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§8.2.1 explains Luce’s views on the primitives of decision under uncertainty, deviating from Savage (1954)
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| §8.2.1 explains Luce’s views on the primitives of decision under uncertainty, deviating from Savage (1954).
criticizing the dangerous role of technical axioms such as continuity: §9.1 has the good discussion of the dangerous empirical status of technical axioms such as continuity and solvability, often overlooked. In the presence of other axioms, they do have empirical content but it may not be clear what that content is. See also §6.6 of Pfanzagl (1968), and Schmeidler (1971). cancellation axioms: Theorem 9.2.1 (p. 430) gives necessary and sufficient conditions for additive representation of finitely many preferences (can be incomplete on any subset of a product set) through cancellation axioms. Unfortunately, the authors use an irreflexivity condition for an extended relation and it takes some time to see that this is equivalent to imposing all cancellation axioms. §10.9.2 distinguishes between fundamental and derived measurement: “As we use the term, an attribute is called fundamental if its measurement does not depend on the measurement of anything else. … If, as is usual, one places derived in opposition to fundamental, …” Most of the section discusses how other authors used the terms, and some confusions. ---------------------------------------------------- SELECTION OF MATERIAL FOR STUDENTS For students of preference axiomatizations of decision theory, here is a selection of material from the book that is useful to read. The general techniques of this book allow for appealing and mathematically general theorems because they show how to obtain cardinality efficiently. The techniques of this book are mostly based on Hölder’s lemma, which is more efficient than the mixture-set techniques of the Anscombe-Aumann framework. The knowledge has been lost by present (2015) generations, which is why nowadays in decision under uncertainty (ambiguity) the Anscombe-Aumann framework is usually used, to my regret. ------------------------------------------------------ Preface: read Ch. 1 on general measurement procedures: study Ch. 2 on first derivations of numerical representations: study except:
Ch. 3 on measurement with an operation: study except: §3.2.2 (periodic case): skip §3.4 (measurement when operation is incomplete) gives the really powerful mathematical tools from which much in this book is derived. It can however be skipped if only the gist of the book is to be learnt. §3.6: skim §3.7 (essential maxima): skip §3.10.1: skim §3.10.2: important §3.12: c onditional connectedness: skip §3.14 intro: read §3.14.1 (riskiness): skip Ch. 4: useful but can be skipped if only the gist of the book is to be learnt. If you study it, can skip §4.6 (cross-modality), 4.10 (absolute difference), and 4.12 (strongly conditional indifference structures). Ch. 5: useful but can be skipped if only the gist of the book is to be learnt. If you study it: §5.4.1 (QM-algebra) is useful for the study of ambiguity because the set of unambiguous events will not be an algebra, but can be a QM algebra. §5.6 (conditional qual. prob): can skim §5.8 (stochastic independence as a primitive): can skip Ch. 6: most important chapter §6.5.1: skip §6.5.5 important for nonEU that imposes the EU axioms on subspaces. §6.7: skim §6.9: bisymmetry is a way to turn additive representations into SEU and discounted utility, alternatively to my tradeoff technique. §6.11 (many components): most important section in book. Ch. 7 on polynomial measurement: nice but can skim Ch. 8 on risk/uncertainty: skip because outdated Ch. 9 on finite sets: study §9.1-9.2: important §9.4 (applications): skip §9.5: polynomial: skip Ch. 10 on dimensional laws: skip ------------------------------------------------------ %} Krantz, David H., R. Duncan Luce, Patrick Suppes, & Amos Tversky (1971), “Foundations of Measurement, Vol. I (Additive and Polynomial Representations).” Academic Press, New York. (2nd edn. 2007, Dover Publications, New York.) {% %} Krantz, David H. & Geoffrey F. Miller (1990) “Judgments of Likelihood Evidence,” Dept. of Psychology, Columbia University, New York. {% Fig. 4 shows that Gorman’s (1968) result was not known among mathematical psychologists. %} Krantz, David H. & Amos Tversky (1971) “Conjoint-Measurement Analysis of Composition Rules in Psychology,” Psychological Review 78, 151–169. {% introduced the beautiful and important concept of relative curvature for subjective dimensions; i.e., one scale is more curved than another measure of similarity; %} Krantz, David H. & Amos Tversky (1975) “Similarity of Rectangles: An Analysis of Subjective Dimensions,” Journal of Mathematical Psychology 12, 4–34. {% preference for flexibility %} Kraus, Alan & Jacob Sagi (2006) “Inter-Temporal Preference for Flexibility and Risky Choice?,” Journal of Mathematical Economics 42, 698–709. {% %} Kraus, Alan & Jacob Sagi (2006) “Asset Pricing with Unforeseen Contingencies?,” Journal of Financial Economics 82, 417–453. {% May explain if Aristotel had some sort of concept of utility. The author had many papers on Bentham, utility, etc. %} Kraus, Oskar (1903) “Die Aristotelische Werttheorie in Ihrer Beziehungen zu den Lehren der Modernen Psychologenschule,” Zeitschrift für die Gesamte Staatswissenschaften 61, 573–592. {% real incentives/hypothetical choice: seem to consider how actual behavior can be predicted from (hypothetical!) attitude questions. %} Kraus, Stephen J. (1995) “Attitudes and the Prediction of Behavior: A Meta-Analysis of the Empirical Literature,” Personality and Social Psychology Bulletin 21, 58‑75. {% Study insurance for low-probability large-loss events. Discuss that many people do NOT insure here. Mimic it in the lab with subjects getting money and risking to loose it. Social comparison effects are less robust. People underweight others’ information. %} Krawczyk, Michal W., Stefan T. Trautmann, & Gijs van de Kuilen (2017) “Catastrophic Risk: Social Influences on Insurance Decisions,” Theory and Decision 82, 309–326. {% risky utility u = transform of strength of preference v, haven’t checked if latter doesn’t exist %} Krelle, Wilhelm E. (1968) “Präferenz- und Entscheidungstheorie.” Mohr, Tübingen. {% risky utility u = transform of strength of preference v, haven’t checked if latter doesn’t exist %} Krelle, Wilhelm E. (1984) “Remarks to Professor Allais’ Contributions to the Theory of Expected Utility and Related Subjects.” In Ole Hagen & Fred Wenstop (eds.) Progress in Utility and Risk Theory, 173–180, Reidel, Dordrecht. {% Acceptance of small risky gambles and scores on math tests is associated with inventory accumulation among Kenyan shopkeepers. The authors argue that loss aversion plays a big role here. %} Kremer, Michael, Jean Lee, Jonathan Robinson, & Olga Rostapshova (2013) “Behavioral Biases and Firm Behavior: Evidence from Kenyan Retail Shops,” American Economic Review, Papers and Proceedings 103, 362–368. {% %} Kreps, David M. (1977) “Decision Problems with Expected Utility Criteria, I: Upper and Lower Convergent Utility,” Mathematics of Operations Research 2, 45–53. {% preference for flexibility %} Kreps, David M. (1979) “A Representation Theorem for Preference for Flexibility,” Econometrica 47, 565–577. {% Kreps 1988 Eqs. 4.4 and 7.13 argues that state-dependent expected utility is like additive decomposability. Does he use “Axiom 0” as name for DUR assumption? P. 101 mentions that Anscombe-Aumann’s enrichment is OK normatively if person can imagine, but descriptively is highly problematic (in case of coming as auxiliary structure. P. 120: “Savage’s theory, which is the crowning glory of choice theory, …” P. 127, beginning of Ch. 9: “This is actually part of his theory of choice under uncertainty, which is, as much as anything, the crowning achievement of single-person decision theory.” %} Kreps, David M. (1988) “Notes on the Theory of Choice.” Westview Press, Boulder, Colorado. {% %} Kreps, David M. (1990) “A Course in Microeconomic Theory.” Princeton University Press, Princeton, NJ. {% small worlds? %} Kreps, David M. (1992) “Static Choice in the Presence of Unforeseen Contingencies.” In Partha Dasgupta, David Gale, Oliver Hart, & Eric S. Maskin (eds.) Economic Analysis of Market and Games: Essays in Honor of Frank Hahn, MIT Press, Cambridge, MA. {% source-dependent utility: the first paper to have this clearly. dynamic consistency (DC); p. 189, following Axiom 2.1, states version of context-independence; Paper does dynamic decision under risk, with consumption at each time point; Axiom 3.11 (“Temporal consistency”) is what is nowadays called dynamic consistency, maybe with forgone-branch independence included I am not sure; Theorem 2 on p. 195 then shows the way I always look at the models of Luce/Segal: given DC, you can consider only prior choice. It is nicely repeated in words following Corollary 2 on p. 196; Axiom 6.1 resembles forgone-branch independence (often called consequentialism) but also requires independence of past consumption which is far less innocuous than real forgone-branch independence. They assume EU at every single-stage but give up the RCLA assumption and, thus, permit nonindifference to the timing of the resolution of uncertainty. A simplified version can be found in §2 of Grant, Kajii, & Polak (1998, JET) “Intrinsic Preference for Information,” in §1 of Ahlbrecht & Weber (1997, Theory and Decision), and in Ch. 20 of Gollier (2001). According to Grant et al., Kreps & Porteus (1978) were the first to introduce preference for early resolution of uncertainty. The basic model is, for two-stage gambles: j=1;n pjVU1(EU(zj)) where: EU(zj) is expected utility under some utility function U applied to a second-stage lottery zj. V is a transformation function serving as a vNM utility function in the first stage. Whereas U only captures risk attitude, V also captures attitude towards the timing of the resolution of uncertainty. VU1 is convex iff early resolution is always preferred to late. %} Kreps, David M. & Evan L. Porteus (1978) “Temporal Resolution of Uncertainty and Dynamic Choice Theory,” Econometrica 46, 185–200. {% dynamic consistency: favors abandoning RCLA when time is physical. %} Kreps, David M. & Evan L. Porteus (1979) “Dynamic Choice Theory and Dynamic Programming,” Econometrica 47, 91–100. {% consequentialism/pragmatism: putting everything relevant in consequences makes model intractable; P. 82 seems to argue for nonindifference towards the timing of the resolution of uncertainty %} Kreps, David M. & Evan L. Porteus (1979) “Temporal von Neumann-Morgenstern and Induced Preferences,” Journal of Economic Theory 20, 81–109. {% %} Kreps, David & Joel Sobel (1994) “Signalling.” In Robert J. Aumann & Sergio Hart (eds.) Handbook of Game Theory, Volume II, 849–867. Elsevier, Amsterdam. {% %} Kreps, David M. & Robert Wilson (1982) “Sequential Equilibria,” Econometrica 50, 863–894. {% As pointed out by Fishburn, this paper was the first to introduce the skew-symmetric bilinear utility theory of Fishburn. %} Kreweras, Germain (1961) “Sur une Possibilité de Rationaliser les Intransitivités,” La Décision, Colloques Internationaux CNRS, 27–32. {% %} Kriegler, Elmar, Jim W. Hall, Hermann Held, Richard Dawson, and & Joachim Schellnhuber (2009) “Imprecise Probability Assessment of Tipping Points in the Climate System,” Proceedings of the National Academy of Sciences 106, 5041–5046. {% %} Krischer, Jeffrey P. (1980) “An Annotated Bibliography of Decision Analytic Applications to Health Care,” Operations Research 28, 97–113. {% equity-versus-efficiency: seems to be on it %} Kritikos, Alexander & Friedel Bolle (2001) “Distributional Concerns: Equity- or Efficiency-Oriented?,” Economics Letters 73, 333–338. {% foundations of statistics; foundations of probability Nice books on history and discussions of probability %} Krüger, Lorenz, Lorraine J. Daston, & Michael Heidelberg (1987, eds.) “The Probabilistic Revolution, Vol. 1: Ideas in History,” MIT Press, Cambridge, MA. {% foundations of statistics; foundations of probability Nice books on history and discussions of probability %} Krüger, Lorenz, Gerd Gigerenzer, & Mary S. Morgan (1987, eds.) “The Probabilistic Revolution, Vol. 2: Ideas in the Sciences,” MIT Press, Cambridge, MA. {% %} Krueger, Norris F. & Peter R. Dickson (1994) “How Believing in Ourselves Increases Risk Taking: Perceived Self-Efficacy and Opportunity Recognition,” Decision Sciences 25, 385–400. {% %} Krugman, Paul (1998) “Two Cheers for Formalism,” Economic Journal 108, 1829–1836. {% utility elicitation; shows that patients have difficulty in relating to probabilities. %} Krumins, Peter E., Stephan D. Fihn, & Daniel L. Kent (1988) “Symptom Severity and Patients’ Values in the Decision to Perform a Transurethral Resection of the Prostate,” Medical Decision Making 8, 1–8. {% %} Krusell, Per P. & Anthony A. Smith (2003) “Consumption-Savings Decisions with Quasi-Geometric Discounting, Econometrica 71, 365–375. {% risky utility u = transform of strength of preference v; concave utility for gains, convex utility for losses: Fig. 1 has some results for 12 subjects, but it is not clear, e.g. regarding reference level 0.5 and the use or not of mixed gambles. %} Krzysztofowicz, Roman (1983) “Strength of Preferences and Risk Attitude in Utility Measurement,” Organizational Behavior and Human Performance 31, 88–113. {% Studies a model by Hagen that combines linearly expectation and variance and skewness. %} Krzysztofowicz, Roman (1994) “Filtering Risk Effect in Standard-Gamble Utility Measurement.” In Maurice Allais & Ole Hagen (eds.) “Cardinalism; A Fundamental Approach,” 233–248, Kluwer Academic Publishers, Dordrecht. {% Studies, both empirically and axiomatically, lotteries with only one nonzero outcome, assumes strength of preferences over these lotteries given, and then derives weighting functions and value functions. inverse-S: §5.2 finds support for inverse-S weighting function and EU for nonextreme probabilities. (EU+a*sup+b*inf) risky utility u = strength of preference v (or other riskless cardinal utility, often called value): §4.2.5 discusses idea of transformation between value function v and risky utility function u and says that transformation idea does not seem to be correct. P. 253: influence formulation for str. of pr. %} Krzysztofowicz, Roman (1994) “Generic Utility Theory: Explanatory Model, Behavioral Hypotheses, Empirical Evidence.” In Maurice Allais & Ole Hagen (eds.) “Cardinalism; A Fundamental Approach,” 249–288, Kluwer Academic Publishers, Dordrecht. {% %} Krzysztofowicz, Roman & Lucien Duckstein (1980) “Assessment Errors in Multiattribute Utility Functions,” Organizational Behavior and Human Performance 26, 326–348. {% risky utility u = strength of preference v (or other riskless cardinal utility, often called value): state this very explicitly in second paragraph of their paper! So, don’t want risky u to be transform of riskless v! decreasing ARA/increasing RRA & utility elicitation: power family did somewhat better than exponential, much better than logarithmic or linear utility measurement: correct for probability distortion. They use the term “risk function of probability” instead of probability weighting. %} Krzysztofowicz, Roman & John B. Koch (1989) “Estimation of Cardinal Utility Based on a Nonlinear Theory,” Annals of Operations Research 19, 181–204. {% Seems to have Risk averse for gains, risk seeking for losses %} Kuhl, Julius (1978) “Standard Setting and Risk Preference: An Elaboration of the Theory of Achievement Motivation and an Empirical Test,” Psychological Review 85, 239–248. {% %} Kübler, Dorothea & Georg Weizsäcker (2006) “Limited Depth of Reasoning and Failure of Cascade Formation in the Laboratory,” Review of Economic Studies 71, 425–441. {% Consider choices from budget sets over two periods, depending on prices and initial wealth, assuming the classical time-separable EU. Give conditions on preferences/utility under which utilities, beliefs, and discounting are identifiable. A sufficient condition is if some indirect marginal utilities are linearly independent. This holds often, but not for instance if utility is linear/exponential (CARA). Local data often suffices. %} Kübler, Felix & Herakles Polemarchakis (2017) “The Identification of Beliefs from Asset Demand,” Econometrica 85, 1219–1238. {% revealed preference: consider a finite state space {s1,…,sn}, acts, and preferences over those. However, the state space is also endowed with objective probabilities (p1,…,pn). They assume (p1,…,pn) variable, getting a rich domain. Give necessary and sufficient conditions for expected utility maximization for a finite set of choices. %} Kübler, Felix, Larry Selden, & Xiao Wei (2014) “Asset Demand Based Tests of Expected Utility Maximization,” American Economic Review 104, 3459–3480. {% Tradeoff method.; revealed preference: Assume Savage model but with finite state space. Assume that objective probabilities of the states are given. Then axioms such as my tradeoff consistency can be used to give SEU. Only, this SEU model may use subjective probabilities different than the objective ones. They propose an axiom to then give identity of probabilites, generalizing Werner’s (2005) risk aversion: there must exist a sure outcome such that in its neighborhood all acts with EV equal to that outcome are either all more preferred or all less preferred (if U´´ < 0 there). The case of always U´´ = 0 with linear utility also works. Their analysis does need sufficient differentiability of U. They consider two richer domains: The probabilities of the states can vary, but preferences are only between acts with the same probabilities involved. Then tradeoff consistency can ensure the same utility function for different probabilities. And then, yet more general: prefs can be between acts with different probabilities involved. Such prefs can be matched through certainty equivalents and transitivity. %} Kübler, Felix, Larry Selden, & Xiao Wei (2017) “What Are Asset Demand Tests of Expected Utility Really Testing?,” Economic Journal 127, 784–808. {% inverse-S (= likelihood insensitivity) related to emotions: In risky choice, fearful subjects are more risk averse than angry subjects. If the uncertainty concerns the move of the other in a coordination game, then the effect is opposite. So, this is a kind of source dependence. %} Kugler, Tamar, Terry Connolly, & Lisa D. Ordóñez (2012) “Emotion, Decision, and Risk: Betting on Gambles versus Betting on People,” Journal of Behavioral Decision Making 25, 123–134. {% Risk averse for gains, risk seeking for losses: meta-analysis of 136 empirical studies of framing. Framing means that a problem can be formulated in two logically equivalent ways, one suggesting gain outcomes and the other losses. Then, it also means that the gain formulation gives most risk aversion, and the loss formulation gives most risk seeking (p. 29). Seems that this study does not investigate that, but instead whether there is less risk aversion for losses than for gains (unidirectional test). The former, bidirectional, seems to be examined by Kühberger, Schulte-Mecklenbeck, & Perner (1999). Takes statistics of the papers considered, carry out statistical analyses over them, and find 72% of studies confirming framing (p. 35), if I understand right. Strongest effect if study has risky versus riskless options, not risky versus risky, if framing is by variable reference point, not salience of outcomes, and, amazingly, in within-subject designs and not between-subjects. Another survey of framing is Levin, Schneider, & Gaeth (1998). %} Kühberger, Anton (1998) “The Influence of Framing on Risky Decisions: A Meta-Analysis,” Organizational Behavior and Human Decision Processes 75, 23–55. {% Hypothetical choice with framing effects in Asian disease in choice, rating, and ranking. Framing does more to evaluation of riskless options than of risky options. %} Kühberger, Anton & Patricia Gradl (2013) “Choice, Rating, and Ranking: Framing Effects with Different Response Modes,” Journal of Behavioral Decision Making 26, 109–117. {% suspicion under ambiguity: seem to find that people behave under ambiguity as if they play against a better-informed opponent. %} Kühberger, Anton & Josef Perner (2003) “The Role of Competition and Knowledge in the Ellsberg Task,” Journal of Behavioral Decision Making 16, 181–191. {% Meta-analysis of Asian-disease like studies. Risk averse for gains, risk seeking for losses: is found. Pp. 216-217: more risk aversion for gains than risk seeking for losses. P. 217: risk seeking for small-probability gains: not found, only weak risk aversion. P. 217: risk aversion for small-probability losses: neither found, only weak risk seeking. Pp. 225-226: losses from prior endowment mechanism, argues that subjects may integrate the prior endowment, and then invokes the house-money effect, to explain the risk seeking found. decreasing ARA/increasing RRA: may have that; I should check %} Kühberger, Anton, Michael Schulte-Mecklenbeck, & Josef Perner (1999) “The Effects of Framing, Reflection, Probability, and Payoff on Risk Preference in Choice Tasks,” Organizational Behavior and Human Decision Processes 78, 204–231. {% real incentives/hypothetical choice: point out that differences between real and hypothetical choice may be because hypothetical is with high payoffs and real is with low. In general are positive for hypothetical choice. Seem to find no difference between real and hypothetical choice. decreasing ARA/increasing RRA: may have that; I should check %} Kühberger, Anton, Michael Schulte-Mecklenbeck, & Josef Perner (2002) “Framing Decisions: Hypothetical and Real,” Organizational Behavior and Human Decision Processes 89, 1162–1176. {% Discuss framing effects such as in Asian disease. P. 316, very correctly, points out that the problem is not well done by Tversky & Kahneman (1981) because, when saying that 200 people die, they don’t say what happens to the rest. Give several references to others who pointed this out. They compare prospect theory to their preferred fuzzy-trace theory. Here is a typical example of how the latter goes (p. 318). If saving 200 for sure: “some will be saved.” If saving either 600 (p = 1/3) or none: some will be saved or none will be saved. And, awel, then the former is preferred. So this is how fuzzy trace theory works more or less. %} Kühberger, Anton & Carmen Tanner (2010) “Risky Choice Framing: Task versions and a Comparison of Prospect Theory and Fuzzy-Trace Theory,” Journal of Behavioral Decision Making 23, 314–329. {% normal/extensive form %} Kuhn, Harold W. (1953) “Extensive Games and the Problem of Information.” In Harold W. Kuhn & Albert W. Tucker (eds.) Contributions to the Theory of Games I, 193–216, Princeton University Press, Princeton NJ. {% cancellation axioms; Gives nice didactical presentation of solving linear equations, and consistency of those; recommended to me by Aldo Rustichini. Scott (1964) showed how one can derive additively decomposable representations theorems from this result. %} Kuhn, Harold W. (1956) “Solvability and Consistency for Linear Equations and Inequalities,” American Mathematical Monthly 63, 217–232. {% Discusses, for one thing, the mass action interpretation of game theory that Nash wrote in his Ph.D. thesis but did not publish, in the contribution by Weibull and elsewhere. %} Kuhn, Harold W., John C. Harsanyi, Reinhard Selten, Jörgen W. Weibull, Eric van Damme, John F. Nash Jr., & Peter Hammerstein (1996) “The Work of John Nash in Game Theory: Nobel Seminar, December 8, 1994,” Journal of Economic Theory 69, 153–185. {% all hypothetical; ambiguity seeking for losses: finds that for negatively framed decisions, ambiguity seeking was more common. For positive framing, ambiguity seeking is more common. reflection at individual level for ambiguity: although Experiment 1 has within-individual data, it is not reported regarding this. (What is called within-subject analysis is ANOVA still testing group averages.) Experiment 2 is only probability estimations and, again, reports only group averages. %} Kuhn, Kristine M. (1997) “Communicating Uncertainty: Framing Effects on Responses to Vague Probabilities,” Organizational Behavior and Human Decision Processes 71, 55–83. {% %} Kuhn, Kristine M. & David V. Budescu (1996) “The Relative Importance of Probabilities, Outcomes, and Vagueness in Hazard Risk Decisions,” Organizational Behavior and Human Decision Processes 68, 301–317. {% Dutch book: extends de Finetti’s book making result to general logical structures. %} Kühr, Jan & Daniele Mundici (2007) “De Finetti Theorem & Borel States in [0, 1]-Valued Algebraic Logic,” International Journal of Approximate Reasoning 46, 605–616. {% one-dimensional utility %} Kukushkin, Nikolai S. (2003) “Acyclicity of Monotonic Endomorphisms,” {% %} Kun He (1990) “An Ancillarity Paradox in the Estimation of Multinomial Probabilities,” Journal of the American Statistical Association 85, 824–828. {% Children with good grades at high school do better in universities. %} Kuncel, Nathan R. & Sarah A. Hezlett (2007) “Standardized Tests Predict Graduate Students’ Success,” Science 315, 23 February 2007, no. 5815, pp. 1080–1081. {% %} Kunreuther, Howard C. et al. (1978) “Disaster Insurance Protection: Public Policy Lessons.” Wiley, New York. {% crowding-out: raising tax-rebates failed to increase support for siting nuclear repository in Nevada. %} Kunreuther, Howard C. & Douglas Easterling (1990) “Are Risk-benefit Tradeoffs Possible in Siting Hazardous Facilities?,” American Economic Review 80, 252–256. {% %} Kunreuther, Howard C. & M.V. Raieev Gowda (1990) “Integrating Insurance and Risk Management for Hazardous Wastes.” Kluwer Academic Publishers, Dordrecht. {% Seems to discuss ambiguity premium. %} Kunreuther, Howard C. & Robin M. Hogarth (1992) “How Does Ambiguity Affect Insurance Decisions? .” In Georges Dionne (ed.) “Contributions to Insurance Economics,” 307–324, Kluwer, Dordrecht. {% Application of ambiguity theory; Summarize a series of studies by Kunreuther et al., showing that professional actuaries charge higher prices under ambiguity than under known probabilities; this will of course be partially due to asymmetric information and avoidance of winner’s curse. The latter is mentioned on p. 38 of Hogarth & Kunreuther (1992). %} Kunreuther, Howard C., Robin M. Hogarth, & Jacqueline Meszaros (1993) “Insurer Ambiguity and Market Failure,” Journal of Risk and Uncertainty 7, 71–81. {% %} Kunreuther, Howard C., Jacqueline Meszaros, Robin M. Hogarth, & Mark Spranca (1995) “Ambiguity and Underwriter Decision Processes,” Journal of Economic Behavior and Organization 26, 337–352. {% small probabilities: p. 105 cites evidence that people may overestimate, but also ignore, small probabilities; inverse-S: Studies 1 and 2 show that people are unresponsive to changes in the order of magnitude of a low probability. Study 3 puts such different probabilities side by side and then people are responsive to them. So, it is not for motivational reasons, but for cognitive reasons. (cognitive ability related to likelihood insensitivity (= inverse-S)) %} Kunreuther, Howard C., Nathan Novemsky, & Daniel Kahneman (2001) “Making Low Probabilities Useful,” Journal of Risk and Uncertainty 23, 103–120. {% small probabilities risk seeking for small-probability gains: nice example that small probabilities are often ignored. Give bounded-rationality arguments: for very small probability, even if the catastrophe is large, it is not worth the time to think and have transaction costs about. %} Kunreuther, Howard C. & Mark Pauly (2003) “Neglecting Disaster: Why Don’t People Insure against Large Losses,” Journal of Risk and Uncertainty 28, 5–21. {% %} Kunreuther, Howard C., Mark V. Pauly, & Stacey McMorrow (2013) “Insurance and Behavioral Economics: Improving Decisions in the Most Misunderstood Industry.” Cambridge University Press, Cambridge UK. {% questionnaire versus choice utility: suggest that questionnaires may be useful even though economists do not want them. Did telephone surveys on people throughout the US facing risks of floods. Also did experimental lottery choices in the lab. Unfortunately, do not report the data. P. 67, 2nd and 3rd paras, find, remarkably, that people want insurance for “relatively high” probability risks, not for small risks. Don’t say what “relatively high” means. %} Kunreuther, Howard C. & Paul Slovic (1978) “Economics, Psychology and Protective Behavior,” American Economic Review 68, 64–69. {% %} Kupperman, M., Stephen C. Shiboski, David H. Feeny, M.E.P. Elkin, and M.A.E. Washington (1997) “Can Preference Scores for Discrete States be Used to Derive Preference Scores for an Entire Path of Events? An Application to Prenatal Diagnosis,” Medical Decision Making 42, 42–55. {% http://dx.doi.org/10.1371/journal.pone.0007362; One thing they point out (as in Dasgupta & Maskin 2005): an aggregate of exponential discounters will be a hyperbolic discounter. Thus, if all individuals in society are constant discounters, then the representative agent is hyperbolic. It can als be aggregation within an individual, who is uncertain which exponential discounting to take. %} Kurth-Nelson, Zeb, & A. David Redish (2009) “Temporal-Difference Reinforcement Learning with Distributed Representations,” PLoS ONE 4(10), e7362. {% paternalism/Humean-view-of-preference: He proposes to take a representative sample into the lab, and from them get unbiased estimates. Contrary to what has sometimes been suggested, Kurz does not propose to estimate biases quantitatively so as to correct for them I think. P. 333 makes the assumption that under hypothetical choice, subjects have no reason to lie: “Assumption 2. In the absence of any reward or loss due to the revelation of true preferences, individuals have the intrinsic desire to tell the truth and thus be prepared to reveal their true demands.” %} Kurz, Mordecai (1974) “Experimental Approach to the Determination of the Demand for Public Goods,” Journal of Public Economics 3, 329–348. {% They measure probability weighting in prospect theory in a context of precautionary saving, and find that then the weighting function is more pessimistic. They did data-fitting on many choices from which CEs (certainty equivalents) were derived using power utility and the Goldstein & Einhorn family (for which they refer to Gonzalez & Wu 1999). They confirm inverse-S. %} Kusev, Petko, Paul van Schaik, Peter Ayton, John Dent, & Nick Chater (2009) “Exaggerated Risk: Prospect Theory and Probability Weighting In Risky Choice,” Journal of Experimental Psychology: Learning, Memory, and Cognition 35, 1487–1505. {% In studies on coherent risk measures, he is usually credited for introducing the assumption of decision under risk (state space is endowed with probability measure, and acts' preference value depends solely on the probability distribution they generate over outcomes), called law invariance. %} Kusuoka, Shigeo (2001) “On Law Invariant Coherent Risk Measures,” Advances in Mathematical Economics 3, 83–95. {% Hein used this work in Copenhagen. %} Kyburg, Henry E., Jr. (1970) “Probability and Inductive Logic.” MacMillan, London. {% foundations of probability; foundations of statistics; %} Kyburg, Henry E., Jr. (1983) “Epistemology and Inference.” University of Minnesota Press, Minneapolis, MN. {% updating; About convex sets of probability distributions as in multiple priors. %} Kyburg, Henry E., Jr. (1987) “Bayesian and Non-Bayesian Evidential Updating,” Artificial Intelligence 31, 271–293. {% updating %} Kyburg, Henry E., Jr. (1988) “Addendum to Bayesian and Non-Bayesian Evidential Updating,” Artificial Intelligence 36, 265–266. {% updating; foundations of probability %} Kyburg, Henry E., Jr. (1990) “Uncertainty and the Conditioning of Beliefs.” In George M. von Furstenberg (ed.) Acting under Uncertainty: Multidisciplinary Conceptions, 77–94, Kluwer Academic Publishers, Dordrecht. {% Dutch book, p. 3-22 foundations of probability; foundations of statistics; %} Kyburg, Henry E., Jr. & Howard E. Smokler (1964, eds.) Studies in Subjective Probability. Wiley, New York. (2nd edn. 1980, Krieger Publishing Co., New York.) {% Show how rational expectations implies time inconsistency, unerlining the value of policy maker’s credible commitment to a policy rule. Nobel prize 2004. Remarkable is that, contrary to Strotz (1957), the time inconsistency need not be due to nonconstant discounting, but can occur if the policymakers share the public’s objectives, are not myopic, and understand the structure of the economy perfectly. The time inconsistency is due to strategic aspects. %} Kydland, Finn E. & Edward C. Prescott (1977) “Rules rather than Discretion: The Inconsistency of Optimal Plans,” Journal of Political Economy 85, 473–491. {% %} Kydland, Finn & Edward Prescott (1982) “Time to Build and Aggregate Fluctuations,” Econometrica 50, 1345–1370. {% PT, applications: %} Kyle, Albert S., Hui Ou-Yang, & Wei Xiong (2006) Prospect Theory and Liquidation Decisions, Journal of Economic Theory 129, 273–288. {% probability elicitation: reviews the biases and heuristics works by Kahneman & Tversky and others, and works on probability elicitation. Does not consider prospect theory. Says statisticians should pay more attention to this literature, but doesn’t do much more than reviewing the literature. %} Kynn, Mary (2008) “The ‘Heuristics and Biases’ Bias in Expert Elicitation,” Journal of the Royal Statistical Society: Series A (Statistics in Society) 171, 1–26. {% The author redoes the Wu, Zhang, & Abdellaoui (2005) study, testing CPT (I prefer to call it PT) against OPT with a probability tradeoff idea, but for losses (WZA did gains). He shares a problem with WZA, being that he does not really do OPT for two nonzero outcomes, but the separate-probability transformation, which he still calls OPT as do WZA. His Eq. 1 on p. 541 cites Fennema & Wakker 97 for it, but the latter only considered mixed prospects and not loss-zero prospects as this paper does. Thus, Eq. 1 is not really OPT if p3=0. Other than that the paper is well done in theory and experiment. It rejects OPT if sure outcomes are involved. Otherwise OPT and CPT are accepted. So this provides evidence supporting CPT. No real incentives but flat payment. %} L’Haridon, Olivier (2009) “Behavior in the Loss Domain: An Experiment Using the Probability Trade-Off Consistency Condition,” Journal of Economic Psychology 30, 540–551. {% %} L’Haridon, Olivier (2018); website to illustrate probability weighting functions: https://olivierlharidon.shinyapps.io/probability_weighting_functions/ {% %} l’Haridon, Olivier & Corina Paraschiv (2009) “Point de Référence et Aversion aux Pertes: Quel Intérêt pour les Gestionnaires?,” Gérer et Comprendre 97, 60–69. {% %} l’Haridon, Olivier & Corina Paraschiv (2009) “Choix Individuel et Décision Fondée sur l’Expérience: Une Étude Expérimentale,” Revue Economique 60, 949–978. {% %} l’Haridon, Olivier & Laetitia Placido (2008) “An Allais Paradox for Generalized Expected Utility Theories?,” Economics Bulletin 4, 1–6. {% They test the most important paradox of Machina (2009), being the reflection example. They confirm what is so natural, being that f6 > f5 because f6 has one outcome, 4, resulting with known probability ½, whereas f5 has all outcomes ambiguous. For exactly the same reason, ambiguity averse people will have f7 > f8. Strange that Machina did not want to commit to these predictions. A follow-up question could be to test for strength of preference, so as to exclude indifferences. %} l’Haridon, Olivier & Laetitia Placido (2010) “Betting on Machina's Reflection Example: An Experiment on Ambiguity,” Theory and Decision 69, 375–393. {% %} l’Haridon, Olivier & Ferdinand M. Vieider (2015) “All over the Map: Heterogeneity of Risk Preferences across Individuals, Contexts, and Countries,” working paper. {% ambiguity seeking for losses %} La-Ornual, Dolchai (2010) “Individual Decision Making under Ambiguity,” Ph.D. dissertation, INSEAD, Fontainebleau, France. {% MAUT for CEU (Choquet expected utility). Argues for attribute-wise sign-dependence, rather than overall. %} Labreuche, Christophe & Michel Grabisch (2003) “The Choquet Integral for the Aggregation of Interval Scales in Multicriteria Decision Making,” Fuzzy Sets and Systems 137, 11–26. {% %} Labreuche, Christophe & Michel Grabisch (2006) “Generalized Choquet-Like Aggregation Functions for Handling Bipolar Scales,” European Journal of Operational Research 172, 931–955. {% They investigate that patients evaluate their position higher than nonpatients who evaluate it hypothically. They show that it cannot be (just) explained by different endpoints/scalings, because it also occurs in relative evaluations. %} Lacey, Heather P., Angela Fagerlin, George F. Loewenstein, Dylan M. Smith, Jason Riis & Peter A. Ubel (2009) “Are They Really That Happy? Exploring Scale Recalibration in Estimates of Well-Being,” Health Psychology 27, 669–675. {% Formulate a variation of EU where both regret and disappointment are incorporated, and show how particular assumptions on the form of utility lead to empirical predictions such as the Allais paradox. %} Laciana, Carlos E. & Elke U. Weber (2008) “Correcting Expected Utility for Comparisons between Alternative Outcomes: A Unified Parameterization of Regret and Disappointment,” Journal of Risk and Uncertainty 36, 1–17. {% foundations of statistics: a textbook in statistics that is completely in the Bayesian de Finetti spirit, using many geometric explanations. %} Lad, Frank (1996) “Operational Subjective Statistical Methods. (A Mathematical, Philosophical, and Historical Introduction.” Wiley, New York. {% If uncertainty is resolved in the future, then subjects are more risk seeking. %} Ladouceur, Robert & Marie Mayrand (1987) “The Level of Involvement and the Timing of Betting in Roulette,” The Journal of Psychology: Interdisciplinary and Applied 121, 169–176. {% real incentives/hypothetical choice: 30 subjects did some 4 hypothetical risky choices, and 32 did it real, having all questions played for real (so income effect …). The real choices gave more risk aversion. No results are given on whether subjects are risk averse or risk seeking. They used the choice list to measure probability equivalents. They do not explain well how exactly they implemented the real incentives (“they would actually play their chosen risk levels for the amounts of money in the items” on p. 829 is not clear to me). %} Lafferty, Terence & Kenneth L. Higbee (1974) “Realism and Risk Taking,” Psychological Reports 34, 827–829. {% P. 24 suggests that decreasing absolute risk aversion is common. %} Laffont, Jean-Jacques (1993) “The Economics of Uncertainty and Information.” MIT Press, Cambridge, MA. {% real incentives/hypothetical choice: for time preferences: investigate it, and find no difference between real and hypothetical choice. 6 students for many weeks had to choose daily either to get something like $0.50 immediately or $1 some days/weeks later (in real incentives maximal delay considered was 1 month, see p. 178 1st column penultimate para). To avoid saving and so on they could not keep the money but had to spend it immediately upon receipt on candies, so as to enforce consuming and avoid saving. This is in itself a nice idea. Explicitly do not do RIS, but pay all choices. They avoid income effects in the sense that subjects can never get more than one consumption-set per day. They want subjects to first have experienced the options before choosing themselves, so subjects first got some delayed or nondelayed options just like that. Each subject first did hypothetical choice and when that treatment was over did real incentives treatment. Although there is a nice basis, there are several problems. One thing is that subjects can resort to outside options. They can buy the candies outside the experiment. So if they prefer it now then they can still choose the delayed option but buy immediately after in the store. Problem is that I think that they do not measure so much discounting, which for days or weeks should be very weak, but they rather measure attitudes toward hunger. Big drawback is that subjects who chose the delayed reward had to come back to the lab later just to get the delayed reward which, given the small stake per case, is huge transaction costs. The discussion, top of p. 185, does not account for this properly, suggesting subjects had to come to the lab anyhow. This is not true. Subjects for future options had to come especially to the lab for getting them and then would get no other choice or anything (p. 179). For real incentives the starting choice of the bisectionprocedure was the indifference value found with hypothetical (p. 178 end), introducing a strong framing/bias to have real the same as hypothetical. %} Lagorio, Carla H. & Gregory J. Madden (2005) “Delay Discounting of Real and Hypothetical Rewards: III. Steady-State Assessments, Forced-Choice Trials, and All Real Rewards,” Behavioural Processes 69, 173–187. {% %} Lahdelmaa, Risto & Pekka Salminen (2009) “Prospect Theory and Stochastic Multicriteria Acceptability Analysis (SMAA),” Omega 37, 961–971. {% When a lottery is allocated to a peer, 15% of subjects change their choice in the direction of the peer. When the peer chose a lottery rather than getting it allocated, 30% of subjects change choice towards peer. Then imitation also plays a role. The change came about most when the lottery for the peer was riskless. This suggests, as explained p. 76 end of 2nd para, that people may more easily imitating each other in taking insurance than to purchase stocks. %} Lahno, Amrei M. & Marta Serra-Garcia (2015) “Peer Effects in Risk Taking: Envy or Conformity?,” Journal of Risk and Uncertainty 50, 73–95. {% dynamic consistency; DC = stationarity: first sentence of abstract opens up with this; Golden egg: a goose that lays golden eggs, is very useful in the long run, but it is difficult, if not impossible, to realize these benefits immediately. Many illiquid assets are like that. Develops a golden eggs model for a consumer who discounts hyperbolically and can do some form of precommitment. Economic implications and equilibria are derived. This paper popularized the quasi-hyperbolic discounting introduced by Phelps & Pollak (1968). %} Laibson, David I. (1997) “Golden Eggs and Hyperbolic Discounting,” Quarterly Journal of Economics 112, 443–477. {% small worlds %} Laibson, David I. (1998) “Life-Cycle Consumption and Hyperbolic Discount Functions,” European Economic Review 42, 861–871. {% First part of paper describes Amos’ work. Second part of §4 and §5 describe authors’ viewpoints on future. P. 8: “Folk wisdom holds that “Prospect theory,” with 1703 cites as of 1996, is the most-cited paper ever published in Econometrica.” This is indeed a rumour that has been around for many years, so it was not introduced by Laibson & Zeckhauser (1998) and they do describe something going on in the field. Kim, Morse, & Zingales (2006, Table 2) shows that the paper is the second-most cited in all of Economics (and also in Econometrica). P. 8: “He showed that nonrational behavior can be identified and predicted, and that it has important implications for real world economics.” P. 14 says that extreme underweighting of high probabilities makes insurance attractive. This is not true, it is extreme overweighting of low probabilities, in cumulative prospect theory. paternalism/Humean-view-of-preference: p. 20, on Amos: “and did not challenge the central normative judgments of the profession.” P. 21: “Amos Tversky pioneered the archeology of cognition.” I remember from conversations with Amos that he indeed studied things from the cognitive perspective. He wanted to trace down the biases in human brains similarly to the cognitive illusions. real incentives/hypothetical choice: §4.1 explains that real incentives are not so important for Amos. Download 7.23 Mb. Share with your friends:
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