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§3.3, p. 37 of 1972 version, has Theorem 3 (so, Theorem 3.3.3 in Savage’s notation) with item 7 stating solvability for P: for every event E and every 0
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| §3.3, p. 37 of 1972 version, has Theorem 3 (so, Theorem 3.3.3 in Savage’s notation) with item 7 stating solvability for P: for every event E and every 0 < < P(E) there is a subset B E with P(B) = .
§ 3.4, pp. 42-43: that his results all hold true on sigma-algebras, but that at least his proof does not work on algebras. Kopylov (2007) will extend the result to algebras of events, and even mosaics. Savage (1972, pp. 57-58): “To approach the matter in a somewhat different way, there seem to be some probability relations about which we feel relatively “sure” as compared with others. When our opinions, as reflected in real or envisaged action, are inconsistent, we sacrifice the unsure opinions to the sure ones. The notion of “sure” and “unsure” introduced here is vague, and my complaint is precisely that neither the theory of personal probability, as it is developed in this book, nor any other device known to me renders the notion less vague.” linear utility for small stakes: p. 60, on book making argument of de Finetti: “but it seems to me a somewhat less satisfactory approach than the one sponsored here, because it must assume either that the bets are for infinitesimal sums or … that the utility of money is linear.” P. 91: for small amounts, utility is approximately linear risky utility u = transform of strength of preference v, latter doesn’t exist: p. 91, “the now almost obsolete economic notion of utility in riskless situations, a notion still sometimes confused with the one under discussion.” P. 94 (using Bernoulli’s term moral worth for utility): “It seems mystical, however, to talk about moral worth apart from probability and, having done so, doubly mystical to postulate that this undefined quantity serves as a utility.” P. 94, on Bernoulli’s logarithmic utility: “To this day, no other function has been suggested as a better prototype for Everyman’s utility function.” P. 95, “Cramer therefore concluded, and I think rightly, that the utility of cash must be bounded, at least from above.” Then Savage says there must also be lower bounds. P. 96 (of 72 ed.) says that utility is ordinal if only to determine choice between riskless options, says that useful requirements may be discovered in the future that do make utility cardinal, says “That possibility remains academic to date”. P. 101, end of second paragraph: ... the law of the conservation of energy ... new sorts of energy are so defined as to keep the law true. Whole p. 101 discusses point that theories can in principle explain everything, at the cost however of becoming tautological. P. 103: example of car with or without radio. Seems to say that individuals with same evidence can have different beliefs. value of information: seems to write somewhere “the person is free to ignore the observation. That obvious fact is the theory’s expression of the commonplace that knowledge is not disadvantageous.” derived concepts in pref. axioms: using concepts derived from prefs in axioms: back of front leaf has first defined concepts and then axioms using these, for virtually all postulates (P2, P3, P4, P7). Main text uses derived concepts in P3 (p. 26) and P7 (pp. 77-78). biseparable utility: for his EU; %} Savage, Leonard J. (1954) “The Foundations of Statistics.” Wiley, New York. (2nd edn. 1972, Dover Publications, New York.) {% %} Savage, Leonard J. (1961) “The Foundations of Statistics Reconsidered.” In Proceedings of the Fourth Berkeley Symposium on Mathematics and Probability, Berkeley, University of California Press. {% P. 17: likelihood follows from subjective probabilities + Form. Bayes. Seems that he says having learned about the Stopping Rule Principle from Barnard in 1952 and then considering it patently wrong, to now considering it patently right. So in 1952 he had little awarness of the likelihood principle. paternalism/Humean-view-of-preference: Adrian F.M. Smith seems to have written: “Consistency is not necessarily a virtue: one can be consistently obnoxious.” %} Savage, Leonard J. (1962) “The Foundations of Statistical Inference.” Wiley, New York. {% %} Savage, Leonard J. (1962) “Discussion on a Paper by A. Birnbaum [On the Foundations of Statistical Inference],” Journal of the American Statistical Association 57, 307–308. {% conditional probability P. 308 first full para and p. 309 first full para (pointed out to me by Bob Clemen and Bob Nau): “In what sense is this theory normative? It is intended that a reflective person who finds himself about to behave in conflict with the theory will reconsider. … To use the preference theory is to search for incoherence among potential decisions, of which you, the user of the theory, must then revise one or more. The theory itself does not say which way back to coherence is to be chosen, and presumably should not be expected to.” %} Savage, Leonard J. (1967) “Difficulties in the Theory of Personal Probability,” Philosophy of Science 34, 305–310. {% proper scoring rules: p. 785 discusses that proper scoring rules assume linear utility. Section 9.4 proves that the logarithm and its linear transformations are the only proper scoring rules for three or more nonnull events that are local (have payment under some event depend only on score assigned to that event, and not on how the scores for the other events). Most papers in the literature prove this only under differentiability assumptions, but Savage proves it in full generality. random incentive system: p. 785 1st column suggests it, ascribing it to personal communication with W. Allen Wallis, and referring to Allais (1952) for it. linear utility for small stakes: p. 786: “Within sufficiently narrow limits, any person’s utilities can be expected to be practically linear.” %} Savage, Leonard J. (1971) “Elicitation of Personal Probabilities and Expectations,” Journal of the American Statistical Association 66, 783–801. {% %} Savage, Leonard J. (1973) “Probability in Science: A Personalistic Account.” In Patrick Suppes, Leon Henkin, Athanase Joja, & Grigore C. Moisil (eds.) Logic, Methodology and Philosophy of Science IV, 417–428, North-Holland, Amsterdam. {% foundations of statistics %} Savage, Leonard J. (1976; John W. Pratt, ed.) “On Rereading R.A. Fisher,” Annals of Statistics 44, 441–500. { % Meta-analysis of data on WTP-WTA discrepancy. Find that iterative bidding and within-subjects designs decrease disparity; out-of-pocket payments increase disparity. Explicitly stating price: nonsignificant. %} Sayman, Serdar & Ayse Öncüler (2005) “Effects of Study Design Characteristics on the WTA-WTP Disparity: A Meta Analytic Framework,” Journal of Economic Psychology 26, 289–312. {% decreasing/increasing impatience: find the usual decreasing impatience for long periods, but increasing for short (less than a week). Time consistency is equated with dynamic consistency (where, for fixed calendar time of consumption, the calendar time of choice changes and then should not matter). It is also referred to as longitudinal test of time inconsistency. Cross-sectional test of time consistency is stationarity (calendar time of decision is always now, and calendar time of consumption changes). P. 471 2nd column last para points out that equating the two involves the implicit assumption of time invariance (decisions go by stopwatch time; so these authors do not confuse DC = stationarity). P. 473 2nd column 2nd para does it again. Yet some sentences are hard to read because they refer to changes in time without specifying if consumption time or decision time is changing. Table 1 lists many studies in the literature, where only three really test longitudinal (p. 472 last para). real incentives/hypothetical choice: for time preferences: study 1 has real incentives, with monetary outcomes. %} Sayman, Serdar & Ayse Öncüler (2009) “An Investigation of Time-Inconsistency,” Management Science 55, 470–482. {% Subsumed by their 2012 JBDM paper with Philipp Koellinger. This Feb. 20 paper however serves to settle priority on their modified WTP, which they have. %} Schade, Christian & Howard Kunreuther (2001) “Worry and Mental Accounting with Protective Measures,” {% losses from prior endowment mechanism & between-random incentive system (paying only some subjects; p. 535). Only some subjects play for real, get prior endowment and then pay back. But nicely and convincingly implemented: N = 263 students were told they own a valuable painting ($2000), given a picture, told that small risk of losing, and asked premium to insure. Only two randomly chosen played for real at the end. Did modified WTP (introduced by Schade & Kunreuther 2001 in their working paper), where the random prize is drawn at the beginning (but left unknown; no info such as probability distribution is given to the subjects about this). Marvelous way to give them reference point. Found that feelings of worry better predict premium than subjective probability estimate, but little surprise it is because feeling of worry is quite the same as fear-of-loss so willingness to pay. Many subjects pay nothing for insurance, others do remarkably much. They pay more under ambiguity than under risk. They are remarkably insensitive to changes in likelihood (even by a factor 1000), suggesting insensitivity. %} Schade, Christian, Howard Kunreuther, & Philipp Koellinger (2012) “Protecting against Low-Probability Disasters: The Role of Worry,” Journal of Behavioral Decision Making 25, 534–543. {% Investigate how prior gains or losses affect future coordination-game behavior. %} Schade, Christian, Andreas Schroeder, & Kai Oliver Krause (2010) “Coordination after Gains and Losses: Is Prospect Theory’s Value Function Predictive for Games?,” Journal of Mathematical Psychology 54, 426–445. {% foundations of probability: argues that probability cannot exist in a deterministic world. %} Schaffer, Jonathan (2007) “Deterministic Chance?,” British Journal for the Philosophy of Science 58, 113–140. {% %} Schakenraad, Jan (1989) “Data-Analyse en Modelkeuze: Een Indeling van Standaard-Analyse-Technieken in Multivariaat en Meerdimensioneel,” Kwantitatieve Methoden 31, 147–161. {% Bayes’ formula intuitively %} Schaller, Mark (1992) “Sample Size, Aggregation, and Statistical Reasoning in Social inference,” Journal of Experimental Social Psychology 28, 65–85. {% %} Schank, Roger C. & Ellen J. Langer, (1994, ed.) “Beliefs, Reasoning, and Decision Making: Psycho-Logic in Honor of Bob Abelson.” Erlbaum Associates Inc., Hillsdale. {% Study how to communicate probabilities. %} Schapira, Marilyn M., Anne B. Nattinger, & Colleen A. McHorney (2001) “Frequency or Probability? A Qualitative Study of Risk Communication Formats Used in Health Care,” Medical Decision Making 21, 459–467. {% Shows that a power of utility to fit data is about 0.92 (1 1.92, CRRA index) on average for data on Paraguaya farmer data set of 2002 (N = 188) if reference point is chosen 0, but is something like 2500 if wealth level is chosen as reference point. This finding is explained theoretically in Wakker (2008, Health Economics, Example 4.2). The author suggests that there is a relation with Rabin’s calibration theorem. %} Schechter, Laura (2007) “Risk Aversion and Expected-Utility Theory: A Calibration Exercise,” Journal of Risk and Uncertainty 35, 67-76. {% Empirical tests of bargaining solutions %} Schellenberg, James A. (1988) “A Comparative Test of Three Models for Solving ‘The Bargaining Problem’,” Behavioral Science 33, 81–96. {% %} Schelling, Thomas C. (1968) “The Life You Save May Be Your Own.” In Samuel B. Chase jr., (ed.) Problems in Public Expenditure Analysis, 127–162, Brookings Institution, Washington DC. {% %} Schelling, Thomas C. (1978) “Egonomics, or the Art of Self-Management,” American Economic Review 68, 290–294. {% DC = stationarity; p. 6: different selves compete for command. favors resolute choice: p. 1 1st para of Section I favors the McClennen-Machina approach of going for prior commitment. P. 4 end of 1st para shows the different views on gender differences of those days: “useless outcries and womanish lamentations.” %} Schelling, Thomas C. (1984) “Self-Command in Practice, in Policy, and in a Theory of Rational Choice,” American Economic Review, Papers and Proceedings 74, 1–11. {% %} Schelling, Thomas C. (1984) “Choice and Consequence; Perspectives of an Errant Economist.” Harvard University Press, Cambridge, MA. {% %} Schelling, Thomas C. (1988) “The Mind as a Consuming Organ.” In David E. Bell, Howard Raiffa, & Amos Tversky (1988, eds.) “Decision Making, Descriptive, Normative, and Prescriptive Interactions,” 343–357, Cambridge University Press, Cambridge. {% foundations of statistics; considers p-value for H0 that is a continuum %} Schervish, Mark J. (1996) “P Values: What They Are and What They Are Not,” American Statistician 50, 203–206. {% Seem to generalize Schervish, Seidenfeld, & Kadane (1995, Annals of Statistics) by considering choice functions rather than binary relations. %} Schervish, Mark J. & Teddy Seidenfeld (2010) “Coherent Choice Functions under Uncertainty,” Synthese 172, 157–176. {% state-dependent utility; §5 shows how Savage’s small worlds in fact reduce to state-dependent expected utility. %} Schervish, Mark J., Teddy Seidenfeld, & Joseph B. Kadane (1990) “State-Dependent Utilities,” Journal of the American Statistical Association 85, 840–847. {% state-dependent utility When do aggregated state-dependent SEU models of agents give SEU model for group? Almost always they turn out to be state-independent. They do this for Anscombe -Aumann model. Research question: how about tradeoff consistency agents? %} Schervish, Mark J., Teddy Seidenfeld, & Joseph B. Kadane (1991) “Shared Preferences and State-Dependent Utilities,” Management Science 37, 1575–1589. {% From Seidenfeld’s email: seems to use a (not-necessarily convex) set S of pairs of probabilities and utilities (p, u), with the criterion that horse-lottery1 is strictly preferred to horse-lottery2 iff the former has greater expected utility than the latter for each probability-utility pair (p,u) in the set S. %} Schervish, Mark J., Teddy Seidenfeld, & Joseph B. Kadane (1995) “A Representation of Partially Ordered Preferences,” Annals of Statistics 23, 2168–2217. {% %} Schervish, Mark J., Teddy Seidenfeld, & Joseph B. Kadane (2000) “How Sets of Coherent Probabilities May Serve as Models for Degrees of Incoherence,” International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 8, 347–355. {% Variations on Levi’s E-admissibility. %} Schervish, Mark J., Teddy Seidenfeld, & Joseph B. Kadane (2009) “Self Knowledge, Uncertainty and Choice,” Synthese 172, 157–176. {% De Finetti (1974) showed that coherence à la Dutch book and in proper scoring rules is equivalent for the quadratic scoring rule. This paper generalizes this to a number of other scoring rules. %} Schervish, Mark J., Teddy Seidenfeld, & Joseph B. Kadane (2009) “Proper Scoring Rules, Dominated Forecasts, and Coherence,” Decision Analysis 6, 202–221. {% Dutch book: various stricter and less strict dominance conditions are considered, and infinitely many fair prices. Appendix A gives a convenient discussion of integration w.r.t. finitely additive measures. %} Schervish, Mark J., Teddy Seidenfeld, & Joseph B. Kadane (2014) “Dominating Countably Many Forecasts,” Annals of Statistics 42, 728–756. {% free-will/determinism %} Schick, Fredrick (1979) “Self Knowledge, Uncertainty and Choice,” British Journal for the Philosophy of Science 30, 235–252. {% Dutch book; seems to show that nonEU can lead to dynamic inconsistency. %} Schick, Fredrick (1986) “Dutch Bookies and Money Pumps,” Journal of Philosophy 83, 112–119. {% doi 10.3758/s13423-014-0684-4 Compare Bayesian hierarchical estimation, where parameter estimations of one subject are influenced by data of others (meta-population), with estimations strictly at the individual level. Do predictive exercise, with choices repeated at a later time. Bayesian hierarchical estimation is more stable, and predicts better according to one, but not to two other, criteria. They do it for PT and Birnbaum’s TAX. For PT take power utility and Goldstein-Einhorn weighting family. They take the same utility power for gains and losses, but allow sign-dependence of probability weighting. Table 1 gives the parameter estimates, with utility power = 0.54, loss aversion only 1.2, inverse-S the same for gains and losses nicely supporting its cognitive interpretation. (cognitive ability related to likelihood insensitivity (= inverse-S)) Strangely enough, elevation much higher for losses than for gains. Fortunately, the authors use the term sensitivity both for probability weighting and utility curvature. Unfortunately, they did not implement the outcomes as described, but divided them by a factor not specified on p. 395. The choice error and utility elevation parameters interacted strongly, which can be understood from the Luce-error model used. %} Scheibehenne, Benjamin & Thorsten Pachur (2015) “Using Bayesian Hierarchical Parameter Estimation to Assess the Generalizability of Cognitive Models of Choice,” Psychonomic Bulletin and Review 22, 391–407. {% %} Schiereck, Dirk, Werner DeBondt, & Martin Weber (1999) “Contrarian and Momentum Strategies in Germany,” Financial Analyst Journal 6, 104–116. {% On bipolar scales. %} Schimmack, Ulrich (2001) “Pleasure, Displeasure, and Mixed Feelings: Are Semantic Opposites Mutually Exclusive?,” Cognition and Emotion 15, 81–97. {% Anscombe-Aumann (AA) model; null events versus unawareness. %} Schipper, Burkhard C. (2013) “Awareness-Dependent Subjective Expected Utility,” International Journal of Game Theory 42, 725–753. {% survey on belief measurement; p. 463 footnote 5 suggests that the logarithmic proper scoring rule is the only one that is proper for more than two events, with payment for any event depending only on that event (locality), although the footnote seems to consider only two events where it is not only the logarithmic function. The authors suggest that this result is hard to find in the literature. On the basis of this footnote I asked some people if they know about proofs in the literature. In the end, Jingni Yang found a general proof in Savage (1971 §9.4). P. 465 Proposition 1: for every proper scoring rule different than quadratic there is a distribution where quadratic gives better incentives to tell truth. So, in a way, quadratic is not Pareto inferior. P. 469 2nd para suggests that Offerman et al. (2009) could only handle probabilistic sophistication, but this is not so. Offerman et al. consider as Case 3 probabilistic sophistication, and then Case 4 as its generalization where probabilistic sophistication need no more hold, and they also handle that case. Weele (12Oct2015, email) explained to me that the text here is ambiguous. They had meant this text to refer back only to §2.4.3, which is about probabilistic sophistication, and did not mean to suggest that Offerman et al. cannot handle probabilistic sophistication. The authors point out several times, e.g. p. 473 top, that we have no standard of true subjective beliefs usually. §4.1 discusses how belief elicitation can distort decision making to be measured later. %} Schlag, Karl H., James Tremewan, & Joël J. van der Weele (2015) “A Penny for Your Thoughts: A Survey of Methods for Eliciting Beliefs,” Experimental Economics 18, 457–490. {% DOI: http://dx.doi.org/10.4236/tel.2013.31006 probability elicitation: consider proper scoring rules when paying in probability of winning a prize and then show that one can easily elicit quantiles and moments. They assume expected utility in this. Similar is Hossain & Okui (2013). %} Schlag, Karl H. & Joël J. van der Weele (2013) “Eliciting Probabilities, Means, Medians, Variances and Covariances without Assuming Risk Neutrality,” Theoretical Economics Letters 3, 38–42. {% An expert should provide an interval estimate of a variable. He should be off (true variable outside estimated interval) no more than 1-gamma times, which can encourage him to take the interval large. However, given the restriction, he gets rewarded for taking the interval as tight as possible. It is obvious that the expert will choose a threshold and incorporate all values with probability density exceeding the threshold. Question is how to make him choose the right threshold, giving probability gamma. A most likely interval rewarding formula is proposed (p. 458). The purpose is that, as long as the expert’s subjective probability of an interval stated is smaller than gamma, it pays to enlarge, and when it is bigger than gamma, it pays to reduce. In the optimum, the first-order condition should imply a probability gamma. The result holds under EU where utility is concave (or linear). A question is why the criterion to have exactly subjective probability gamma (in the spirit of classical statistical hypothesis testing, a theory not respected by me I must say). Section 4 gives examples. %} Schlag, Karl H. & Joël J. van der Weele (2015) “A Method to Elicit Beliefs as Most Likely Intervals,” Judgment and Decision Making 10, 456–468. {% value of information: seems to be the first to present the value of information under EU, if not we give priority to Ramsey (1990) who at least demonstrated that the value of info is nonnegative under EU. %} Schlaifer, Robert O. (1959) “Probability and Statistics for Business Decisions: An Introduction to Managerial Economics under Uncertainty.” McGraw-Hill, New York. {% substitution-derivation of EU: §4.4.5 shows how SEU follows from decision tree principles (where end-point outcomes are replaced by lotteries between highest and lowest outcome). %} Schlaifer, Robert O. (1969) “Analysis of Decisions under Uncertainty.” McGraw-Hill, New York. {% utility families parametric %} Schlaifer, Robert O. (1971) “Computer Programs for Elementary Decision Analysis.” Division of Research, Graduate School of Business Administration, Harvard University, Boston. {% information aversion %} Schlee, Edward E. (1990) “The Value of Information in Anticipated Utility Theory,” Journal of Risk and Uncertainty 3, 83–92. {% risk aversion %} Schlee, Edward E. (1990) “Multivariate Risk Aversion and Consumer Choice,” International Economic Review 31, 737–745. {% %} Schlee, Edward E. (1992) “Marshall, Jevons, and the Development of the Expected Utility Hypothesis,” History of Political Economy 24, 729–744. {% information aversion %} Schlee, Edward E. (1997) “The Sure Thing Principle and the Value of Information,” Theory and Decision 42, 21–36; correction see Schlee, Edward E. (1998) “The Sure-Thing Principle and the Value of Information: Corrigenda,” Theory and Decision 45, 199–200. {% information aversion. He points out that such an aversion is obvious if the information becomes public, e.g. in insurance. %} Schlee, Edward E. (2001) “The Value of Information in Efficient Risk Sharing Arrangements,” American Economic Review 91, 509–524. {% %} Schliesser, Eric (2005) “Galilean Reflections on Milton Friedman's “Methodology of Positive Economics,” with Thoughts on Vernon Smith’s “Economics in the Laboratory” ,” Philosphy of the Social Sciences 35, 50–74. {% free-will/determinism: criticizes Libet’s work for not really operationalizing free will %} Schlosser, Markus E. (2014) “The Neuroscientific Study of Free Will: A Diagnosis of the Controversy,” Synthese 191, 245–262. {% %} Schmeidler, David (1969) “The Nucleolus of a Characteristic Function Game,” SIAM Journal of Applied Mathematics 17, 1163–1170. {% Shows: assume connected topological space, with binary relation that is transitive, has weakly preferred and weakly dispreferred sets closed, and strictly preferred and strictly dispreferred sets open. Then the binary relation must be complete. %} Schmeidler, David (1971) “A Condition for the Completeness of Partial Preference Relations,” Econometrica 39, 403–404. {% Exact means that the capacity is the minimum of dominating probability measures. %} Schmeidler, David (1972) “Cores of Exact Games,” Journal of Mathematical Analysis and Applications 40, 214–225. {% %} Schmeidler, David (1982) “Subjective Probability without Additivity,” Foerder Institut of Economic Research, Tel Aviv University, Tel Aviv, Israel. (Rewritten as Schmeidler, David (1984) “Subjective Probability and Expected Utility without Additivity.” Caress working paper 84–21 (first part), University of Pennsylvania, Center for Analytic Research in Economics and the Social Sciences, Philadelphia, PA.) {% %} Schmeidler, David (1984) “Nonadditive Probabilities and Convex Games.” Caress working paper 84–21 (second part), University of Pennsylvania, Center for Analytic Research in Economics and the Social Sciences, Philadelphia, PA. {% Compare to Anger (1977). Propositions 1, 2, and 3 do not assume monotonicity. %} Schmeidler, David (1986) “Integral Representation without Additivity,” Proceedings of the American Mathematical Society 97, 255–261. {% biseparable utility event/utility driven ambiguity model: event-driven schrift p. 401; argues against prior probabilities of statistics, against probability sophistication; does not say clearly that for risk one should do EU, although comment 4.2 argues normatively against probability transformation of RDU. Says nowhere clearly if capacity reflects only belief and not attitude towards belief, although some places do suggest that a bit. P. 576 nicely points out that in Schmeidler’s view, completeness is the most restrictive axiom: “Out of the seven axioms listed here the completeness of the preferences seems to me the most restrictive and most imposing assumption of the theory.” Pp. 586-587 points out that his model can accommodate the co-existence of gambling and insurance. %} Schmeidler, David (1989) “Subjective Probability and Expected Utility without Additivity,” Econometrica 57, 571–587. {% %} Schmeidler, David & Karl Vind (1972) “Fair Net Trades,” Econometrica 40, 637–642. {% %} Schmeidler, David & Peter P. Wakker (1987) “Expected Utility and Mathematical Expectation.” In John Eatwell, Murray Milgate, & Peter K. Newman (eds.) The New Palgrave: A Dictionary of Economics, Vol. 2, 229–232, The MacMillan Press, London. Link to paper
Schmeltzer, Christophe, Jean-Paul Caverni, & Massimo Warglien (2004) “How Does Preference Reversal Appear and Disappear? Effects of the Evaluation Mode,” Journal of Behavioral Decision Making 17, 395–408. {% random incentive system: show that more risk seeking if paying both of two lottery choices than if paying by RIS. %} Schmidt, Barbara & Johannes Hewig (2015) “Paying Out One or All Trials: A Behavioral Economic Evaluation of Payment Methods in a Prototypical Risky Decision Study,” Psychological Record 65, 245–250. {% %} Schmidt, Ulrich (1996) “Demand for Coinsurance and Bilateral Risk-Sharing with Rank-Dependent Utility,” Risk Decision and Policy 1, 217–228. {% Takes vNM EU with utility u only for risky lotteries, for riskless lotteries an alternative function v iso u is used. If vu, then necessarily, stochastic dominance is violated. This is a correct version of what Gafni et al. tried to do but couldn’t because they thought to follow EU everywhere, not being aware that everywhere includes also riskless lotteries. %} Schmidt, Ulrich (1998) “A Measurement of the Certainty Effect,” Journal of Mathematical Psychology 42, 32–47. {% This paper presents some trivial results. It describes some probability weighting functions and observes that certainty effect models can be described through these probability transformations. %} Schmidt, Ulrich (2000) “The Certainty Effect and Boundary Effects with Transformed Probabilities,” Economics Letters 67, 29–33. {% %} Schmidt, Ulrich (2001) “Lottery Dependent Utility: A Reexamination,” Theory and Decision 50, 35–58. {% Tradeoff method: used theoretically, both for outcomes and for decision weights. This paper is the first to study prospect theory with varying status quo. It gives preference conditions for all kinds of relations between weighting functions and value functions corresponding with different status quos. %} Schmidt, Ulrich (2003) “Reference Dependence in Cumulative Prospect Theory,” Journal of Mathematical Psychology 47, 122–131. {% survey on nonEU %} Schmidt, Ulrich (2004) “Alternatives to Expected Utility: Some Formal Theories.” In Salvador Barberà, Peter J. Hammond, & Christian Seidl (eds.) Handbook of Utility Theory II, Ch. 15, 757–838, Kluwer Academic Publishers, Dordrecht. {% Uses prospect theory to analyze insurance. Considers two reference points, being prior or posterior position, and finds that mostly people either take full insurance or no insurance at all. %} Schmidt, Ulrich (2016) “Insurance Demand under Prospect Theory: A Graphical Analysis,” Journal of Risk and Insurance 83, 77–89. {% error theory for risky choice %} Schmidt, Ulrich & John D. Hey (2004) “Are Preference Reversals Errors? An Experimental Investigation,” Journal of Risk and Uncertainty 29, 207–218. {% N = 24 subjects. Those with many choice inconsistencies have more violations of EU than those with few for 14 risky Allais-type pairs of choices, but it is opposite for one 3-color Ellsberg type choice. This suggests that in the risky Allais-type choices the percentage violating EU was always below 50%, and in the Ellsberg it was above 50%. This is in agreement with the finding in the literature that for moderate payments (between 0 and 40 pounds in this paper) the Allais effect is not very strong. %} Schmidt, Ulrich & Tibor Neugebauer (2007) “Testing Expected Utility in the Presence of Errors,” Economic Journal 117, 470–485. {% They take prospect theory where the reference outcome need not be constant, but can depend on the state of nature, as in Sugden (2003, JET). Then they consider preference reversals such as a P-prospect (0.97:$4) versus a $-prospect (0.31:$16). They do not consider straight certainty equivalent determination from ping-pong choices for instance, but only WTA: the subject is first endowed with the prospect, can focus on this as reference outcome (not constant, obviously), and then evaluates giving up the $-prospect for a sure amount x as a (0.97:$4+x, 0.03:x), and the P-prospect as (0.31:$16+x, 0.69:x). They then show that under usual Tversky & Kahneman (1992) parametrizations of PT, preference reversals are accommodated. They, finally, add numerical calculations of which parameter combinations can accommodate preference reversals, and numerical analyses of which parameter combinations of PT generate preference reversals. %} Schmidt, Ulrich, Chris Starmer, & Robert Sugden (2008) “Third-Generation Prospect Theory,” Journal of Risk and Uncertainty 36, 203–223. {% Test loss aversion preference condition of Tversky & Wakker (1993), nicely made tractable through loss aversion premiums characterized in Theorem 1 (absolute premium) and Theorem 3 (relative premium). It is, then, the first parameter-free test of loss aversion. Their findings on loss aversion and gain seeking (I use “gain seeking” as the opposite of “loss aversion”) depend much on the criteria that they used to classify subjects, the power it has, and the noise in the data, as they mention on p. 244. The authors find about as many subjects classified as loss averse as as gain seeking, but those that are loss averse are more extremely so than those that are gain seeking. This could contribute to loss aversion being found at aggregate levels. They found considerably more frequent, and extreme, loss aversion for women than for men (gender differences in risk attitudes). This study does suggest that loss aversion is more volatile and less universal than sometimes thought. %} Schmidt, Ulrich & Stefan Traub (2002) “An Experimental Test of Loss Aversion,” Journal of Risk and Uncertainty 25, 233–249. {% dynamic consistency: test dynamic principles that impy independence. Isolate coalescing from RCLA and find that coalescing is violated, but compound independence and RCLA are not. %} Schmidt, Ulrich & Christian Seidl (2014) “Reconsidering the Common Ratio Eeffect: The Roles of Compound Independence, Reduction, and Coalescing,” Theory and Decision 77, 323–339. {% Endowing subjects with the highest prize of the lottery reverses the income effect of the WTP-WTA discrepancy, but does not affect it much, further illustrating that the income effect cannot explain the discrepancy. The discrepancy is reduced when background risk is added, which could be used to improve the measurements. They used a small sample, N = 24. %} Schmidt, Ulrich & Stefan Traub (2009) “An Experimental Investigation of the Disparity between WTA and WTP for Lotteries,” Theory and Decision 66, 229–262. {% N = 24 subjects. Do binary choice, WTA (although only by asking subjects to imagine that they possess prospect), and WTP (where right before subjects get endowed with maximum prize). Test common consequence effect, away from certainty effect. Find no real violations for choice, but do, and then as fanning out (less risk aversion if better prospects), for WTA and WTP. Point out that testing common consequence effect for pricing such as WTA and WTP has (almost) never been done before. %} Schmidt, Ulrich & Stefan T. Trautmann (2014) “Common Consequence Effects in Pricing and Choice,” Theory and Decision 76, 1–7. {% Derive PT with linear utility with kink at zero from cosigned comonotonic additivity (nicely called independence of common increments), generalizing Chateauneuf (1991) to PT. %} Schmidt, Ulrich & Horst Zank (2001) “An Axiomatization of Linear Cumulative Prospect Theory with Applications to Portfolio Selection and Insurance Demand,” School of Economic Studies, The University of Manchester. {% Tradeoff method %} Schmidt, Ulrich & Horst Zank (2001) “A New Axiomatization of Rank-Dependent Expected Utility with Tradeoff Consistency for Equally Likely Outcomes,” Journal of Mathematical Economics 35, 483–491. {% Derive PT with linear utility with kink at zero from cosigned comonotonic additivity (nicely called independence of common increments), generalizing Chateauneuf (1991) to PT. %} Schmidt, Ulrich & Horst Zank (2001) “An Axiomatization of Linear Cumulative Prospect Theory with Applications to Portfolio Selection and Insurance Demand,” School of Economic Studies, The University of Manchester. {% Define weak loss aversion as y0.5(y) >´ x0.5(x) (>´ denotes strict preference) whenever x > y 0 (Kahneman & Tversky, 1979, p. 279), and strong loss aversion as y + (y) + (12)P >´ x + (x) + (12)P whenever x > y 0, where is a probability, x and y are degenerate prospects, the mixing is probabilistically, and the outcomes x and y have the same rank in both mixtures, and so do x and y. Under EU and OPT (’79 prospect theory) these conditions are equivalent to utility differences for losses exceeding those for gains. Under ’92 PT (CPT), an equality comes in with ratios of weighting functions. Authors plead strongly for a definition of loss aversion entirely in terms of preferences, and not in terms of theory-dependent concepts such as utility. P. 164 para –3: for probability weighting functions that are “too steep” at zero, the loss-aversion condition of the authors cannot be satisfied. The authors write that such weighting functions are unreasonable. %} Schmidt, Ulrich & Horst Zank (2005) “What is Loss Aversion?,” Journal of Risk and Uncertainty 30, 157–167. {% Characterize PT with linear utility for risk. They properly assign priority to a 2002 version of Schmidt & Zank (2009) that appeared later but was written earlier. RDU with linear utility has been characterized by Chateauneuf (1991, JME), De Waegenaere & Wakker (2001), and Diecidue & Wakker (2002). This paper extends sign dependence to those results. %} Schmidt, Ulrich & Horst Zank (2007) “Linear Cumulative Prospect Theory with Applications to Portfolio Selection and Insurance Demand,” Decisions in Economics and Finance 30, 1–18. {% Study strong risk aversion under prospect theory. Holds iff: (i) For gains, U concave and w+ convex; (ii) For losses, U concave and w- concave (or convex if you do, like they do, top-bottom iso the conventional bottom-up integration for losses); (iii) The ratio of the left- and right-derivatives of utility at zero should exceed w+´(p)/w-´(p) (w+ weighting for gains, w- for losses) at each p in (0,1). Here, (i) and (ii) are like Chew, Karni, & Safra (1987), (iii) is the new thing. Utility can be linear for gains and losses, strictly convex at zero, if probability weightings are accordingly, in particular have appropriate jump(s) at 1. %} Schmidt, Ulrich & Horst Zank (2008) “Risk Aversion in Cumulative Prospect Theory,” Management Science 54, 208–216. {% Characterize PT with linear utility for uncertainty through a rank-sign weakening of additivity. Although this paper appeared later than Schmidt & Zank (2007), it preceded it in writing and Schmidt & Zank (2007) properly assign priority to this paper. RDU with linear utility has been characterized by Chateauneuf (1991, JME), De Waegenaere & Wakker (2001), and Diecidue & Wakker (2002). This paper extends sign dependence to those results. First consider only finite state space with nonnull states (at least three of them) and strictly increasing linear utility. Then do general state space with null-invariance (being nonnull for one rank-ordering and sign then for all) where they handle all bounded prospects using supnorm continuity. They use a theorem of Chew & Wakker (1993) to obtain their result. In their integration for losses, they (unfortunately!) do top-down integration instead of the bottom-up integration that was used by Tversky & Kahneman (1992) and that is conventional. %} Schmidt, Ulrich & Horst Zank (2009) “A Simple Model of Cumulative Prospect Theory,” Journal of Mathematical Economics 45, 308–319. {% Tradeoff method: used theoretically. Big issue in PT is what the reference point can be. Many want to derive it endogenously. This paper does so, by taking it as the inflection point of utility. The essential condition, constant diminishing sensitivity (p. 104) is nice: for every outcome, either there should be consistent concavity above (if it is a gain) or consistent convexity below (if it is a loss). It is formulated such that it also implies PT by a kind of implied tradeoff consistency (Theorem 1, p. 106). If there are outcomes of both kind, then their strict inequality conditions imply that there is one unique outcome that is of both kinds: this is the reference point. They also present a more general condition (one-sided comonotonic tradeoff consistency, p. 107), which does not commit to concave or convex, but only requires that for each outcome either the utility standard sequences are consistent above this outcome (then it is a gain) or below (then it is a loss). They again state it in such a manner that it automatically implies PT, by capturing a kind of tradeoff consistency (Theorem 2, p. 108). Very nice! Would be nice to derive it from loss aversion, which the authors state as an important topic for future research. Schmidt, Ulrich & Horst Zank (2012) “A Genuine Foundation of Prospect Theory,” Journal of Risk and Uncertainty 42, 97–113. {% EU+a*sup+b*inf; They vary upon this model by dropping the a-worst part of the distribution and the b-best part of the distribution, and then overweighting what is minimal and maximal. %} Schmidt, Ulrich & Alexander Zimper (2007) “Security and Potential Level Preferences with Thresholds,” Journal of Mathematical Psychology 51, 279–289. {% time preference; do not explicitly relate preference for increasing/decreasing to violations of monotonicity %} Schmitt, David R. & Theorore D. Kemper (1996) “Preference for Different Sequences of Increasing and Decreasing Rewards,” Organizational Behavior and Human Decision Processes 66, 89–101. {% %} Schmittlein, David C., Jinho Kim, & Donald G. Morrison (1990) “Combining Forecasts: Operational Adjustments to Theoretically Optimal Rules,” Management Science 36, 1044–1056. {% suspicion under ambiguity: he pointed this out and provides simple game-theoretic analysis leading to maxmin. The final sentence of the abstract is: “If one adopts the view-point that the Savage axioms only apply to decisions under an uncertain but indifferent world, and not to decisions made in game-like situations with a rational opponent, then the results of Ellsberg’s experiment cannot be considered as evidence against the rationality of the Savage axioms.” (game theory can/cannot be seen as decision under uncertainty) %} Schneeweiss, Hans (1973) “The Ellsberg Paradox from the Point of View of Game Theory,” Inference and Decision 1, 65–78. {% criticism of monotonicity in Anscombe-Aumann (1963) for ambiguity: Consider AA framework. Under probabilistic sophistication, independence for risky choice becomes equivalent to monotonicity and SEU An experiment shows that monotonicit is violated in a systematic direction by half the subjects, and this is strongly correlated with just violating independence in the regular Allais paradox. The experiment considers the common consequence version of Allais’ paradox. With M denoting $106, the conditional choice is between M on balls 1-11 versus 5M on balls 2-11 and 0M on ball 1. - First they do the regular Allais paradox, where there are 89 other balls in the same urn (so it has 100 balls in total), and in one choice situation the common consequence is 1M under these balls so that the certainty effect comes in, and in the other situation one receives 0M under these balls so no certainty effect. - Then they do an uncertainty version. There are no more than the 11 balls in the urn. But now a horse race takes place, with 100 symmetric horses. In both situation the conditional choice is only if horse 1-11 wins the race. The conditional outcome on horses 12-100 is either 1M, so that the certainty effect comes in, or 0M, and then no certainty effect. Under probabilistic sophistication (+ RCLA) the two choice situations should be identical. %} Schneider, Florian & Martin Schonger (2017) “An Experimental Test of the Anscombe-Aumann Monotonicity Axiom,” working paper. {% %} Schneider, Friedrich & Heinrich W. Ursprung (2008) “The 2008 GEA Journal-Ranking for the Economics Profession,” German Economic Review 9, 532–538. {% The decision maker is a convex combination between a rational EU maximizing constant discounter and a prospect theory maximizing nonconstant discounter. The model can accommodate many anomalies. %} Schneider, Mark (2016) “Dual Process Utility Theory: A Model of Decision under Risk and over Time,” working paper. {% %} Schneider, Mark & Jonathan W. Leland (2015) “Reference Dependence, Cooperation, and Coordination in Games,” Judgement and Decision Making 10, 123–129. {% They study ambiguity in the Anscombe-Aumann framework. They propose a new ambiguity model that reminds me of Gul's (1991) disappointment aversion model, although that is not cited. For an act, a separation is made between the bad states that have an outcome (is horse-race lottery) worse than the act itself (disappointment) and the good ones that have a better outcome (elation). Then the subjective probabilities (those are assumed in the model for the horses) of the bad states are overweighted by a factor 1+, those of the good states are overweighted by a factor 1, and then there is renormalization; if my diagonal reading made me understand properly. Because objective probabilities are available, matching and calibration can be done. The main axiom, Axiom 6 (p. 28) requires existence of a such that … and then recalibration with objective probabilities. The main point of the analysis is that unique subjective probabilities on the horses result, and this is interesting. It means that we have probabilistic sophistication within the horse race, and that it fits within the source method. The model seems to satisfy Siniscalchi's Complementary independence (p. 28), which means that it cannot accommodate the empirically prevailing insensitivity or reflection. %} Schneider, Mark A. & Manuel A. Nunez (2015) “A Simple Mean–Dispersion Model of Ambiguity Attitudes,” Journal of Mathematical Economics 58, 25–31. {% Hypothetical choice. Spill-over effect: first experiencing losses increases risk seeking, and first experiencing gains increases risk aversion, the latter going against previous findings on house money effects as the authors indicate. %} Schneider, Sandra, Sandra Kauffman & Andrea Ranieri (2016) “The Effects of Surrounding Positive and Negative Experiences on Risk Taking,” Judgment and Decision Making 11, 424–440. {% N = 60; essentially hypothetical; gain- and loss questions were separated by a week. P. 541 1st column explains some of data analysis but I do not understand. The authors claim that for examining risk aversion, a value function must be specified, and they take 2/3 power for gains and ¾ power for losses. This leaves me in the blue what their concept of risk aversion is. Some lines below it is written that they analyze risk aversion “if we ignore for the moment effects due to probability weighting” and again I have no clue what they are doing. PT falsified: risk averse for gains, risk seeking for losses: seem to be risk neutral for losses; multioutcome lotteries; conclude that OPT does not do well. %} Schneider, Sandra L. & Lola L. Lopes (1986) “Reflection in Preferences under Risk: Who and when May Suggest why,” Journal of Experimental Psychology: Human Perception and Performance 12, 535–548. {% Agents doing CAPM with a deviation measure can be described by having generalised mean-risk preferences with certain constraints on the utility function. %} Schoch, Daniel (2017) “Generalised Mean-Risk Preferences,” Journal of Economic Theory 168, 12–26. {% Discusses history+basic references of certainty factors and the like %} Schocken, Shimon & Tim Finin (1990) “Meta-Interpreters for Rule-Based Inference under Uncertainty,” Decision Support Systems 6, 165–181. {% risky utility u = transform of strength of preference v, latter doesn’t exist: Schoemaker is real strong on that, calling other things oversights. Takes separate-outcome-probability-transformation model as point of departure, does not seem to be aware that for normative purposes (stoch. dom.) that reduces to EU (e.g., p. 537). Volgens Marcel zegt’ie that EU nice theorie is zonder relevantie voor realworld decision making Table 1: SEU = SEU P. 536 cites Burks (1977)!! However, only for describing unresolved philosophical problems in the area of probability. %} Schoemaker, Paul J.H. (1982) “The Expected Utility Model: Its Variations, Purposes, Evidence and Limitations,” Journal of Economic Literature 20, 529–563. {% N > 200; real incentives/hypothetical choice: p. 1455 etc.: compares real choice to hypothetical choice with a large sample but finds no significant difference. Bit more risk aversion for real incentives, as is the common finding. More difference for losses than for gains. concave utility for gains, convex utility for losses: is found (p. 1453) Risk averse for gains, risk seeking for losses: is found (p. 1453). With much risk aversion for mixed. reflection at individual level for risk: is found (Table 1 second subtable; risk aversion for gains is combined with risk most seeking for losses (2/3) of cases, but risk seeking for gains is combined with same risk seeking as risk aversion for losses. P. 1454 2nd para gives statistics that confirm, althoughconcluding sentence p. 1455 l. 2 says weak relation. Nicely, also considers correlations between gain- and loss risk aversion indexes. They are all weakly negative for gains and losses, CE (certainty equivalent; = 0.22), CE ( = 0.15), OE (outcome equivalent) ( = 0.38). No p-values are given. %} Schoemaker, Paul J.H. (1990) “Are Risk-Attitudes Related across Domains and Response Modes?,” Management Science 36, 1451–1463. {% Para on pp. 2-3: SEU = SEU. The author seems to think that Chew’s weighted utility and Savage’s SEU both involve probability transformation, and that the difference is that for Savage the transformations still satisfy the axioms of probability and for weighted utility they do not. This is far from the truth. %} Schoemaker, Paul J.H. (1992) “Subjective Expected Utility Theory Revisited: A Reduction ad Absurdem Paradox,” Theory and Decision 36, 1–21. {% Seem to find that presenting risky decisions in context of insurance enhances risk aversion. %} Schoemaker, Paul J.H. & John C. Hershey (1979) “An Experimental Study of Insurance Decisions,” Journal of Risk and Insurance 46, 603–618. {% %} Schokkaert, Erik & Bert Overlaet (1989) “Moral Intuitions and Economic Models of Distributive Justice,” Social Choice and Welfare 6, 19–31. {% decreasing/increasing impatience: find counter-evidence against the commonly assumed decreasing impatience and/or present effect. Subadditive discounting: first discounting from t1 to t2, and then from t2 to t3, can be different, and usually bigger, than immediately from t1 to t3, as demonstrated in recent papers by Read and others. This paper refines for very small intervals, where it can be superadditive. %} Scholten, Marc & Daniel Read (2006) “Discounting by Intervals: A Generalized Model of Intertemporal Choice,” Management Science 52, 1424–1436. {% intertemporal separability criticized: probably Propose an attribute-oriented, rather than prospect-evaluation-oriented, approach to intertemporal choice, with tradeoffs put central and basic separabilities NOT assumed. Use this to accommodate all existing violations of discounted utility. %} Scholten, Marc & Daniel Read (2010) “Intertemporal Tradeoffs,” Psychological Review 117, 925–944. {% Discuss Markowitz’ 4-fold pattern with risk seeking for small gains and risk aversion for large gains, these things being reflected for losses. This can be reconciled with prospect theory if utility for large gains is sufficiently concave to overcome risk seeking induced by probability overweighting. They consider logarithmic utility ln (x + a), transformed properly. Drawback is that this function can only be concave for gains. risky utility u = strength of preference v (or other riskless cardinal utility, often called value): they argue that their risky utility function is also suited for intertemporal choice. %} Scholten, Marc & Daniel Read (2014) “Prospect Theory and the “Forgotten” Fourfold Pattern of Risk Preferences,” Journal of Risk and Uncertainty 48, 67–83. {% dominance violation by pref. for increasing income: they seem to show that adding a small positive receipt before a delayed payment or adding a small positive delayed receipt after an immediate receipt makes subjects prefer it less, violating dominance. Seem to explain it by preference for improvement. May also be special effects of the 0 outcome in the spirit of Birnbaum, Coffey, Mellers, & Weiss (1992), something discussed by the authors. %} Scholten, Marc & Daniel Read (2014) “Better is Worse, Worse Is Better: Violations of Dominance in Intertemporal Choice,” Decision 1, 215–222. {% preferring streams of increasing income: p. 1178 2nd colum 1st para writes that evidence is not clear. There is asymmetric hidden-zero effect: assume indifference between small-soon large-late: (s:) ~ (:). If we point out to subjects that large-late means receiving nothing now, then preference goes to small-soon. But if we point out that small-soon means receiving nothing later, then preference is not affected. The authors introduce a tradeoff model. Here at a time point not so much the amount received then, but the total cumulated money amount received up to that point, matters. It is used to calculate some average cumulated amount, but also a sort of average duration, where the average of duration is taken weighted by cumulated amount up to that point. Then pairs of average cumulated amount and average duration are evaluated, trading off one against the other. The model fits several empirical findings well, and also data. The model reminds me of the theoretical Blavatskyy (2016), who used a similar weighted sum of cumulative payoffs. %} Scholten, Marc, Daniel Read, & Adam Sanborn (2016) “Cumulative Weighing of Time in Intertemporal Tradeoffs,” Journal of Experimental Psychology: General 145, 1177–1205. {% Psychologist at Pittsburg, uses term “verbal overshadowing” to indicate when decisions are better intuitive (e.g. decision under stress). intuitive versus analytical decisions; Adding verbal descriptions of psychological experiences may only hinder a subject to experience properly. This can be related to the analytical-versus-intuitive debates from decision theory, where adding analytical info may only confuse a subject. %} Schooler Jonathan W., Stellan Ohlsson, & Kevin Brooks (1993) “Thoughts beyond Words: When Language Overshadows Insight,” Journal of Experimental Psychology: General 122: 166183. {% survey on belief measurement: %} Schotter, Andrew, & Isabel Trevino (2014) “Belief Elicitation in the Laboratory,” Annual Review of Economics 6, 103–128. {% Aumann & Serrano (2008) proposed a global index of riskiness of a prospect: For a lottery and a level of wealth, the risk factor is the risk tolerance (reciprocal of the Arrow-Pratt index of risk aversion) for which the lottery, at that level of wealth, is equivalent to not gambling. It is real-valued for prospects with both positive and negative outcomes. This paper does the same in a relative sense. They consider lotteries with positive outcomes, at both sides of 1. They consider the risk tolerance (reciprocal of now the relative indx of risk aversion) for which the lottery is equivalent to having 1 for sure. It is real-valued for prospects with outcomes at both sides of 1. Outcomes are best interpreted as returns per unit invested. The literature uses the term risk tolerance both for the reciprocal of absolute risk aversion used by Aumann & Serrano, and the reciprocal of relative risk aversion used in this paper. %} Schreiber, Amnon (2014) “Economic Indices of Absolute and Relative Riskiness,” Economic Theory 56, 309–331. {% Use RIS. Use choice list (as did so many before Holt & Laury 2002) to get certainty equivalents. gender differences in risk attitudes: in insurance-framed decisions, women are as risk averse as men. In the abstract framing women are more risk averse for gains and more risk seeking for losses, suggesting more pronounced inverse-S. Loss prospects were identical to gain prospects in final wealth, but were implemented by losses from prior endowment mechanism, so that it was really only framing. reflection at individual level for risk: they do not report this; Risk averse for gains, risk seeking for losses: I did not find whether there is risk aversion for gains and risk seeking for losses. %} Schubert, Renate, Martin Brown, Matthias Gysler, & Hans-Wolfgang Brachinger (1999) “Financial Decision-Making: Are Women Really more Risk-Averse?,” American Economic Review, Papers and Proceedings 89, 381–385. {% %} Schultz, Henri (1938) “The Theory and Measurement of Demand.” University of Chicago Press, Chicago. {% QALY measurement: they often take body height. %} Schultz, T. Paul (2002) “Wage Gains Associated with Height as a Form of Health Human Capital,” American Economic Review 92, 349‑353. {% %} Schulzer, Michael, Douglas R. Anderson, & Stephen M. Drance (1991) “Sensitivity and Specificity of a Diagnostic Test Determined by Repeated Observations in the Absence of an External Standard,” Journal of Clinical Psychology 44, 1167–1179. {% P. 831: utility = representational: “the unholy alliance between economics and Benthamite philosophy,” it is directed against Benthamite utilitarianism. Appendix to Ch. 7 describes history of utility, criticizes Benthamite utility again and again, in the context of utilitarianism. For example, in §3, “impression that marginal utility theory depended upon utilitarian or hedonist premisses—Bentham certainly thought so—and could be attacked successfully by attacking these. Jevons was the chief culprit: he even went so far as to call economic theory a ‘calculus of pleasure and pain’ ” Download 7.23 Mb. Share with your friends:
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