in Wakker (2004, Psychological Review, Figure 2a) that that is plausible for the cognitive component of probability transformation. uncertainty amplifies risk: confirms it. The fewer cases in memory and the worse the similarity function, the more inverse-S. %} Gayer, Gabrielle (2010) “Perception of Probabilities in Situations of Risk; A Case Based Approach,” Games and Economic Behavior 68, 130–143. {% CBDT; Consider prices for houses for rent, where speculation will play no role, and for sale, where speculation will play a role. Compare two ways to determine the price of a house: (1) Rule-based. Regress it on a number of properties such as size, distance to shopping center, and so on. (2) Case-based. Derive the price as a similarity-weighted mean of prices of other, similar, houses. Here the properties of houses are similarity-weighted averages of the other prices, where the similarity weight of two houses is derived by transforming a dimension-weighted Euclidean distance between houses when characterized through a vector or properties (I guess the same as above). They don’t sum the similarity-weighted prices but average them. They find that for buying prices the rule-based method works best and for renting the case-based, and give arguments for it. %} Gayer, Gabrielle, Itzhak Gilboa, & Offer Lieberman (2007) “Rule-Based and Case-Based Reasoning in Housing Prices,” B.E. Journal of Theoretical Economics 7, Iss. 1 Article 10. {% Seems to give the following example. Patient had left and right hemisphere separated. Right hemisphere was told to wave hand. Left hemisphere observed the waving but did not know why and, as explanation, came up with explanations such as just seeing a friend. Moral of this story may be that our mind, to some extent, does not make decisions but rationalizes them in retrospect. %} Gazzaniga, Michael S. & Joseph E. LeDoux (1978) “The Integrated Mind.” Plenum, New York. {% Total utility theory: nice reference where total utility theory is applied in a rather straightforward manner: terminal cancer patients with bone metastases receive radiotherapy. What is better, once a dose of 10 Gy, or five times a dose of 4.5 Gy? The two treatments are given to randomized trials, patients or doctors or both report pain scores at several time points, treatments are compared according to the pain scores. Other relevant dimensions are costs (11 times 10 Gy is cheaper) and side effects. %} Gaze, Mark N., Charles G. Kelly, Gillian R. Kerr et al. (1997) “Pain Relief and Quality of Life Following Radiotherapy for Bone Metastases: A Randomised Trial of Two Fractionation Schedules,” Radiotherapy and Oncologie 45, 109–116. {% Seems to have introduced psychological game theory. Unfortunately, also this term, taking psychology—a field broader and more diverse than economics—as one concept. It is like psychologists using the term “economic game theory” because games involve money, or “mathematical game theory” because on page 2 they used a formula. %} Geanakoplos, John, David Pearce, & Ennio Stacchetti (1989) “Psychological Games and Sequential Rationality,” Games and Economic Behavior 1, 60–79. {% 12 participants chose repeatedly (768 times), 24 blocks of each 32 times, between two fifty-fifty gambles yielding a gain or loss of x for x=5 or x=25 cents. So they must choose whether x=5 or x=25. They received sum total at end of each block. As William explained to me on August 21, 2002, in an email, the latter happened only if that total was positive. If the total was negative it was not subtracted. 52% of the choices were risk seeking, so x=25 iso x=5. Given that the incentive system enhances risk seeking, it is not amazing that there was some more risk seeking. Brain-activities for losses were qualitatively different than for gains. After a preceding loss people became more risk-seeking than after a preceding gain. In the first quarter of blocks, there were 58% risky choices (x=25), in the last 48%. Because participants could also see what their alternative choice would have yielded, they could feel regret. But, regret did not do much. I did not find it mentioned what percentage overall was risk seeking (choose x = 25 cents) or risk averse (choose x = 5 cents). How the real incentives were implemented (did they have to pay really if the lost?) is not explained. %} Gehring, William J. & Adrian R. Willoughby (2002) “The Medial Frontal Cortex and the Rapid Processing of Monetary Gains and Losses,” Science 295, 2279–2282. {% %} Geiger, Gebhard (2002) “On the Statistical Foundations of Non-Linear Utility Theory: The Case of Status Quo-Dependent Preferences,” European Journal of Operational Research 136, 449–465. {% Takes a very general model for decision under risk, with weak ordering and a weakened version of stochastic dominance (Axiom 4, p. 119). There is not only the prospects p and q to be chosen from but also another prospect r that is something like your background risk or reference point. So the choice is between p|r and q|r. It is not clear to me if choosing p means you get p instead of r, or you get p in addition to r. P. 124 suggests something like uncertainty about r being implemented before or after p. Besides weak ordering and weakened stochastic dominance, Axiom 5 is imposed (if preferences given r are the same as without r given, then r must be equivalent to receiving 0). Then a general functional satisfying these requirements is defined. %} Geiger, Gebhard (2008) “An Axiomatic Account of Status Quo-Dependent Non-Expected Utility: Pragmatic Constraints on Rational Choice under Risk,” Mathematical Social Sciences 55, 116–142. {% Derives a very general model on multiattribute nonEU, with probability-dependent utility. In the proof of Theorem 2, I did not see why the limit of W(x´) could not be strictly less than W(x), in other words, where continuity in outcome comes from. (Axiom 2 is continuity in probabilistic mixing.) %} Geiger, Gebhard (2012) “Multi-Attribute Non-Expected Utility,” Annals of Operations Research 196, 269–292. {% common knowledge %} Geneakoplos, John & Herakles M. Polemarchakis (1982) “We Can’t Disagree Forever,” Journal of Economic Theory 28, 192–200. {% %} Genesove, David & Christopher Mayer (2001) “Loss Aversion and Seller Behavior: Evidence from the Housing Market,” Quarterly Journal of Economics 116, 1233–1260. {% revealed preference %} Gensemer, Susan H. (1991) “Revealed Preference and Intransitive Indifference,” Journal of Economic Theory 54, 98–105. {% They reproduce the WTP-WTA disparity and relate it to all kinds of things such as introspective scales and also loss aversion in risky tasks. They find that loss aversion has much influence (p. 904 last para preceding §3.5). End of section 1 appropriately criticizes Plott & Zeiler. %} Georgantzís, Nikolaos & Daniel Navarro-Martínez (2010) “Understanding the WTA-WTP Gap: Attitudes, Feelings, Uncertainty and Personality,” Journal of Economic Psychology 31, 895–907. {% risky utility u = strength of preference v (or other riskless cardinal utility, often called value): discusses ordinal-cardinal and vNM’s role in that, although not specifically about strength of preferences. Argues that in cardinal view not the vNM independence axiom, but weak ordering and in particular indifference, is the problem. I found the paper confused. Has nice citations of Marx and Aristotle. P. 515: conservation of influence: “For this is in fact what utility represents; the common essence of all wants, the unique want into which all wants can be merged.” [italics from original] P. 525 looks silly: “a sure alternative and a risk proposition, being relatively heterogeneous, can in no case be indifferent.” Seem to show that a hexagon-type condition implies additive representation. This had been known in web theory (Blaschke & Bol, 1938) before. %} Georgescu-Roegen, Nicholas (1954) “Choice, Expectations and Measurability,” Quarterly Journal of Economics 68, 503–534. {% %} Georgescu-Roegen, Nicholas (1969) “The Relation between Binary and Multiple Choices: Some Comments and Further Results,” Econometrica 37, 728–730. {% Several continuity conditions (upper/lower, open/closed) that are equivelent under completeness, are no longer so under incompleteness. This paper investigates logical relations, with variations of Schmeidler (1971). %} Gerasimou, Georgios (2013) “On Continuity of Incomplete Preferences,” Social Choice and Welfare 41, 157–167. {% information aversion When the allies bombed Germany in WWII, they deliberately let information leak to the Germans to let them know (through double spies) that one of the potential targets would not be bombed. %} Gerchak, Yigal & Frank R. Safayeni (1993) “Perfect Information with Negative Value: An Intriguing War Story and a Possible Explanation,” Dept. of Management Science, University of Waterloo, Waterloo, Ontario, Canada. {% §1 briefly explains the rational expectations model (i.e., that expectations are a martingale). §2 briefly discusses Keynes’ ideas. %} Gerrard, Bill (1994) “Beyond Rational Expectations: A Constructive Interpretation of Keynes’s Analysis of Behaviour under Uncertainty,” Economic Journal 104, 327–337. {% %} Gescheider, George A. (1988) “Psycho-Physical Scaling,” American Review of Psychology 39, 169–200. {% bisection > matching: Chapter 3: The Classical Psychophysical Methods". Discuss direct matching, choice lists, and bisection in psychophysics. Bisection avoids a number of biases. It seems to be called the staircase method. These things were debated already in psychophysics in the 1960s. %} Gescheider, George A. (1997) “Psychophysics: the Fundamentals; 3rd edn.” Lawrence Erlbaum Associates. {% %} Geweke, John F. (1992) “Decision Making under Risk and Uncertainty; New Models and Empirical Findings.” Kluwer Academic Publishers, Dordrecht. {% Seems that probability weighting explains their data on horse race betting well. %} Gandhi, Amit, and Ricardo Serrano-Padial (2012) “From Aggregate Betting Data to Individual Risk Preferences” {% %} Ghirardato, Paolo (1994) “Agency Theory with Non-Additive Uncertainty,” University of California at Berkeley. {% %} Ghirardato, Paolo (1997) “On Independence for Non-Additive Measures, with a Fubini Theorem,” Journal of Economic Theory 73, 261–291. {% With belief functions, model with subpartition describing all that is observed and acts are correspondences; to them Savage’s axioms are applied, leading to a probability distribution over subsets of outcomes, which, in turn, is uniquely related to a belief function over outcomes, being its Möbius inverse. Is similar to Jaffray & I, generalizing it in an appealing manner. %} Ghirardato, Paolo (2001) “Coping with Ignorance: Unforeseen Contingencies and Non-Additive Uncertainty,” Economic Theory 17, 247–276. {% Uses dynamic consistency and consequentialism to model Savage’s SEU plus Bayesian updating. Not very new (in a lecture Paolo called the result a folk theorem), but done neatly and maybe the nicest paper to demonstrate how dynamic principles imply EU. The only choice options are static functions from state space to outcomes; i.e., the static analogues of strategies. This automatically implies RCLA. Paolo clearly and explicitly says so two paras above Axiom 1. For each event A, a conditional pref A is given. Can be interpreted as anticipated-conditional, or ex post. Paolo explicitly leaves both open. In this setup, a choice f A g, such as considered in DC (dynamic consistency) (axiom 2) for f and g disagreeing outside of A, is not easily depicted in a conventional decision tree. It is therefore easier to first assume consequentialism (axiom 7). This axiom does not refer to de novo decisions, such not occurring in the model, but says that A ignores the counterfactual part (so that de novo decisions can be meaningfully defined, independently of what counterfactual part is assumed). With that given, Paolo's DC reduces to the usual DC that [ if agreement outside of A] agrees with [A if agreement outside of A]. Paolo's DC also requires agreement of [ if agreement outside of A] with [A if no agreement outside of A] which is a bit hard to interpret. %} Ghirardato, Paolo (2002) “Revisiting Savage in a Conditional World,” Economic Theory 20, 83–92. {% Two functions are comonotonic iff the Choquet integral of the sum is the sum of the Choquet integrals for every capacity. The authors show an analogous result for multiple priors: two functions are affine-related (one function being affine transform of the other) if and only if the MP value of the sum is the sum of the MP model for every convex set of probability distributions. The analogy does not go through for another aspect of comonotonicity: comonotonic additivity holds iff the representation is a Choquet integral. There is no analogous statement for MP and affine relatedness. %} Ghirardato, Paolo, Peter Klibanoff, & Massimo Marinacci (1998) “Additivity with Multiple Priors,” Journal of Mathematical Economics 30, 405–420. {% updating %} Ghirardato, Paolo & Michel Le Breton (2000) “Choquet Rationalizability,” Journal of Economic Theory 90, 277–285. {% event/utility driven ambiguity model: event-driven The authors refer to unpublished work by Nehring for similar ideas. They consider a representation f --> (f)infPC∫SU(f(s))dP + (1(f)) supPC∫SU(f(s))dP where f is an act mapping S to outcomes, C is a set of probability measures on S, ∫S is the integral over S, U is utility, and 0 1. Arrow-Hurwicz is the special case of constant and C the set of all probability measures. Without any restriction, this model has little predictive power because of the generality of depending on f in every possible way, apart from the EU evaluation of risk and the required certainty equivalence. We can always let C be the set of all probability measures, so that inf is the worst outcome of f and sup the best, and with (f) we can get whatever is the desired midpoint between their utilities. The authors impose the following restriction on C. Let ' be the preference relation. They define as the unambiguous part '* the preferences f '* g whenever f + (1)c ' g + (1)c for all from [0,1] and acts c (by taking close to 0, they can let the decision take place in the comonotonic set with rank-ordering or whatever circumstances as dictated by c, so whatever they want it to be). '* is a nice and valuable idea. As regards the mixing operation on acts, they assume the Anscombe-Aumann structure on S, amounting simply to a convex space of outcomes with linear utility U and statewise mixing for the acts. So the unambiguous preferences are those that reflect vNM independence and behave according to EU. '* is like an EU preference, only it is not complete. Then they use the appealing representation of Castagnoli, Maccheroni, & Marinacci (2003), and others, that f '* g if and only if there is unanimous agreement that ∫SU(f(s))dP ∫SU(g(s))dP for all P from a set C. They take the set C above to be this set. This makes the representation operational, although I would not call it observable because it still is an existence result not fundamentally different from the existence result of for instance Gilboa & Schmeidler (1989). The sup of expected utilities above turns out to correspond to the lowest sure outcome x* that has x* '* f, and the inf of expected utilities above corresponds to the highest sure outcome x* that has x* '* f. So the value of f is between x* and x*, and (f) is derived from this. The set C turns out to be the smallest set that could be used. (f) is constant (independent of f) if and only if x* and x* completely determine the preference value of f (Proposition 19). This, appealing, result I consider the main result of this paper because for tractability reasons it is desirable that not be very general. They interpret '* as unambiguous preferences, C as reflecting the state of belief and of ambiguity of the decision maker, and (f) as reflecting attitude towards ambiguity. It means that for the special case of multiple priors they take the whole set of priors as reflecting belief, and not decision attitude. For example, if there is DUR with known probabilities, the agent does RDU with convex probability transformation w, so that we have CEU (Choquet expected utility) with convex nonadditive measure w(P(.)), then this model can be written as multiple priors (the priors are the CORE of w(P(.))), and then the authors consider this to reflect ambiguous beliefs. The authors discuss the point just raised. First, p. 137 next-to-last para discusses that absence of and neutrality towards ambiguity cannot be distinguished in their approach, and that they equate SEU with unambiguous. P. 138 then mentions the big problem that what they call ambiguity also comprises the part of risk attitude that deviates from expected utility (see above example of RDU with convex w). Amarante (2009, §3.1) criticizes the interpretation. Eichberger, Grant, Kelsey, & Koshevoy (2011, JET) show that for finite state spaces the /1 model below can only exist, under the axioms of this paper, if = 1 or = 0, that is when it is maxmin or maxmax as known before. This takes the heart out of the axiomatization of -maxmin in this paper. %} Ghirardato, Paolo, Fabio Maccheroni, & Massimo Marinacci (2004) “Differentiating Ambiguity and Ambiguity Attitude,” Journal of Economic Theory 118, 133–173. {% Assume that value of outcomes x has been quantified through utilities U(x). Assume that preference functional is I(Uof) for a functional I. I is interpreted as belief (I would say, “related to belief”). Assume further that U is unique up to some family of transformations. It is required that I not be affected by applying such transformations. It is shown that, if the family of transformations for U is ordinal, then the definition does not work well. If the family is cardinal, then I must satisfy something like certainty-independence. For binary acts I must then be a rank-dependent functional (“biseparable model” as the authors call it). This, most appealing, result is not stated formally but only informally in the 2nd para of §3 on p. 135, strangely enough. For binary acts the latter also suffices, as is trivial. This if-and-only-if result for binary acts had been known before (Theorems 7.1 & 7.2.2 in Luce & Narens 1985). The authors GMM mention that, in their terminology, not every biseparable model works, but I think that this is so only because for acts with more than two outcomes biseparability does not impose many restrictions so that weird things can happen there. For binary acts RDU is iff, as Luce & Narens showed. %} Ghirardato, Paolo, Fabio Maccheroni, & Massimo Marinacci (2005) “Certainty Independence and the Separation of Utility and Beliefs,” Journal of Economic Theory 120, 129–136. {% Decision under uncertainty. Assume that a Choquet expected utility representation exists for all binary acts. CE denotes certainty equivalent. Then, under appropriate rank-ordering, CE(CE(x,y),CE(v,w)) ~ CE(CE(x,v),CE(y,w)) follows from substitution; this is bisymmetry. They define a midpoint operation x*z = y, assigning midpoint y to x and z, by CE(CE(x,x),CE(z,z)) ~ CE(CE(x,y),CE(y,z)), for x > y > z. Substitution shows that y is the midpoint of x and z in utility units. By repeated procedures we can, thus, get (where mixing is always in utility units) x/4 + 3z/4, 3x/4 + z/4, etc., so ax + (1-a)z for a dense subset of a’s in [0,1] (all dyadic a’s). By limit taking, or approximately, we can get it for all a in [0,1]. Note that eliciting all these mixtures amounts to the same as eliciting the utility function itself. The authors argue that now the mixing operation is observable, behavioral as they call it, and that it can be used as a primitive in axioms. They subsequently reformulate preference axioms in the literature in this manner for extraneous mixing à la Anscombe-Aumann (1963). derived concepts in pref. axioms: a difficulty is that the mixture operation becomes observable only after a long elicitation procedure. Preference axiomatizations in terms of this are in fact very complex axioms, not easily testable. For instance, f ~ g ==> f/3 + 2h/3 ~ g/3 + 2h/3, mixture independence for mixture weight 1/3, can never be verified exactly, because weight 1/3 can never be obtained exactly; it can only be verified approximately or in the limit. When Hübner & Suck (1993) similarly used a preference condition in terms of observables that involves infinitely many preferences, they explicitly mentioned this as a weak point on p 638. The axioms could have been stated directly in terms of utility as well as in terms of the mixing operation, because utility can be elicited as easily, in fact through the same observations, as the mixture operation. (Sugden, Journal of Economic Theory 1993, similarly demonstrated how utility can be elicited and then used it as a primitive in axioms. I would not call that behavioral for the same reasons.) I consider this approach derived measurement. While their axiomatizations are logically true, they do not have the behavioral status and appeal of preference axiomatizations that can be stated directly in terms of a small number of preferences. The results of this paper are logical equivalences between two statements in theoretical terms. The authors could have avoided these problems for Choquet expected utility by imposing their axioms only for .5/.5 mixtures, which given continuity will imply the whole axiom. They have such, more appealing, results in the 2003 extended version of this paper. Besides Choquet expected utility, the authors also characterize multiple priors, and Bewley’s model under the special assumption that there is an event E for which subjective expected utility holds, implying that all probability measures in the set of priors assign the same probability to E. This rules out, for instance, probabilistic risk attitudes with RDU with the probability weighting strictly convex. %} Ghirardato, Paolo, Fabio Maccheroni, Massimo Marinacci, & Marciano Siniscalchi (2003) “A Subjective Spin on Roulette Wheels,” Econometrica 71, 1897–1908. {% criticizing the dangerous role of technical axioms such as continuity: Krantz et al. (1971 §9.1), and other works, explain that “technical” axioms such as continuity are dangerous because they add implications to intuitive axioms, and we don’t know exactly what those are. The authors refer to Krantz et al. for this point, and illustrate it by other examples, regarding the technical assumption of solvability (range convexity as they call it) of a capacity. The main point is that under CEU/RDU and convex-rangedness, the existence of one symmetric event such as implied by complement-symmetry preference axioms for that event (betting on or betting against the event gives same likelihood ordering) and convexity as implied by what is often interpreted as ambiguity aversion, together imply additivity and SEU. It is like a continuous strictly increasing function w from [0,1] to [0,1] with w(0) = 0 and w(1) = 1, if it is convex and if there is a p with w(p) + w(1p) = 1 (implying that not both w(p) and w(1p) can be below the diagonal), then w must be linear. The authors argue, on p. 609 end of §3, that the existence of such an event (or such a p) is a weak assumption, and then put the blame on convex-rangedness. %} Ghirardato, Paolo & Massimo Marinacci (2001) “Range Convexity and Ambiguity Averse Preferences,” Economic Theory 17, 599–617. {% event/utility driven ambiguity model: event-driven That preferences satisfying CEU (Choquet expected utility) on binary (two-valued) acts can be useful and interesting has been observed before (Miyamoto & Wakker 1996 OR; Luce 2000 Ch. 3), as it has been that such acts suffice to identify utility and the capacity. But no-one used this insight as clearly and thoroughly as this paper does. The results obtained apply to all theories that agree with CEU on binary acts, such as multiple priors, Gul’s disappointment aversion theory, prospect theory only for gains or only for losses, and -Hurwicz. In most places the paper interprets the capacity (= weighting function), nicely, as willingness to bet. Sometimes, however, it interprets the capacity as belief (claiming a separation of tastes and beliefs), which is questionable. They point this out in §5.2, p. 879. The authors do not want to use objective given probabilities. Then it is hard, or impossible, to separate out the risk attitude component from the capacity (and take what remains as ambiguity component). This does not justify, however, the assumption of the authors that there be no risk attitude in the capacity, and that the capacity consists merely of ambiguity attitude. In the terminology that the authors use, probabilistic risk attitude ends up in the wrong place. It should be part of risk attitude, not of ambiguity attitude as it now is. In the authors’ terminology, “risk attitude” refers merely to utility. biseparable utility: emphasized much and a central topic in this paper. They use the term biseparable for it. They impose the Chew & Karni (1994) CEU axioms on binary acts only, giving the CEU representation only there. Show that results on utility, such as u2 being concave transform of u1 iff certainty equivalents for u2 smaller than for u1, can be derived in their model as well; i.e., if SEU on a comonotonic subset for two states of nature. They, however, make the nonbehavioral assumption of equal capacity for the two decision makers (they suggest they have an axiom for that but don’t give it). For real outcomes, they adapt preference for diversification and quasi-convexity characterizations of concave utility to their model. binary prospects identify U and W; §5.1, on probabilistic beliefs for binary acts: this is also in Pfanzagl (1959). %} Ghirardato, Paolo & Massimo Marinacci (2001) “Risk, Ambiguity, and the Separation of Utility and Beliefs,” Mathematics of Operations Research 26, 864–890. {% Tradeoff method: use it on p. 264 and elsewhere to characterize identity of two utility functions in their cardinal symmetry. I think that a better title of this paper would have been: “A Separation of Utility and Uncertainty Attitude.” They consider CEU (Choquet expected utility) (or, similarly, multiple priors) for two-outcome gambles. Interpret utility U as “cardinal” risk attitude, and capacity as ambiguity attitude. A problem is that all of risk attitude outside expected utility, such as Allais paradox, probabilistic risk attitude (probability transformation in RDU), thus ends up in ambiguity attitude and not in risk attitude. The authors signal and discuss this problem on p. 257, 274-275, and several times in the Discussion section. They don’t want to use given probabilities (usually described broadly as “extraneous device”), which is why they don’t isolate probabilistic risk attitude from ambiguity attitude. They provide arguments against probabilistic sophistication as ambiguity-neutrality in the Discussion section, arguments that I agree with. (But my solution is different: I recommend using (“extraneously-”)given probabilities as ambiguity neutrality.) Sometimes (p. 256 l. 7) they interpret the capacity as belief. Mostly they, nicely, interpret it as willingness to bet. P. 257 l. 12-14 is misleading because Savage did not consider ambiguity as a normatively compelling argument against expected utility. derived concepts in pref. axioms: p. 265 discusses a preference condition that would require the whole elicitation of a continuum of a utility scale: “This extension requires the exact measurement of the two preferences’ canonical utility indices, and is thus “less behavioral” than the one we just anticipated.” P. 276 states it as: “Nonetheless, this ranking requires the full elicitation of the DM’s canonical utility indices, and thus is operationally more complex than that in Definition 7.” Exactly these criticisms apply to the endogenous mixture operation used as behavioral in Ghirardato, Maccheroni, Marinacci, & Siniscalchi (2003, Econometrica). They use the Yaari-definition of higher certainty equivalents. Call a second decision maker more uncertainty averse than a first if the second always has lower certainty equivalents. Under identical utilities (implied by their cardinal symmetry) they then call the first more ambiguity averse. It implies, and under CEU is equivalent to, the capacity of the second being dominated by the first. They define SEU as ambiguity neutral and define ambiguity aversion in an absolute sense as existence of SEU with same utility that is less ambiguity averse. The latter holds iff the capacity is pointwise dominated by an additive probability, in other words, has a nonempty CORE. This is an axiomatization in the sense of necessary and sufficient, a logical equivalence between two statements about theoretical concepts. It is not a decision-axiomatization because both conditions are not stated in terms of directly observable choices: the existence of the less ambiguity averse SEU is not directly observable (derived concepts in pref. axioms). The authors signal this problem on p. 256, saying that their definition of ambiguity neutrality is behavioral but computationally demanding. Their definition of ambiguity aversion had been proposed before by Montesano & Giovannoni (1996 Def. 1 p. 136). The authors do not sufficiently credit this priority, and only write on p. 258: “Montesano and Giovannoni [21] notice a connection between absolute ambiguity aversion in the CEU model and nonemptiness of the core, but they base themselves purely on intuitive considerations on Ellsberg's example.” It is troublesome that they can handle ambiguity attitudes, ambiguity neutrality etc., only if there is either ambiguity seeking or ambiguity aversion, and not for more general attitudes towards ambiguity. For insensitive symmetric weighting functions, for instance, their definitions do not detect the ambiguity present. (Ambiguity=amb.av=source.pref) %} Ghirardato, Paolo & Massimo Marinacci (2002) “Ambiguity Made Precise: A Comparative Foundation,” Journal of Economic Theory 102, 251–289. {% %} Ghirardato, Paolo & Marciano Siniscalchi (2010) “A More Robust Definition of Multiple Priors,” working paper, June 2010. {% Consider general multiple prior models, explicitly NOT assuming uncertainty aversion or certainty independence. Use the Anscombe-Aumann setup. They do not explicitly refer to it, but it is because they assume a convex set X of outcomes, preferences over which are represented by an affine function u (their term Bernoullian refers to this being like EU). Show that sets of priors, as from the pretty unambiguous subpreference of Ghirardato, Maccheroni, & Marinacci (2004), are obtained as union of Clarke differentials. The latter are a kind of multidimensional analog of derivatives, but can also be used if a functional is not differentiable. Thus they relate priors to local optimizations. Although it can be called an operationalization of sets of multiple priors, unions of Clark differentials and local linear approximations of preferences are too complex to be used for empirical calibration. This paper is an analog for uncertainty of what Machina (1982) did for risk. %} Ghirardato, Paolo & Marciano Siniscalchi (2012) “Ambiguity in the Small and in the Large,” Econometrica 80, 2827–2847. {% questionnaire for measuring risk aversion: use it and give references in mid p. 87; uncertainty amplifies risk: find that. They use subjective general questionnaires to assess risk aversion and ambiguity aversion of people. Also use a Kachelmeier (1993) list of risky choices to assess risk attitude (which, unfortunately, gave risk neutrality for all 39 subjects so that it was not sufficiently discriminating). Then let N=39 students decide on how many inspections to carry out in a supposed manufacturing plant where, subjects, however, received real performance-contingent payments. For high risk and high ambiguity they find aversion, for low risk no aversion and for low ambiguity also no aversion. (p. 86 when in the five hypotheses H1-H5 they write “explain” they mean that aversion is exhibited). %} Ghosh, Dipankar & Manash R. Ray (1997) “Risk, Ambiguity and Decision Choice: Some Additional Evidence,” Decision Sciences 28, 81–104. {% CEs (certainty equivalents) are used to define comparative ambiguity attitudes in a general convex preference model for ambiguity. %} Giammarino, Flavia & Pauline Barrieu (2013) “Indifference Pricing with Uncertainty Averse Preferences,” Journal of Mathematical Economics 49, 22–27. {% The paper considers belief functions via the Möbius inverse, as in Dempster’s random messages. It provides a detailed comparison beween a model by Jaffray & Wakker (JW) and one by Giang & Shenoy (GS). The latter considers only (partially) consonant belief functions (Def. 6 p. 42): their Möbius inverse lives on disjoint groups that are all telescopically nested, which means nested (for each pair one is a subset of the other) and in that sense is less general. But JW deal only with Dempster-type setups where the mixture weights used in Möbius inverse are exogenously given objective probabilities (“disambiguate the foci of belief;” p. 50) and in that sense are less general. The paper considers a sequential consistency condition as in Sarin & Wakker (1998) that is violated by JW but satisfied by GS. %} Giang, Phan H. (2012) “Decision with Dempster–Shafer Belief Functions: Decision under Ignorance and Sequential Consistency,” International Journal of Approximate Reasoning 53, 38-53. {% Presents a model similar to Jaffray (1989 ORL), but does not know or cite Jaffray. Assumes that risk with known probabilities is one extreme, complete ignorance is another (here he does cite Cohen & Jaffray 1980), and (§3) considers also cases in between where, unlike most of the modern ambiguity AA models, the roulette precedes horses, which I think is better (Wakker 2010 §10.7.3). Uses Arrow-Hurwicz to model complete ignorance, where only minimal and maximal possible outcomes matter. Uses and Anscombe-Aumann (AA) multi-stage setup, and relaxes the collaps-event assumption. It does hold within one source (my term) but not between. So, in AA, roulette before horse is different than horse before roulette. Derives comparative results as being more tolerant for ignorance from Yaari-type certainty equivalent comparisons. Discusses Ellsberg, multiple priors, and belief functions. Does not discuss modern (2015) ambiguity models although as an aside it cites the smooth KMM (2005) paper. %} Giang, Phan H. (2015) “Decision Making under Uncertainty Comprising Complete Ignorance and Probability,” International Journal of Approximate Reasoning 62, 27–45. {% completeness-criticisms: this paper has the nice idea of incomplete preferences (called necessary) that are next extended using preference conditions. %} Giarlotta, Alfio & Salvatore Greco (2013) “Necessary and Possible Preference Structures,” Journal of Mathematical Economics 49, 163–182. {% %} Gibbard, Alan & William L. Harper (1987) “Counterfactuals and Two Kinds of Expected Utility,” In Peter Gärdenfors & Nils-Eric Sahlin (eds.) Decision, Probability, and Utility, 341–376, Cambridge University Press, Cambridge. {% %} Gibbons, Robert (1992) “A Primer in Game Theory.” Prentice-Hall, London. {% decision under stress %} Giesen, Carin, Arne Maas, & Marco Vriens (1989) “Stress among Farm Women: A Structural Approach,” Behavioral Medicine 15, 53–62. {% Suggest that VAS is better than TTO, SG, or WTP (SG doesn’t do well). There are, however, many many problems in the methodology and goodness-scores. (differentiation/inconsistency) used in this study. %} Giesler, Brian R. et al. (1999) “Assessing the Performance of Utility Techniques in the Absence of a Gold Standard,” Medical Care 37, 580–588. {% Pp. 260-261, Examples 1 and 2, show that the author does not understand probability other than frequentist, leading to silly viewpoints on statistical inference in a single case. %} Gigerenzer, Gerd (1991) “From Tools to Theories: A Heuristic of Discovery in Cognitive Psychology,” Psychological Review 98, 254–267. {% Origins and limits of overconfidence %} Gigerenzer, Gerd (1996) “Why do Frequency Formats Improve Bayesian Reasoning? Cognitive Algorithms Work on Information, Which Needs Representation,” Behavioral and Brain Sciences 19, 23. {% Pp. 26-27 seem to write: [there are three major interpretations of probability] "Of the three interpretations of probability, the subjective interpretation is the most liberal about expressing uncertainties as quantitative probabilities." (Then anecdote about surgeon doing first ever heart-transplantation. The wife of the patient asks to the surgeon: “What chance do you give him?” The surgeon answers: “An 80 percent chance.”) “[the surgeon's] “80 percent” reflected a degree of belief, or subjective probability. In the subjective view, uncertainties can always be transformed into risks, even in novel situations, as long as they satisfy the laws of probability - such as that probabilities of an exhaustive and exclusive set alternatives such as survival and death add up to 1. Thus [the surgeon's statement that the patient] had an 80 percent chance of survival is meaningful provided that the surgeon also held that there was a 20 percent chance of his patient not surviving.” %} Gigerenzer, Gerd (2002) “Reckoning with Risk: Learning to Live with Uncertainty.” Penguin Books, London. {% %} Gigerenzer, Gerd (2008) “Rationality for Mortals: Risk and Rules of Thumb.” Oxford University Press, New York. {% The nice writing style of Gigerenzer with inspiring metaphors showing deep understandings. But it is also selling lemons. That this is ecologically rather than logically based (p. 651 1st column 2nd para) sounds nice and clever at first but does not survive serious thinking. Is ecological the trivial point of finding environments where heuristics survive? “Simon’s insight that the minds of living systems should be understood relative to the environment in which they evolved, rather than to the tenets of classical rationality” (p. 651 1st column l. -13) is mixing unrelated concepts. “They did not report such a test. We shall.” (p. 651 2ne column 1st sentence) is bombastic. Heuristics as studied here are interesting, but serve different purposes than quantitative theories such as prospect theory and expected utility. The authors’ continued search for competitions between these is unfounded. P. 654 2nd column ll. 7-10: that German and US students can worse compare seizes of cities in their own country than in the other is hard to believe. %} Gigerenzer, Gerd & Daniel G. Goldstein (1996) “Reasoning the Fast and Frugal Way: Models of Bounded Rationality,” Psychological Review 103, 650–669. {% %} Gigerenzer, Gerd, Ullrich Hoffrage, & Heinz Kleinbölting (1991) “Probabilistic Mental Models: A Brunswikian Theory of Confidence,” Psychological Review 98, 506–528. {% A.o., discusses and references is-ought distinction. %} Gigerenzer, Gerd & Thomas Sturm (2012) “How (Far) Can Rationality Be Naturalized?,” Synthese 187, 243–268. {% foundations of probability: history %} Gigerenzer, Gerd, Zeno Swijting, Theodore M. Porter, Lorraine J. Daston, & John Beatty (1990) “The Empire of Chance: How Probability Changed Science and Everyday Life.” Cambridge University Press, Cambridge. {% Do Ellsberg paradox where, however, subjects are allowed to sample from the urns, which obviously leads to preference for the ambiguous urn if favorable to one color. Model this by assuming that subjects do some sort of classical-statistics hypothesis testing. %} Gigliotti, Gary & Barry Sopher (1996) “The Testing Principle: Inductive Reasoning and the Ellsberg Paradox,” Thinking and Reasoning 2, 33–49. {% real incentives/hypothetical choice: for time preferences: seems to be decreasing/increasing impatience: find counter-evidence against the commonly assumed decreasing impatience and/or present effect. %} Gigliotti, Gary & Barry Sopher (2004) “Analysis of Intertemporal Choice: A New Framework and Experimental Results,” Theory and Decision 55, 209–233. {% This paper contains the nice observation that under RDU (= CEU (Choquet expected utility)) the decomposition W = f(P) with f strictly increasing amounts to exactly the same in a mathematical sense as imposing the qualitative probability axioms (having a P that orders events the same as W). So, probabilistic sophistication comes here from only qualitative probability and does not need the stronger conditions that Machina & Schmeidler (1992) had to impose for general probabilistic sophistication. The paper does try to formulate axioms, but, as Gilboa (1986, personal communication) pointed out there is something missing. Convex-rangedness of W does imply solvability of the more-likely-than relation, but not the Archimedeanity that is needed to get P. In other words, although W is quantitative and satisfies some sort of Archimedeanity in its ordinal class, it does not satisfy the additive Archimedeanity that is needed to give P. It does not exclude infinitely many equally likely disjoint nonnull events in terms of P. %} Gilboa, Itzhak (1985) “Subjective Distortions of Probabilities and Non-Additive Probabilities,” Working paper 18–85, Foerder Institute for Economic Research, Tel-Aviv University, Ramat Aviv, Israel. {% %} Gilboa, Itzhak (1986) “Non-Additive Probability Measures and Their Applications in Expected Utility Theory,” Ph.D. dissertation, Dept. of Economics, University of Amsterdam. {% biseparable utility %} Gilboa, Itzhak (1987) “Expected Utility with Purely Subjective Non-Additive Probabilities,” Journal of Mathematical Economics 16, 65–88. {% %} Gilboa, Itzhak (1988) “The Complexity of Computing Best-Response Automata in Repeated Games,” Journal of Economic Theory 45, 342–352. {% EU+a*sup+b*inf %} Gilboa, Itzhak (1988) “A Combination of Expected Utility Theory and Maxmin Decision Criteria,” Journal of Mathematical Psychology 32, 405–420. {% Games with incomplete knowledge, common knowledge %} Gilboa, Itzhak (1988) “Information and Meta Information.” In Moshe Y. Vardi (ed.) Proceedings of the Second Conference on Theoretical Aspects of Reasoning about Knowledge, 227–243, Morgan-Kaufmann, Los Altos, CA. {% %} Gilboa, Itzhak (1989) “Duality in Non-Additive Expected Utility Theory,” Annals of Operations Research 19, 405–414. {% %} Gilboa, Itzhak (1989) “Additivizations of NonAdditive Measures,” Mathematics of Operations Research 14, 1–17. {% preferring streams of increasing income; intertemporal separability criticized: p. 1155, bottom states that separability is more convincing for uncertainty than for other contexts. %} Gilboa, Itzhak (1989) “Expectation and Variation in Multi-Period Decisions,” Econometrica 57, 1153–1169. {% %} Gilboa, Itzhak (1990) “A Necessary but Insufficient Condition for the Stochastic Binary Choice Problem,” Journal of Mathematical Psychology 34, 371–393. {% %} Gilboa, Itzhak (1990) “Philosophical Applications of Kolmogorov’s Complexity Measure.” {% %} Gilboa, Itzhak (1993) “Hempel, Good, and Bayes.” {% free-will/determinism %} Gilboa, Itzhak (1994) “Can Free Choice Be Known?”. In Cristina Bicchieri, Richard C. Jeffrey, and Brian F. Skyrms (eds.) The Logic of Strategy, Oxford University Press, 163–174. {% foundations of statistics %} Gilboa, Itzhak (1994) “Teaching Statistics: A Letter to Colleagues.” {% %} Gilboa, Itzhak (1995) Book Review of: Steven J. Brams (1994) “Theory of Moves.” Cambridge University Press, New York; Games and Economic Behavior 10, 368–372. {% dynamic consistency %} Gilboa, Itzhak (1997) “A Comment on the Absent Minded Driver Paradox,” Games and Economic Behavior 20, 25–30. {% %} Gilboa, Itzhak (1998) “Counter-Counterfactuals,” Games and Economic Behavior 24, 175–180. {% %} Gilboa, Itzhak (2004, ed.) “Uncertainty in Economic Theory: Essays in Honor of David Schmeidler’s 65th Birthday.” Routledge, London. {% On Goodman’s paradox. Takes properties as functions of time (which is the novelty of Goodman) but then defines underlying constants such as “green at all times” and argues that green is easier to state in terms of such constants than grue. That green-at-all-times is a better constant than grue-at-all-times is, I guess, determined by evolution. Similarly one could, I guess, let evolution decide directly at the level of functions that green is a better function than grue. %} Gilboa, Itzhak (2007) “Green is Simpler than Grue.” {% free-will/determinism %} Gilboa, Itzhak (2007) “Free Will: A Rational Illusion.” {% criticisms of Savage’s basic mode: in several places. Text on decision under uncertainty based on what Gilboa teaches. The text pays much attention to methodological issues, based on Gilboa’s philosophical background, and is more oriented towards the probability-uncertainty part than towards the utility part. Download 7.23 Mb. Share with your friends:
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