Bibliography
§11.2.3 gives a sufficient condition for young people to be more risk averse
Download 7.23 Mb.
|
- Navigate this page:
- Risk averse for gains, risk seeking for losses
| §11.2.3 gives a sufficient condition for young people to be more risk averse
. Pp. 11-12, §1.4.2, treats my dynamic discussion of the Allais paradox. HARA utilities play a central role. Ch. 5 is on the equity premium puzzle, which is presented as a central problem for the field. Proposition 11 on p. 83 in §6.1 gives the appealing diffidence theorem of Gollier & Kimball, the application of the separating hyperplane theorem. Ch. 19 is on the Samuelson-Merton result for saving-portfolio. source-dependent utility: Ch. 20 gives an elementary treatment of the Kreps & Porteus (1978) model. §21.4.2, p. 317, gives the Arrow-Lind theorem. Ch. 23 is nice, on the nontrivial derivation of the representative agents’s characteristics from the characteristics of the individual agents. The average behavior need not result from the average of the individual risk parameters. Sometimes, the absolute risk tolerance of the representative agent equals the average absolute risk tolerance of the individual agents, but such a result does not hold for prudence. Ch. 24 is on the value of information, Blackwell theorem etc. The concluding sentence is: “Far from that I believe that this book calls for another round of theoretical and empirical research.” Epilogue, p 424ff., argues that it is remarkable that there are so few studies into risk aversion (he means utility curvature). %} Gollier, Christian (2001) “The Economics of Risk and Time.” MIT Press, Cambridge MA. {% Discounting: p. 150 explains why saving money yields profits: because we expect that future consumption will be better than past consumption. Paper shows that uncertainty about growth rate, plus prudence, reduces the optimal discount factor. P. 163: French Commissariat au Plan recommends to use 8% discounting, most developed countries do between 5% and 8%. Author suggests 5% for periods between 50 and 100 years, and 1.5% for over 200 years. %} Gollier, Christian (2002) “Discounting an Uncertain Future,” Journal of Public Economics 85, 149–166. {% When growth is almost surely nonnegative, the yield curve is decreasing if and only if RRA is decreasing with wealth. %} Gollier, Christian (2003) “Time Horizon and the Discount Rate,” Journal of Economic Theory 107, 463–473. {% Net present value can give phenomena on increasing/decreasing discounting that are different than net future value. Paradox is resolved by having risk aversion and reckoning with consumption stream. %} Gollier, Christian (2010) “Expected Net Present Value, Expected Net Future Value, and the Ramsey Rule,” Journal of Environmental Economics and Management 59, 142–148. {% Two-good multiperiod model with substitutability between goods and uncertainty, and then what optimal discounting is. Can be really different for the different groups. The author, based on data, proposed 3.2% as discount rate for consumption and 1.2% for biodiversity. %} Gollier, Christian (2010) “Ecological Discounting,” Journal of Economic Theory 145, 830–859. {% Application of ambiguity theory; Uses the smooth ambiguity model to investigate the effect of increase in ambiguity aversion on the standard portfolio problem of dividing money to be invested over a safe and an ambiguous asset. Increasing ambiguity aversion is by making the 2nd order utility transformation more concave while keeping 1st order utility u, and keeping first- and second-order probabilities fixed. In general, increased ambiguity aversion need not always reduce investment in the portfolio. It does so mostly, e.g. if utilities are power/exponential for normal distributions, or if the set of priors can be ranked according to maximum-likelihood ordering. %} Gollier, Christian (2011) “Portfolio Choices and Asset Prices: The Comparative Statics of Ambiguity Aversion,” Review of Economic Studies 78, 1329–1344. {% When choosing between several prospects, the maximum outcome possible is given a special role, and regret is taken with respect to it. Aversion to risk of regret then leads to risk seeking for small-probability gains (increasing the highest outcome enhances regret elsewhere) and can on restricted domains be related to optimistic probability weighting (may be more than inverse-S weighting) in RDU. %} Gollier, Christian (2015) “Aversion to Risk of Regret and Preference for Positively Skewed Risks,” working paper. {% %} Gollier, Christian & Mark J. Machina (1995, eds.) “Non-Expected Utility and Risk Management.” Kluwer Academic Publishers, Dordrecht. {% decreasing/increasing impatience: if all individuals have constant discounting but are heterogeneous, then the representative agent will have decreasing impatience, if decreasing absolute risk aversion holds for all. %} Gollier, Christian & Richard J. Zeckhauser (2005) “Aggregation of Heterogeneous Time Preferences,” Journal of Political Economy 113, 878–896. {% Belief consonance: people dislike situations where they have different views than others, and try to avoid those. %} Golman, Russell & George Loewenstein (2016) “The Preference for Belief Consonance,” Journal of Economic Perspectives 30, 165–188. {% information aversion: the paper considers intrinsic value of information. It extensively reviews cases and literature of this phenomenon, and its many implications. %} Golman, Russell & George Loewenstein (2017) “Information Avoidance,” Journal of Economic Literature 55, 96–135. {% CBDT; They consider choices between stocks using case-based decision theory. Take CBDT as to be used if we do decision under uncertainty but don’t know the states, similarly as Gilboa & Schmeidler often take it (e.g., p. 731, beginning of Conclusion). They pay much attention to the choice of an aspiration level. Given that similarity weights need not always sum to the same, the choice of utility level 0 is crucial. This is what the aspiration level serves for. It can obviously be compared to the reference point of prospect theory. In Eq. 8 they, more or less ad hoc, choose a parametric family of similarity functions, and use this to fit data. Pp. 730-1, correctly, points out that if with case-based reasoning one could make profit in the stock-exchange market, then the market would be predictable and arbitrage would be possible. Rest of p. 731 has far-reaching conjectures on CBDT thus improving market efficiency. %} Golosnoy, Vasyl & Yarema Okhrin (2008) “General Uncertainty in Portfolio Selection: A Case-Based Decision Approach,” Journal of Economic Behavior and Organization 67, 718–734. {% Asked one time preference question to 13-year olds in longitudinal Swedish data set. Find negative relationship between discounting and school performance, health, labour supply, and income. Males and high-ability children gain more from being future oriented. Measured cognitive spatial ability. %} Golsteyn, Bart H.H., Hans Grönqvist, & Lena Lindahl (2014) “Adolescent Time Preferences Predict Lifetime Outcomes,” Economic Journal 124, F739–F761. {% This paper is the introduction to an impressive special issue on how psychologists and economists can learn from each others measurements of subjective decision attitudes or personality traits. Pp. 2-3 point out that test-retest reliability, and predictive tests are more common psychometric requirements for personality traits in psychology than for subjective decision attitudes in economics. Then it continues that economists may have fewer anchoring biases because their outcomes (e.g. monetary reward) are more objectively defined. §3 is on stability of decision attitudes, which may sometimes be assumed too easily in economics. The third para, that psychologists define stability in a rank-order sense and not in a cardinal or absolute way, was strange to read for me. Then several studies into stability are cited. %} Golsteyn, Bart H.H. & Hannah Schildberg-Hörisch (2017) “Challenges in Research on Preferences and Personality Traits: Measurement, Stability, and Inference,” Journal of Economic Psychology 60, 1–6. {% Propose a new discount function for discrete time, and argue through examples that it has reasonable implications. It is a common generalization of constant discounting and quasi-hyperbolic discounting, and can accommodate increasing impatience. Central is the exponential discounting bias, that people even if wanting to do exponential discounting numerically underestimate how fast this decreases over time. %} Gomes, Orlando, Alexandra Ferreira-Lopes, & Tiago Neves Sequeira (2014) “Exponential Discounting Bias,” Journal of Economics 113, 31–57. {% Ch. 11 presents MadMax, a program for eliciting additive utilities. %} Gonzales, Christophe (1996) “Utilités Additives: Existence et Construction,” Ph.D. dissertation, spécialité Informatique, Université de Paris 6, France. {% %} Gonzales, Christophe (1996) “Additive Utilities when Some Components Are Solvable and Others Are Not,” Journal of Mathematical Psychology 40, 141–151. {% %} Gonzales, Christophe (1997) “Additive Utilities without Solvability on All Components.” In Andranik Tangian & Josef Gruber (eds.) Lecture Notes in Economics and Mathematical Systems 453, 64–90, Springer, Berlin. {% cancellation axioms; derives relations between cancellation axioms. %} Gonzales, Christophe (2000) “Two Factor Additive Conjoint Measurement with One Solvable Component,” Journal of Mathematical Psychology 44, 285–309. {% The results of Gonzales (1996, JMP), that were derived under unrestricted solvability, are generalized here to the case of restricted solvability. %} Gonzales, Christophe (2003) “Additive Utilities without Restricted Solvability on All Components,” Journal of Mathematical Psychology 47, 47–65. {% %} Gonzales, Christophe & Jean-Yves Jaffray (1998) “Imprecise Sampling and Direct Decision Making,” Annals of Operations Research 80, 207–235. {% %} González-Vallejo, Claudia C. (2002) “Making Tradeoffs: A New Probabilistic and Context-Sensitive Model of Choice Behavior,” Psychological Review 109, 137–155. {% %} González-Vallejo, Claudia C., Alberto Bonazzi, & Andrea J. Shapiro (1996) “Effects of Vague Probabilities and of Vague Payoffs on Preferences: A Model Comparison Analysis,” Journal of Mathematical Psychology 40, 130–140. {% %} González-Vallejo, Claudia C., Ido Erev, & Thomas S. Wallsten (1994) “Do Decision Quality and Preference Order Depend on whether Probabilities are Verbal or Numerical?,” American Journal of Psychology 107, 157–172. {% PT falsified; find deviating kinds of reflection effects and different parameters when fitting. Main point of this work: propensity to show risk aversion/seeking depend on actual lottery pairs and person’s proclivity. Experiment 1 considered hypothetical choice, Experiment 2 real prizes (possibly given to charity). Stimuli were formulated as investments in the stock market (with selling short also). Risk averse for gains, risk seeking for losses: is found. Further, there is more risk aversion for gains than risk seeking for losses: - See Fig. 1: above 0.5 on y-axis risk seeking is found. Highest 80% risk seeking for losses, lowest 5% risk seeking (so 95% risk aversion) for gains. For most gamble pairs in Appendix C (all with d 0.5) risk aversion is more pronounced than risk seeking. - Table 2 on p. 948: more risk aversion for gains than risk seeking for losses, because always the loss- and gain percentage sum to less than 100%, so that for gains we are closer to zero (total risk aversion) than for losses we are to 100% (total risk seeking). Average 57% risk seeking for losses, 10035 = 65% risk aversion for gains. reflection at individual level for risk: no clear pattern, depending much on particular prospects - Personal communication (email of Claudia of April 7 ’04): in total, 87% of participants have risk aversion for gains, 63% have risk seeking for losses. %} González-Vallejo, Claudia C., Aaron A. Reid, & Joel Schiltz (2003) “Context Effects: The Proportional Difference Model and the Reflection of Preference,” Journal of Experimental Psychology: Learning, Memory, and Cognition 29, 942–953. {% %} González-Vallejo, Claudia C. & Thomas S. Wallsten (1992) “Effects of Probability Mode on Preference Reversal,” Journal of Experimental Psychology: Learning, Memory, and Cognition 18, 855–864. {% Show that people have more difficulties choosing between losses than between gains. fMRI gives that sure choices for gains require less effort than risky choices, but for losses both kinds of choices require the same effort. %} Gonzalez, Cleotilde, Jason Dana, Hideya Koshino, & Marcel A. Just (2005) “The Framing Effect and Risky Decisions: Examining Cognitive Functions with fMRI,” Journal of Economic Psychology 26, 1–20. {% There have been many papers on decision from experience, but when it comes to quantitative modeling and prediction there have only been some ad hoc parametric fittings in choice competitions organized by Erev and others. This paper probably presents the first psychologically founded theory to do so. It is the instance-based learning theory of Gonzalez et al. It predicts, and data confirm, that DFE with repeated payments and DFE with prior sampling and only one payment give the same learning and risk taking decisions, but with sampling there is double more choice switching suggesting there is more exploration there which is natural. %} Gonzalez, Cleotilde & Varun Dutt (2011) “Instance-Based Learning: Integrating Sampling and Repeated Decisions from Experience,” Psychological Review 118, 523–551. {% DOI: 10.1177/0894439312453979 %} Gonzalez, Cleotilde, Lelyn D. Saner, & Laurie Z. Eisenberg (2012) “Learning to Stand in the Other’s Shoes: A Computer Video Game Experience of the Israeli–Palestinian Conflict,” Social Science Computer Review 31, 236–243. {% inverse-S; published as Gonzalez & Wu (1999, Cognitive Psychology) %} Gonzalez, Richard (1993) “New Experiments on the Probability Weighting Function,” presented at the annual meeting of the Society for Mathematical Psychology, Norman, OK. {% I often cite this paper because it has a very good discussion of likelihood insensitivity as discriminatory power (cognitive ability related to likelihood insensitivity (= inverse-S)) PT: data on probability weighting; inverse-S: does nonparametric fitting of PT for 10 participants, using choice-derived certainty equivalents for 2-outcome lotteries. Finds inverse-S for all 10 participants! They do not explain how they sampled the 10 participants, but it seems that they took 10 well behaved participants from a larger pool. Their purpose is to illustrate that their method can give nice measurements at the individual level, and not to do statistics with a representative sample. Real incentives: random incentive system They tested the lower- and upper SA conditions of Tversky & Wakker (1995) and found them well confirmed. P. 157 seems to report that there are substantial interactions between the PT parameters on parametric interaction. %} Gonzalez, Richard & George Wu (1999) “On the Shape of the Probability Weighting Function,” Cognitive Psychology 38, 129–166. {% biseparable utility; binary prospects identify U and W %} Gonzalez, Richard & George Wu (2003) “Composition Rules in Original and Cumulative Prospect Theory,” working paper. {% probability intervals; Introduced the -maxmin model but only for statistical info. %} Good, Isidore J. (1950) “Probability and the Weighing of Evidence.” Hafners, New York. {% Discusses, a.o., Wald’s multiple priors. Calls all kinds of things rational. P. 112 middle, nicely, puts forward that logarithmic payment gives proper scoring rule! %} Good, Isidore J. (1952) “Rational Decisions,” Journal of the Royal Statistical Society Series B 14, 107–114. {% %} Good, Isidore J. (1962) “Subjective Probability as the Measure of a Non-Measurable Set.” In Henry E. Kyburg Jr. & Howard E. Smokler (1964, eds.) Studies in Subjective Probability, Wiley, New York. (2nd edn. 1980, Krieger, New York.) {% Seems to have introduced the term “Johnstone’s sufficientness postulate.” %} Good, Isidore J. (1965) “The Estimation of Probabilities: An Essay on Modern Bayesian Methods.” Massachusetts Institute of Technology Press, Cambridge, MA. {% value of information; Shows that under EU info can never have negative info. This was also noted already in Savage (1954) (?); and even by unpublished Ramsey (see Sahlin, 1990) %} Good, Isidore J. (1967) “On the Principle of Total Evidence,” British Journal for the Philosophy of Science 17, 319–321. {% %} Good, Isidore J. (1977) “Dynamic Probability, Computer Chess and the Measurement of Knowledge.” In Edward W. Elcock & Donald Michie (eds.) Machine Intelligence 8, 139–150, Ellis Harwood and Wiley, London and New York. {% %} Good, Isidore J. (1983) “Good Thinking.” University of Minnesota Press, Minneapolis, MN. {% foundations of statistics %} Good, Isidore J. (1988) “The Interface between Statistics and Philosophy of Science,” Statistical Science 3, 386–412. {% foundations of statistics; §1.3 has a few remarks on the use of the likelihood ratio test %} Good, Isidore J. (1992) “The Bayes/Non-Bayes Compromise: A Brief Review,” Journal of the American Statistical Association 87, 597–606. {% real incentives/hypothetical choice: used real nontrivial payments. %} Goodman, Barbara, Mark Saltzman, Ward Edwards, & David H. Krantz (1979) “Prediction of Bids for Two-Outcome Gambles in a Casino Setting,” Organizational Behavior and Human Performance 24, 382–399. {% conditional probability %} Goodman, Irwin R. & Hung T. Nguyen (1991) “Foundations for an Algebraic Theory of Conditioning,” Fuzzy Sets and Systems 42, 103–117. {% %} Goodman, Irwin R. & Hung T. Nguyen, & Gerald S. Rogers (1991) “On the Scoring Approach to Admissibility of Uncertainty Measures in Expert Systems,” Journal of Mathematical Analysis and Applications 159, 550–594. {% People have special preferences to bet on particular random numbers more than others. Not (only) for illusion of control but also because of pleasure of how numbers fit into scheme etc. %} Goodman, Joseph K. & Julie R. Irwin (2006) “Special Random Numbers: Beyond the Illusion of Control,” Organizational Behavior and Human Decision Processes 99, 161–174. {% Seems to write, on p. 54: “A rule is amended if it yields an inference we are unwilling to accept; an inference is rejected if it violates a rule we are unwilling to amend. The process of justification is the delicate one of making mutual adjustments between rules and accepted inferences; and in the agreement achieved lies the only justification needed for either.” This citation resembles a bit the interaction between decisions derived from a decision analysis and direct intuitive decisions. %} Goodman, Nelson (1965) “Fact, Fiction and Forecast.” Bobbs-Merrill: New York. {% foundations of statistics: the author, properly I think, cricitizes another paper that, blinded by the follies of hypothesis testing, does the wrong thing of saying meta-analyses should reduce the impact of studies that stopped before the originally planned stopping. %} Goodman, Steven N. (2008) “Systematic Reviews Are not Biased by Results from Trials Stopped Early for Benefit,” Journal of Clinical Epidemiology 61, 95–96. {% doi: 10.1126/science.aaf5406 foundations of statistics: criticizes p-values and hypothesis testing, following up on the recent ASA statement. This author has deep understanding, understanding Fisher and Neymann-Pearson well. P. 1180 points out that p-value has interpretation as frequentist probability, to which I add that that is probably why the statistical world erred in taking it as criterion. Nice text on p. 1181 3rd column end of 2nd para on no author ever (being able to) argue for p-value chosen. Nice references, e.g. p. 1181 3rd column on different significance levels in different fields. %} Goodman, Steven N. (2016) “Aligning Statistical and Scientific Reasoning,” Science 352 (6290), 1180–1181. {% Beginning, pp. 6-10 (“Een Belangrijk Misverstand: ‘De Ziekte van Alzheimer is één Ziekte’ “) nicely shows how the disease of Alzheimer is not one existing disease, but a product of the sociology of medical research. Rest, as usual for inaugural lectures, pleas for more attention and money for own research, and less for any other. %} Gool, Wim A. (2001) “Dementie en Misverstand,” inaugural lecture, Medical Dept., University of Amsterdam, the Netherlands. {% If a risk measure for RDU is additive w.r.t. independent risks, then w must be linear (EU) and E exponential. %} Goovaerts, Marc J., Rob Kaas, & Roger J.A. Laeven (2010) “A Note on Additive Risk Measures in Rank-Dependent Utility,” Insurance: Mathematics and Economics 47, 187-189. {% Risk measures and decision models, such as multiple priors, are very similar in a mathematical sense. Conceptually, they are not meant to be the same. Risk measures are supposed to measure only the downside of risk, and to be only one ingredient in decision making. This paper nicely explains this point and discusses all kinds of concepts from the two perspectives. %} Goovaerts, Marc J., Rob Kaas, & Roger J.A. Laeven (2010) “Decision Principles Derived from Risk Measures,” Insurance: Mathematics and Economics 47, 294–302. {% %} Gorbatsjov, Michael. “I have hundred economic consultants at my disposal, and I am sure that one of them is right; if I only knew which one” Citation translated from Dutch, as given in the “Volkskrant” of August 27, 1992. {% %} Gordon, Jean & Edward H. Shortliffe (1985) “A Method for Managing Evidential Reasoning in a Hierarchical Hypothesis Space,” Artificial Intelligence 26, 323–357. {% Gorman 1968 in Econometrica is less general. Murphy (1981) (RESTUD) showed that Gorman’s assumption of arcconnectedness can be weaked to connectedness. %} Gorman, William M. (1968) “The Structure of Utility Functions,” Review of Economic Studies 35, 367–390. {% Blackorby, Charles, Russell Davidson, & David Donaldson (1977) refer to this paper as the first to show that quasi-concave additively decomposable function has only one nonconcave additive value function; already Stigler (1950) had that in footnote 82, saying that Slutsky already had it. %} Gorman, William M. (1970) “Concavity of Additive Utility Functions.” London School of Economics (Lecture Notes). {% %} Gorman, William M. (1971) “Apologia for a Lemma” and “Clontarf Revisited,” Review of Economic Studies 38, 114 and 116. {% %} Gorman, William M. (1976) “Tricks with Utility Functions.” In Michael J. Artis & A. Robert Nobay (eds.) Essays in Economic Analysis, 211–243, Cambridge University Press, Cambridge. {% Shows that the representation of Dubra, Maccheroni, & Ok (2004) can be rewritten in a nice way, closer to Aumann’s (1962) setup. %} Gorno, Leandro (2017) “A Strict Expected Multi-Utility Theorem,” Journal of Mathematical Economics 71, 92–95. {% Classical preference model cannot explain findings. Reference dependence with loss aversion and diminishing sensitivity can. %} Götte, Lorenz, David Huffman, & Ernst Fehr (2004) “Loss Aversion and Labor Supply,” Journal of the European Economic Association 2, 216–228. {% probability communication: present probabilities in different ways, one of them frequencies, other percentages, or experiences. Percentages attenuated common-ratio but augmented common-consequence. %} Gottlieb, Daniel A., Talia Weiss, & Gretchen B. Chapman (2007) “The Format in Which Uncertainty Information Is Presented Affects Decision Biases,” Psychological Science 18, 240–246. {% %} Gourieroux, Christian & Alain Monfort (1995) “Statistics and Econometrics Models.” Cambridge University Press, Cambridge. {% utility families parametric %} Gourieroux, Christian & Alain Monfort (2004) “Infrequent Extreme Risks,” Geneva Papers on Risk and Insurance Theory 29, 5–22. {% marginal utility is diminishing: according to Larrick (1993) one of the first to suggest that under certainty. Seems to take utility as cardinal, suggesting that money could be a convenient unit. Gossen’s second law: in optimum, marginal utility per $ of each good is the same. %} Gossen, Hermann Heinrich (1854) “Entwickelung der Gesetze des Menschlichen Verkehrs, und der daraus Fliessenden Regeln für Menschliches Handeln.” Druck und Verlag von Friedrich Vieweg und Sohn, 1854, Braunschweig. New edn. (1889): Verlag von R.L. Prager, Berlin. Translated into English by Rudolph C. Blitz (1983) “The Laws of Human Relations and the Rules of Human Action Derived therefrom,” MIT Press, Cambridge MA. {% foundations of quantum mechanics %} Goswami, Amit (1990) “Consciousness in Quantum Physics and the Mind-Body Problem,” Journal of Mind and Behavior 11, 75–96. {% %} Gouskova, Elena, F. Thomas Juster, & Frank P. Stafford (2004) “Exploring the Changing Nature of U.S. Stock Market Participation,” 1994-1999, Working Paper, University of Michigan. {% foundations of statistics; review and propose post-data inferences based on frequentist criteria. Suggest that both Bayesians and frequentists can do pre- and post-data inference. That the latter is the more relevant difference, not Bayesian or nonBayesian. Suggest that procedures should satisfy both the Bayesian and the frequentist criteria. %} Goutis, Constantinos & George Casella (1995) “Frequentist Post-Data Inference,” International Statistical Review 63, 325–344. {% %} Gower, Barry (1991) “Hume on Probability,” British Journal for the Philosophy of Science 42, 1–19. {% Didactical survey of Sugeno integral and Choquet integral %} Grabisch, Michel (1996) “The Application of Fuzzy Integrals in Multicriteria Decision Making,” European Journal of Operational Research 89, 445–456. {% %} Grabisch, Michel (2000) “The Interaction and Möbius Representations of Fuzzy Measures on Finite Spaces, k-Additive Measures: A Survey.” In Michel Grabisch, Toshiaki Murofushi & Michio Sugeno (eds.) Fuzzy Measures and Integrals: Theory and Applications, 70–93, Physica-Verlag, Berlin. {% A theory that could, as the author writes, be called ordinal cumulative prospect theory. Outcome set is {xk, ..., x1, x0, x1, xk}. Is ordinal but, xj is xj, so distances to x0 can be compared. Then defines symmetric Sugeno integral also for negative values, so the analogue of the Šipoš (Sipos) integral. Essential step is definition of symmetric maximum, assigning to {a,b} the one farthest from zero, but zero if they are equally far from zero and of opposite sign. He also suggests an asymmetric extension which kind of normalizes, mapping minimal outcome to zero and maximal to one. %} Grabisch, Michel (2003) “The Symmetric Sugeno Integral,” Fuzzy Sets and Systems 139, 473–490. {% A kind of follow-up on Denneberg (1994). %} Grabisch, Michel (2016) “Set Functions, Games and Capacities in Decision Making.” Springer, Berlin. {% Paper considers the measurement of weighting functions for uncertainty. It explains how software developed by the authors and made publically available can be used to best fit data. It does not formulate the context as uncertainty, but as general aggregation, as multiattribute utility. Uncertainty is an important special case though. Then each attribute refers to a state of nature and (x1,…,xn) is a prospect yielding xj if state j obtains. In general multiattribute utility, to define a ranking of the attributes, they must be commensurable, so that values at different attributes can be compared (p. 767). They assume utility identified. P. 771: they take indifference if the functional-difference is closer to 0 than some threshold C. §4 considers all kinds of distance measures to be minimized, usually in utility units. §5 illustrates an application of choosing between students based on their grades. Several approaches in the paper consider data not only of the kind of choices and indifferences between n-tuples, but also data such as “the weight of attributes 1,2,3 should be at least 0.3.” P. 778 bottom explains that their LP, minimum variance, and minimum distance approaches work when data are only preferences between n-tuples, as mostly considered in decision theory. %} Grabisch, Michel, Ivan Kojadinovic, & Patrick Meyer (2008) “A Review of Methods for Capacity Identification in Choquet Integral Based Multi-Attribute Utility Theory; Applications of the Kappalab R Package,” European Journal of Operational Research 186, 766–785. {% Use term multicriteria decision making for the general problem of aggregation, so that decision under uncertainty is a special case. §2.7 presents several special cases of the Choquet integral meant to make it more tractable than the (overly) general general case. %} Grabisch, Michel & Christophe Labreuche (2008) “A Decade of Application of the Choquet and Sugeno Integrals in Multi-Criteria Decision Aid,” 4OR 6, 1–44. {% %} Grabisch, Michel, Jean-Luc Marichal, Radko Mesiar, & Endre Pap (2009) “Aggregation Functions: Encyclopedia of Mathematics and Its Applications 127,” Cambridge University Press, Cambridge, UK. {% A (first part of a) survey of many generalized mean-type aggregator functions and their characterizations in terms of functional equations. These can generate preference representation theorems by interpreting these functionals as certainty equivalents. Definition 20 is multisymmetry. Remark 7 references early studies of the symmetric Choquet integral. %} Grabisch, Michel, Jean-Luc Marichal, Radko Mesiar, & Endre Pap (2011) “Aggregation Functions: Means,” Information Sciences 181, 1–22. {% The second part of their survey, showing primarily how to define and get many aggregator functions and discussing conorms. %} Grabisch, Michel, Jean-Luc Marichal, Radko Mesiar, & Endre Pap (2011) “Aggregation Functions: Construction Methods, Conjunctive, Disjunctive and Mixed Classes,” Information Sciences 181, 23–43. {% Study several equivalent ways of describing nonadditive set functions, Möbius inverses but also several different ways. %} Grabisch, Michel, Jean-Luc Marichal, & Marc Roubens (2000) “Equivalent Representations of Set Functions,” Mathematics of Operations Research 25, 157–178. {% A function is called k-additive if its Möbius-inverse assigns value 0 to all sets of more than k elements. So, there are no interactions involving more than k elements. For each game, a k can be established such that the generalized CORE, containing dominating k-additive functions, is nonempty. A trivial result is k=N with N the total number of elements. But k < N can often be. %} Grabisch, Michel & Pedro Miranda (2007) “On the Vertices of the k-Additive Core,” working paper. {% %} Grabisch, Michel, Toshiaki Murofushi & Michio Sugeno (2000, eds.) “Fuzzy Measures and Integrals: Theory and Applications.” Physica-Verlag, Berlin. {% %} Gradshteyn, Israil S. & Iosof M. Ryzhik (1993, eds.) “Table of Integrals, Series, and Products.” Academic Press, New York. (Translated into English by Alan Jeffrey.) {% Hahn-decomposition theorem can be formulated as: for all measures v, u, there exists a set A such that v is absolutely continuous with respect to u on A, and u is with respect to v on Ac. This condition is generalized in some sense to capacities. §5 defines conditional expectation for capacity v w.r.t sigma sub-algebra S: for every regular function f there exists S-measurable g s.t. ∫Bfdv = ∫Bgdv for all B in S. Under some richness (at least four disjoint nonnull sets or something similar) v has a conditional expectation for every sub-sigma algebra if and only if v is a measure. %} Graf, Siegfried (1980) “A Radon-Nikodym Theorem for Capacities,” Journal für die Reine und Angewandte Mathematik 320, 192–214. {% I read this interesting paper, probably given to me by Stef Tijs when I was a Ph.D. student in the early 1980s, before I started to write this annotated bibliography, made handwritten annotations, and “refound” them 06Nov2016. Many of ”my” opinions are written in this paper. P. 33 argues that game theory should specify the info that players have, for otherwise it is just individual choice. P. 36 last para: conservation of influence (essentially redefining choice as influence), as I pointed out around 1983. %} Grafstein, Robert (1983) “The Social Scientific Interpretation of Game Theory,” Erkenntnis 20, 27–47. {% foundations of statistics: the paper cites Evans et al. (1986). %} Gandenberger, Greg (2015) “A New Proof of the Likelihood Principle,” British Journal for the Philosophy of Science 66, 475–503. {% %} Granger, Clive W.J. & Mark J. Machina (2006) “Structural Attribution of Observed Volatility Clustering,” Journal of Econometrics 135, 15–29. {% %} Grant, Simon (1995) “Subjective Probability without Eventwise Montonicity: Or: How Machina’s Mom May also Be Probabilistically Sophisticated,” Econometrica 63, 159–189. {% %} Grant, Simon & Atsushi Kajii (1998) “AUSI Expected Utility: An Anticipated Utility Theory of Relative Disappointment Aversion,” Journal of Economic Behaviour and Organization 37, 277–290. {% game theory for nonexpected utility %} Grant, Simon & Atsushi Kajii (1995) “A Cardinal Characterization of the Rubinstein-Safra-Thomson Axiomatic Bargaining Theory,” Econometrica 63, 1241–1249. {% “ADI” axiom is indifference-monotonicity %} Grant, Simon, Atsushi Kajii, & Ben Polak (1992) “Many Good Choice Axioms: When Can Many be Treated As One?,” Journal of Economic Theory 56, 313–337. {% %} Grant, Simon, Atsushi Kajii, & Ben Polak (1992) “Many Good Risks: An Interpretation of Multivariate Risk and Risk Aversion without the Independence Axiom,” Journal of Economic Theory 56, 338–351. {% information aversion; later rewritten in several parts; the bulk of the work is in “Intrinsic Preference for Information” %} Grant, Simon, Atsushi Kajii, & Ben Polak (1994) “Love of Information in Non-Expected Utility Theory: Why “Real Men” Are Quasi-Convex,” Working paper, Dept. of Economics, Australian National University, Canberra, Australia. {% %} Grant, Simon, Atsushi Kajii, & Ben Polak (1998) “On the Skiadas “Conditional Preference Approach” to Choice under Uncertainty,” Yale University, Cowles Foundation discussion paper 1178. {% information aversion; Basic paper that starts their work on intrinsic preference for information. Download 7.23 Mb. Share with your friends:
|