Bibliography
Download 7.23 Mb.
|
- Navigate this page:
- Risk averse for gains, risk seeking for losses
| §3.4.7: the midvalue splitting technique; does like Tradeoff method, only, quite inefficiently, uses each time different gauge to find for each pair a midpoint!?
§3.4.8: a hypothetical example of a hypothetical-choice utility measurement. §4.9: example of hypothetical utility measurement. §4.9.5, p. 199 middle (Risk averse for gains, risk seeking for losses): “Experience has indicated that, often in practice, the decision maker may seem to be risk averse in the entire range except for small negative amounts.” This section gives a (hypothetical) example of how reconciling inconsistencies improves the insights of the client. §5.7: if attributes do not satisfy independence conditions, maybe we can redefine the attributes to re-obtain it. §5.8.3 discusses cross-checks, concerning different shapes of multiattribute utility. §6.5, p. 295. Theorem 6.4: Additive iff Fishburn's (1966) marginal independence. dynamic consistency: Meyer, Richard F. (1976) “Preferences over Time.” Ch. 9 in the book. P. 480 uses term “pairwise invariance” for Koopman’s stationarity, restricted to tradeoffs between time point i and i+1, for each i. Kirsten&I: §9.2.2 does discounted utility for finitely many time points, 9.2.3 extends to countably-infinite. §10.2.1, p. 524: Arrow’s impossibility theorem shows that you need interpersonal comparisons. simple decision analysis cases using EU: §7.4 (p. 390 ff.) has no EU but only MAUT in their usual way. %} Keeney, Ralph L. & Howard Raiffa (1976) “Decisions with Multiple Objectives.” Wiley, New York (2nd edn. 1993, Cambridge University Press, Cambridge). {% revealed preference %} Kehoe, Tomothy J. (1992) “Gross Substitutability and the Weak Axiom of Revealed Preference,” Journal of Mathematical Economics 21, 37–50. {% %} Keisler, Jeffrey & Patrick S. Noonan (2012) “Communicating Analytic Results: A Tutorial for Decision Consultants,” Decision Analysis 9, 274–292. {% probability communication: at least, risk communication. Investigate how numeracy is related to proper processing of info. (cognitive ability related to risk/ambiguity aversion). %} Keller, Carmen, Christina Kreuzmair, Rebecca Leins-Hess, & Michael Siegrist (2014) “Numeric and Graphic Risk Information Processing of High and Low Numerates in the Intuitive and Deliberative Decision Modes: An Eye-Tracker Study,” Judgment and Decision Making 9, 420–432. {% probability communication; show that format of showing probabilities depends on way of presentation, interacting with numeracy. (cognitive ability related to risk/ambiguity aversion) %} Keller, Carmen & Michael Siegrist (2009) “Effect of Risk Communication Formats on Risk Perception Depending on Numeracy,” Medical Decision Making 29, 483–490. {% %} Keller, Kevin L. (2003) “Strategic Brand Management: Building, Managing & Measuring Brand Equity;” 2nd edn. Upper Saddle River, New Jersey: Prentice Hall. {% risky utility u = transform of strength of preference v, latter doesn’t exist %} Keller, L. Robin (1985) “An Empirical Investigation of Relative Risk Aversion,” IEEE Transactions on systems, Man, and Cybernetics, SMC-15, 475–482. {% Tests RCLA %} Keller, L. Robin (1985) “Testing of the “Reduction of Compound Alternatives” Principle,” Omega 13, 349–358. {% dynamic consistency %} Keller, L. Robin (1989) “The Role of Generalized Utility Theories in Descriptive, Prescriptive, and Normative Decision Analysis,” Information and Decision Technologies 15, 259–271. {% dynamic consistency; see Alias-literature %} Keller, L. Robin (1992) “Properties of Utility Theories and Related Empirical Phenomena.” In Ward Edwards (ed.) Utility Theories: Measurement and Applications, 3–23, Kluwer Academic Publishers, Dordrecht. {% dynamic consistency %} Keller, L. Robin & Craig W. Kirkwood (1999) “The Founding of INFORMS: A Decision Analysis Perspective,” Operations Research 47, 16–28. {% %} Keller, L. Robin, Rakesh K. Sarin, & Martin Weber (1986) “Empirical Investigation of Some Properties of the Perceived Riskiness of Gambles,” Organizational Behavior and Human Decision Processes 38, 114–130. {% %} Keller, L. Robin, Uzi Segal, & Tan Wang (1993) “The Becker-DeGroot-Marschak Mechanism and Generalized Utility Theories: Theoretical Predictions and Empirical Observations,” Theory and Decision 34, 83–97. {% Use data set of Thaler (1981) and do data fitting. Nice didactical explanation of how data fitting works, with minimizing distance and maximum likelihood. They fit exponential discounting and 1-parameter hyperbolic family 1/(1+t), and latter fits data better than exponential. Assume linear utility. %} Keller, L. Robin & Elisabetta Strazzera (2002) “Examining Predictive Accuracy among Discounting Models,” Journal of Risk and Uncertainty 24, 143–160. {% anonymity protection %} Keller, Wouter J., & Jelke C. Bethlehem (1987) “Disclosure Protection of Micro Data,” CBS Select 4, 87–96; Staatsuitgeverij, The Hague. Also appeared in “Proceedings of the Seminar on Openness and Protection of Privacy in the Information Society,” Voorburg, 92–99. {% %} Kelley, John L., (1955) “General Topology.” Van Nostrand, London. {% Seems to have proved, already way before Shapley (1971), that a convex capacity has a nonempty core. %} Kelley, John L. (1959) “Measureson Boolean Algebras,” Pacific Journal of Mathematics 9, 1165–1175. {% p. 127 indicates that the authors use monadic testing, a common technique in marketing, where subjects are not asked to compare choice alternatives, but evaluate a choice alternative in isolation. This technique avoids contrast effects. This is what Tversky & Fox (1995) introduced for the Ellsberg paradox test of ambiguity aversion. %} Kelly, Bridget, Clare Hughes, Kathy Chapman, Jimmy Chun-Yu Louie, Helen Dixon, Jennifer Crawford, Lesley King, Mike Daube, & Terry Slevin (2009) “Consumer Testing of the Acceptability and Effectiveness of Front-of-Pack Food Labelling Systems for the Australian Grocery Market,” Health Promotion International 24, 120–129. {% %} Kellner, Christian (2015) “Tournaments as a Response to Ambiguity Aversion in Incentive Contracts,” Journal of Economic Theory 159, 627–655. {% Review some applications of ambiguity to game theory. Use maxmin EU model. Study equilibria for cheap talk theoretically. %} Kellner, Christian & Mark T. le Quement (2017) “Modes of Ambiguous Communication,” Games and Economic Behavior 104, 271–292. {% %} Kelsey, David (1993) “Choice under Partial Uncertainty,” International Economic Review 34, 297–308. {% §5.2: Dutch book %} Kelsey, David (1994) “Maxmin Expected Utility and Weight of Evidence,” Oxford Economic Papers 46, 425–444. {% Dutch book %} Kelsey, David (1995) “Dutch Book Arguments and Learning in a Non-Expected Utility Framework,” International Economic Review 36, 187–206. {% game theory as ambiguity: in battle of the sexes with a 3rd option added for the column player, giving her certainty but too low to be part of Nash equilibrium, still many subjects choose it. Ambiguity aversion can help explain this. The column player chooses between three prospects: L gives 300 if opponent chooses B, 0 otherwise; M gives 100 if opponent chooses T, 0 otherwise; R gives a certain payoff of X (which is equal to 60, 120, 170, 200, 230, or 260). 30% of subjects chose R which gives the certain payoff of X=60. The authors interpret this as ambiguity aversion, but risk aversion can interfere. %} Kelsey, David & Sara le Roux (2015) “An Experimental Study on the Effect of Ambiguity in a Coordination Game,” Theory and Decision 79, 667–688. {% %} Kelsey, David & Sara le Roux (2017) “Dragon Slaying with Ambiguity: Theory and Experiments,” Journal of Public Economic Theory 19, 178–197. {% %} Kelsey, David & Shasikanta S. Nandeibam (1996) “On the Measurement of Uncertainty Aversion,” {% Dutch book %} Kelsey, David & Frank Milne (1997) “Induced Preferences, Dynamic Consistency and Dutch Books,” Economica 64, 471–481. {% %} Kelsey, David & Frank Milne (1999) “Induced Preferences, Nonadditive Beliefs, and Multiple Priors,” International Economic Review 40, 455–477. {% %} Kelsey, David & John Quiggin (1992) “Theories of Choice under Ignorance and Uncertainty,” Journal of Economic Surveys 6, 133–153. {% ambiguity seeking for unlikely: p. 529: write in beginning that unlikely uncertain events are overweighted, leading to optimism, but that they will assume universal pessimism nevertheless for reasons of tractability. %} Kelsey, David & Willy Spanjers (2004) “Ambiguity in Partnerships,” Economic Journal 114, 528–546. {% Seems to have said or written: “I often say . . . that when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meager and unsatisfactory kind; it may be the beginning of knowledge, but you have scarcely, in your thoughts, advanced to the stage of science, whatever the matter may be.” It is often referred to, briefly, as “science is measurement.” The Cowles Foundation took this as its motto in its first 20 years (1932-1952), writing it on every book and report. See Christ (1994). Regular name was William Thomson, but was given the title Lord Kelvin. A famous physicist. %} Kelvin, (Lord Kelvin) (1886) I have no concrete reference, seems to be May 1886. {% PT, applications: PT gives some better explanations for paradoxes in transportation theories. Take outcomes that are combinations of time and money. Do not consider tradeoffs between them, but just consider one pair x, 0, and x, with x +2 assuming that for basic utility u we have u(x) = u(x), so that |U(x)/U(x)| is loss aversion. They took x = (30 minutes, €5), and considered prospects with only outcomes x, 0, and x. They use Ellsberg urns with 10 colors, where the urns have known or unknown compositions. The unknown urn was generated by a meta-lottery, so that in fact it was two-stage ambiguity. (second-order probabilities to model ambiguity). They derived probability weighting with a system similar to the preference ladders of Wu & Gonzalez (also in van Assen 1996), with gives a sequence of probabilities 0, p1, …, pn < 1 that are equally spaced in probability weighting, and then they did parametric fitting. I am not sure how the weight w(pn) < 1 was determined. They used the Tversky & Kahneman (1992) and Prelec (1998) one-parameter weighting functions, which commit to inverse-S. Probability weighting more pronounced for ambiguity than for risk. (uncertainty amplifies risk). Ambiguity neutrality around p = 1/3. They find inverse-S but used parametric families (one-parameter of T&K 92 and Prelec 1998) that have it. %} Kemel, Emmanuel & Corina Paraschiv (2013) “Prospect Theory for joint Time and Money Consequences in Risk and Ambiguity,” Transportation Research Part B: Methodological 50, 81–95. {% real incentives/hypothetical choice: find no difference in patterns, but less error for real incentives. Fit PT to data of DFE, both for monetary outcomes and for time (waiting time in sense of time lost as with traffic delays). The authors confirm inverse-S (§4.3.b) probability weighting (also for what is called the incomplete information condition, meaning that subjects are not informed about what the possible outcomes are), which is remarkable because in DFE people usually find the opposite. The authors do not discuss this point. Utility of time gains is almost linear, but is concave for money gains. Average probability weighting is more insensitive and more elevated for time than for money. It is interesting to see if at the individual level there are many differences between probability weighting. The autors report significant correlations between them, but this is a weak test of identity. They find more pessimism than is usual for risk (may be explained by ambiguity aversion) and, hence, less overweighting of small probabilities than is usual with risk. One difficulty I have with all DFE studies is that subjects may have prior beliefs at the beginning of the experiment, before starting the sampling, and the experiments have no control over that. Subjects will believe beforehand that high money gains have small probabilities, and negative money outcomes will not happen. For time outcomes they may have different prior beliefs. %} Kemel, Emmanuel & Muriel Travers (2016) “Comparing Attitudes towards Time and Money in Experience-Based Decisions,” Theory and Decision 80, 71–100. {% Dutch book %} Kemeny, John G. (1955) “Fair Bets and Inductive Probabilities,” Journal of Symbolic Logic 20, 263–273. {% Find very clear framing effects due to framing things as gains or losses, while clearly identical in terms of final outcomes. %} Kern, Mary C. & Dolly Chugh (2009) “Bounded Ethicality: The Perils of Loss Framing,” Psychological Science 20, 378–384. {% %} Kendall, Maurice G. & B. Babington Smith (1940) “On the Method of Paired Comparisons,” Biometrika 31, 324–345. {% %} Keppe, Hans-Jürgen & Martin Weber (1990) “Stochastic Dominance and Incomplete Information on Probabilities,” European Journal of Operational Research 43, 350–355. {% natural sources of ambiguity They find source-preference for sources for which participants are more competent. This work was inspired by Heath & Tversky (1991). They use matching subjective probabilities to measure belief in ambiguous events. source-preference directly tested: for the ambiguous events they measure both certainty equivalents and matching probabilities, and they do so for events and their complements. They report results at the individual level, from which cases of source preference can be deducted. %} Keppe, Hans-Jürgen & Martin Weber (1995) “Judged Knowledge and Ambiguity Aversion,” Theory and Decision 39, 51–77. {% %} Keren, Gideon B. (1984) “On the Importance of Identifying the Correct ‘Problem Space’,” Cognition 16, 121–128. {% probability elicitation; confirmatory bias %} Keren, Gideon B. (1988) “On the Ability of Monitoring Non-Veridical Perceptions and Uncertain Knowledge: Some Calibration Studies,” Acta Psychologica 67, 95–119. {% probability elicitation; confirmatory bias %} Keren, Gideon B. (1991) “Calibration and Probability Judgments: Conceptual and Methodological Issues,” Acta Psychologica 77, 217–273. {% Most of the experiment uses hypothetical choice. real incentives/hypothetical choice: §4.2 reports a test of the Ellsberg paradox where real and hypothetical payments gave the same results. If the traditional 3-color Ellsberg questions are done with losses instead of gains, then there still is ambiguity aversion and it is almost equally strong as for gains (for gains, N=75, 74.7% prefers unambiguous color, for losses, N=59, 67.8% prefers unambiguous). For gambling on two colors (so my subjective probability is 2/3), for gains, N=60, 71.7% prefers unambiguous color, for losses, N=64, 79.7%, prefers unambiguous to ambiguous. So, here is clear evidence against ambiguity seeking for losses. Experiment 3 asked the subjects which event they considered more probable. They designated the unambiguous event as more probable. Remarkably, they even did so if the proportions were slightly favorable to the ambiguous urn. Pity it was always asked for the gain (or NOT-losing) event, so that subjects’ answers may have confounded likelihood with amount of information. Reducing ambiguity by providing (second-order probability) info reduces ambiguity aversion correspondingly. reflection at individual level for ambiguity: paper gives no info because gain-loss was always between-subjects. %} Keren, Gideon B. & Léonie E.M. Gerritsen (1999) “On the Robustness and Possible Accounts of Ambiguity Aversion,” Acta Psychologica 103, 149–172. {% %} Keren, Gideon B. & Jeroen G.W. Raaijmakers (1988) “On Between-Subjects versus Within-Subjects Comparisons in Testing Utility Theory,” Organizational Behavior and Human Decision Processes 41, 233–247. {% time preference; if risk is introduced explicitly then immediacy effect greatly reduces, suggesting that the regular immediacy effect may be due to a kind of implicit risk. %} Keren, Gideon B. & Peter H.M.P. Roelofsma (1995) “Immediacy and Certainty in Intertemporal Choice,” Organizational Behavior and Human Decision Processes 63, 287–297. {% %} Keren, Gideon B. & Karl H. Teigen (2001) “Why is p = .90 better than p = .70? Preference for Definitive Predictions by Lay Consumers of Probability Judgments,” Psychonomic Bulletin and Review 8, 191–2002. {% %} Keren, Gideon B. & Willem A. Wagenaar (1987) “Violation of Utility Theory in Unique and Repeated Gambles,” Journal of Experimental Psychology: Learning, Memory, and Cognition 13, 29–38. {% %} Keren, Gideon B. & Martijn C. Willemsen (2009) “Decision Anomalies, Experimenter Assumptions, and Participants’ Comprehension: Revaluating the Uncertainty Effect,” Journal of Behavioral Decision Making 22, 301–317. {% losses from prior endowment mechanism: use this and discuss it on p. 651. Asked people (some 105) to introspectively predict how bad they would feel when losing money in a prospect. Later, if people really lost, they were asked again. Afterwards they did not judge as bad as predicted. Seems that the first of two experiments manipulated the prospects, by letting either a final gain of $4 or a final loss of $4 result (p. 650 top) whereas the subjects thought it concerned sequence of truly random prospects. The authors conclude that loss aversion is irrational: “To summarize, people believe that losses will have more impact than gains because they fail to anticipate how easily they will cope with losses. This may lead people to make decisions that maximize neither their wealth nor their happiness.” (p. 652, final sentence). A big conclusion from a simple experiment! %} Kermer, Deborah A., Erin Driver-Linn, Timothy D. Wilson, & Daniel T. Gilbert (2006) “Loss Aversion Is an Affective Forecasting Error,” Psychological Science 17, 649–653. {% %} Keskin, Kerim (2013) “Correlated Equilibrium for Agents with Cumulative Prospect Theory Preferences,” working paper. {% %} Keskin, Kerim (2013) “Mixed Strategy Equilibrium for Agents with Cumulative Prospect Theory Preferences,” working paper. {% game theory for nonexpected utility; correlated equilibrium and two mixed strategy equilibria %} Keskin, Kerim (2016) “Equilibrium Notions for Agents with Cumulative Prospect Theory Preferences,” Decision Analysis 13, 192–208. {% The perception of numbers has concrete locations in the brain that depend on cultural background. %} Keus, Inge M., Kathleen M. Jenks, & Wolf Schwarz (2005) “Psychophysiological Evidence that the SNARC Effect Has Its Functional Locus in a Response Selection Stage,” Cognitive Brain Research 24, 48–56. {% Elementary introduction to axiomatics and decisie-theories %} Keuzenkamp, Hugo (1991) “Economen and Ons Verstand - Ronddolen in een Rusteloze Droom,” Intermediair 27–23, June 7, 51–57. {% P. 86: conservation of influence; free-will/determinism: “The differentia of economic laws, as contrasted with purely physical laws, consists in the fact that the former imply voluntary human action.” %} Keynes, John Maynard (1890) “The Scope and Method of Political Economy.” McMillan, London. (2nd edn. 1917.) {% In Collected Works, Royal Economic Society XIV, p. 124, Keynes seems to have used the term Benthamite school for maximization of expectation. P. 75 presents the known and unknown Ellsberg urns as illustration of unknown probabilities. Keynes argues for incomparability of some likelihoods, so, imprecise probability even at the ordinal level. He does, however, not relate these urns to decision making. Therefore he can, I think, not be credited for preceding Ellsberg. He seems to write: “The typical case, in which there may be a practical connection between weight and probable error, may be illustrated by the two cases following of balls drawn from an urn. In each case we require the probability of drawing a white ball; in the first case we know that the urn contains black and white balls in equal proportions; in the second case the proportion of each color is unknown, and each ball is as likely to be black as white. It is evident that in either case the probability of drawing a white ball is 1/2, but that the weight of the argument in favor of this conclusion is greater in the first case” (Keynes, 1921, p. 75) And he seems to write, on p. 313: If two probabilities are equal in degree, ought we, in choosing our course of action, to prefer that one which is based on a greater body of evidence?” (Craig Fox pointed out the combination of these two citations to me.) It may seem that Keynes is at an distance, with only trivially different from zero, from Ellsberg’s discovery. But I disagree. The citation on p. 313 is for decisions in general. The urn is only an illustration of unknown probabilities without relation to decisions. Had Keynes thought for a split-second what the decision in the urn-case had been, he would of course have said immediately what we all know from Ellsberg. But Keynes did not bring decisions up there. More importantly, he did not notice the funny duality, that you prefer betting on an event as well as on its complement (source-preference). Therefore, I think that Ellsberg loses no priority to Keynes. Keynes can be credited for ambiguity aversion, but not more. The above citation, of p. 313, can be linked to the source method idea that the same probability can be weighted differently for different sources. P. 309 discusses that in decisions you can’t foresee the whole future. P. 312, para 6, argues against context-independence P. 348-349 of I think the 1973 edn.: he believes that degrees of belief are not measurable. Even if they are, expected utility may be inadequate. If we take “not measurable” as nonadditive then this suggestion entails the two-stage model; oh well. %} Keynes, John Maynard (1921) “A Treatise on Probability.” McMillan, London. 2nd edn. 1948. {% marginal utility is diminishing, about consumption: p. 31: “the marginal propensity to consume [is] weaker in wealthy community;” also on p. 120 and 349 P. 161-162 seems to write: “Most, probably, of our decisions to do something positive, the full consequences of which will be drawn out over many days to come, can only be taken as a result of animal spirits - of a spontaneous urge to action rather than inaction, and not as the outcome of weighted average of quantitative benefits multiplied by quantitative probabilities. Enterprise only pretends to itself to be mainly actuated by the statements in its own prospectus, however candid and sincere.” Seems to write on p. 161: [A] large proportion of our positive activities depend on spontaneous optimism rather than on a mathematical expectation, whether moral or hedonistic or economic. Most, probably, of our decisions to do something positive, the full consequences of which will be drawn out over many days to come, can only be taken as a result of animal spirits—of a spontaneous urge to action rather than inaction, and not as the outcome of a weighted average of quantitive benefits multiplied by quantitative probabilities. P. 349: “with the growth in wealth [comes] the diminishing marginal propensity to consume” %} Keynes, John Maynard (1935) “The General Theory of Employment, Interest, and Money.” Harvest/HBJ, San Diego, London, Recent edn.: 1964. {% Pp. 212-215: “… at any given time facts and expectations were assumed to be given in a definite and calculable form; and risks, of which, tho [though] admitted, not much notice was taken, was supposed to be capable of an exact actuarial computation. The calculus of probability … was supposed to be capable of reducing uncertainty to the same calculable status as that of certainty itself … Actually, however, we have, as a rule, only the vaguest idea … renders Wealth a peculiarly unsuitable subject for the methods of classical economic theory. … By “uncertain” knowledge, let me explain, I do not mean merely to distinguish what is known for certain from what is only probable. The game of roulette is not subject, in this sense, to uncertainty…. Even the weather is only moderately uncertain. The sense in which I am using the term is that in which the prospect of a European war is uncertain, or the price of copper and the rate of interest twenty years hence … About these matters there is no scientific basis on which to form any calculable probability whatever. We simply do not know. Nevertheless, the necessity for action and for decisions compels us as practical men to do our best to overlook this awkward fact and to behave exactly as we should if we had behind us a good Benthamite calculation of a series of prospective advantages and disadvantages, each multiplied by its appropriate probability, waiting to be summed. … it is subject to sudden and violent changes. … New facts and hopes will, without warning, take charge of human conduct. … All these pretty, polite techniques, made for a well-panelled Board Room and a nicely regulated market, are liable to collapse.” %} Keynes, John Maynard (1937) “The General Theory of Employment,” Quarterly Journal of Economics 51, 209–223. {% %} Khrennikov, Andrei, Irina Basieva, Ehtibar N. Dzhafarov, & Jeromy R. Busemeyer (2014) “Quantum Models for Psychological Measurement: An Unsolved Problem,” PLoS ONE 9(10), e110909. {% I tried to read this in 2017, but it requires too much prior knowledge of quantum mechanics to be understandable to me or my likes. %} Khrennikov, Andrei Yu & Emmanuel Haven (2009) “Quantum Mechanics and Violations of the Sure-Thing Principle: The Use of Probability Interference and Other Concepts,” Journal of Mathematical Psychology 53, 378–388. {% %} Khwaja, Ahmed, Dan Silverman, & Frank Sloan (2007) “Time Preference, Time Discounting, and Smoking Decisions,” Journal of Health Economics 26, 927–941. {% %} Kiebert, Gwendoline M. (1995) “Choices in Oncilogy: Patients’ Valuations of Treatment Outcomes in Terms of Quality and Length of Life.” Ph.D. dissertation, University of Leiden. {% For good health care, a procedure was recommended, of (1) defining the problem, (2) diagnosis of what is going on, (3) specifying the options, and then, interestingly, (4) individualization: specify what is special of this individual patient. This step is explicitly required. Then it continues (5) tradeoffs and choice; (6) implementation. So there should be both evidence-based and individualization. %} Kievit, Job (2017) “Zorg en Kwaliteit: van Individu naar Systeem, naar Beide.” Goodbye speech, Leiden University. {% Z&Z; Examines welfare effects of compulsory insurance versus free-market versus a mix of compulsory plus voluntary, a variation of Dahlby (1981), a paper which seems to be a classic. Assumes two risk types and two health benefits, community rating insurers and risk rating insurers. %} Kifman, Mathias (2002) “Community Rating in Health Insurance and Different Benefit Packages,” Journal of Health Economics 21, 719–737. {% revealed preference %} Kihlstrom, Richard E., Andreu Mas-Colell, & Hugo F. Sonnenschein (1976) “The Demand Theory of the Weak Axiom of Revealed Preference,” Econometrica 44, 971–978. {% They disseminated the strange claim that more risk averse comparison is possible only under the prior restriction of same ordering of riskless outcomes. Peters & Wakker (1987) show, for general outcomes (including commodity bundles as in K&M), that MRA <=> [same ordering of sure outcomes & U more concave]. So same ordering of riskless outcomes need not be presupposed because it simply is implied (modulo minimal outcomes). %} Kihlstrom, Richard E. & Leonard J. Mirman (1974) “Risk Aversion with Many Commodities,” Journal of Economic Theory 8, 361–388. {% proper scoring rules, seem to do proper scoring rules with competition involved. Wonder how this is related to Prelec (2004) Science. %} Kilgour, D. Mark & Yigal Gerchak (2004) “Elicitation of Probabilities Using Competitive Scoring Rules,” Decision Analysis 2, 108–113. {% natural sources of ambiguity; Download 7.23 Mb. Share with your friends:
|