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§4.7 defines generalized utilitarianism as SUMg(u
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| §4.7 defines generalized utilitarianism as SUMg(ui) with ui the utility of individual i (objectively given beforehand, so like money) and g a nonlinear transformation. (They write gn to express the dimension n for later purposes.) So this could be n times expected utility for 1/n probability distributions. Representative utility is g-1 of SUM/n, so certainty equivalent.
P. 102 bottom considers difference of representative utility and average utility, which is risk premium. §4.9 considers information requirements. Imagine that preference is not affected if we add a prospect (add coordinate-dependent constant). This is what my 2010 book calls additivity in Ch. 1. Under some continuity it implies invariance under multiplication by a positive scalar. Thus, any positive affine transformation does not affect preference. The book calls it cardinal unit comparability (CUC; p. 112). This book interprets it as information invariance, an interpretation initiated by Amartya Sen it seems. The condition is appropriate if we know no more than the cardinal class of the preference inputs. In the same spirit we can interpret constant absolure or relative risk aversion as information requirements. Anyway, CUC is like additivity in my 2010 book and axiomatizes subjective expected value maximization. Anonymity then implies same subjective probabilities, so just sum. §4.10 considers fixed population sizes. Same-people independence (p. 115) is joint separability for each fixed n. Theorem 4.7 shows that we get generalized utilitarianism with n-dependent gn, for each n. Then follow some theorems (4.9, 4.10) axiomatizing utilitarianism, which is just the sum of inputs. §4.11 considers variable population size but with comparisons only between n-tuples of the same length. Replication invariance: x y <==> kx ky for each natural k if x and y are of the same length. Theorem 4.22 axiomatizes generalized utilitarianism with same g for each n, as always in this book, g being continuous. Theorems 4.19 & 4.21 prepare, with the latter using population substitution (kind of conditional certainty equivalence substitution; this implies for the representative agent exactly what Nagumo (1930) and Kolmogorov (1930) call associativity) instead of replication invariance (which is implied by it). Wakker (1986, Theory and Decision) is in fact the generalization of Theorem 4.21 to general, possibly noncontinuous, utility. Ch. 5 turns to variable populations with comparisons between n-tuples of different length. In additive representations, it then is important where utility is 0. This is called the critical level. It is comparable to the reference point for prospect theory although not the same (no different dimensions in PT). Section 5.1 p. 130 mentions that continuity now must be strengthened to go across different n. §5.1.3 discusses what is called the repugnant conclusion (Parfit 1976), where the authors are as emotional as several others, something that I have never understood. Tännsjö (2002) seems to agree with me. §5.2.6 discusses average utilitarianism. For fixed n it is the same utilitarianism, but for variable n is makes a difference. Then comes Part B with axioms. §5.5, p. 158, formulates extended continuity, {x n: x y} must be closed for y m also, and same with weak reversed preference. §5.6 defines same-number independence, being joint independence for each fixed n. Utility independence: joint independence if length of the two vectors compared may be different (satisfied under generalized utilitarianism but not under average generalized utilitarianism). Existence independence: preference between two vectors of possibly different length is not affected if common part is added. It implies utility independence but gives links between variable length. P. 160 l. 5-6 defines critical level. There is an existence of critical levels assumption. P. 165, end of §5.6: extended replication invariance: uRv <==> kuRkv extended to u,v of different length. There are also number-dampened models, which have each extra dimension weighted less than the one before. §5.8 discussed average generalized utilitarianism (AGU) and some other models, such as number-dampened, with axiomatizations to come in Ch. 6. §6.2 discusses it again. Part B starts at §6.5. Theorem 6.1 axiomatizes continuous same-number generalized utilitarianism with dimension-dependent utility, and Theorem 6.2 axiomatizes it with dimension-independent utility. These results follow directly from Theorems 4.21 and 4.22. §6.6 has number-sensitive critical levels, §6.7 has them constant, §6.9 considers representative-utility principles (CEs (certainty equivalents) represent). It involves replication equivalence: x ~ kx for each k. Theorem 6.15 axiomatizes it (axioms: continuity, Pareto, minimal increasingness, and replication invariance), with the text following the proof on p. 198 verbally expressing the axiomatization of average generalized utility by adding same-number independence. §6.10 considers number-deampening. Theorem 6.24 axiomatizes power utility by invariance w.r.t. unit change of inputs (called information invariance with respect to ratio scale full comparability). %} Blackorby, Charles, Walter Bossert, & David Donaldson (2005) “Population Issues in Social Choice Theory, Welfare Economics and Ethics.” Cambridge University Press, Cambridge, UK. {% This paper, pointed out to me by Horst Zank in November 2000, proves some interesting representation theorems. It formulates these results in a social choice context, where individual utilities are given as primitives and social preferences are derived. As pointed out on p. 251 third paragraph, the results are isomorphic to preference representations on Ren. Theorem 3 shows that additively decomposable functionals that satisfy CARA (constant absolute risk aversion) are, in fact, expected utility functionals with exponential utility. The result precedes Theorem VII.7.6 of Wakker (1989, Additive Representations of Preferences). Corollary 1.1, the special case of Theorem 1 restricted to monotonicity, shows that additively decomposable functionals which satisfy constant RRA are, in fact, expected utility functionals with power utility. It thereby precedes Theorem VII.7.5 of Wakker (1989, Additive Representations of Preferences). A special aspect of the theorem is that they permit both positive and negative inputs, and characterize a case of power utility xr for positive x, and (x)r for negative x, with positive a scale factor. The authors point out that this result gives a special meaning to the zero outcome. So, the value function often used in prospect theory is already here! There are references to earlier works in social choice theory on similar functionals. %} Blackorby, Charles & David Donaldson (1982) “Ratio-Scale and Translation-Scale Full Interpersonal Comparability without Domain Restrictions: Admissible Social Evaluation Functions,” International Economic Review 23, 249–268. {% Harsanyi’s aggregation %} Blackorby, Charles, David Donaldson, & John A. Weymark (1999) “Harsanyi’s Social Aggregation Theorem for State-Contingent Alternatives,” Journal of Mathematical Economics 32, 369–387. {% dynamic consistency %} Blackorby, Charles, David Nissen, Daniel Primont & Robert R. Russell (1973) “Consistent Intertemporal Decision Making,” Review of Economic Studies 40, 239–248. {% %} Blackorby, Charles, Daniel Primont, & Robert R. Russell (1978) “Duality, Separability and Functional Structure: Theory and Economic Applications.” North-Holland, Amsterdam. {% Paper characterizes SEU by assuming additive representability through separability (Debreu 1960 etc.), and then assuming symmetry of preference with respect to all n states of nature, so that equal probabilities come out. (It suggests something else, being that they work with general n states that may not be equally likely, but then they assume that there exists an underlying refinement such that … etc.) It may be argued that this is decision under risk with known probabilities 1/n, and that what they characterize is a generalized quasi-linear mean. The assumption of replication equivalence (x ~ mx for any n-tuple x where mx means the mn tuple with x repeated m times), often used in axiomatizations of average utility, is not stated explicitly but is implicit in their Assumption 5, and in their implicit assumption in the proof of lemma 2 that u is independent of ||S||. Section IV briefly discusses EU with Utility of gambling (EU only when restricted to nondegenerate prospects). %} Blackorby, Charles, Russell Davidson, & David Donaldson (1977) “A Homiletic Exposition of the Expected Utility Hypothesis,” Economica 44, 351–358. {% %} Blackwell, David (1953) “Equivalent Comparisons of Experiments,” Annals of Mathematical Statistics 24, 265–272. {% %} Blackwell, David & Lester E. Dubins (1962) “Merging of Opinions with Increasing Information,” Annals of Mathematical Statistics 38, 886–896. {% Dutch books. Theorem 4.3.1 shows that for a nontrivial weak order on Ren that satisfies weak monotonicity and additivity, there exist probabilities p1, …, pn such that f > g (>´ denoting strict preference) if f has strictly greater EV. Problem 4.3.1 states the if and only if implication if continuity is added, and also states a mixture-independence (fg implies f + (1)h g + (1)h for all f,g,h and 0 < < 1) that implies additivity and in the presence of continuity is equivalent to additivity. The technique of Theorem 10.1 in Fishburn Peter C. (1982) “The Foundations of Expected Utility” could be used to generalize the result. %} Blackwell, David & Meyer A. Girshick (1954) “Theory of Games and Statistical Decisions.” Wiley, New York. {% Interview patients and see what role unknown probabilies (ambiguity) plays here. %} Blaisdell, Laura L., Caitlin Gutheil, Norbert A. M. Hootsmans, & Paul K. J. Han (2016) “Unknown Risks: Parental Hesitation about Vaccination,” Medical Decision Making 36, 479–489. {% decreasing ARA/increasing RRA: seems to find decreasing, rather than increasing, RRA %} Blake, David (1996) “Efficiency, Risk Aversion and Portfolio Insurance: An Analysis of Financial Asset Portfolios Held by Investors in the United Kingdom,” Economic Journal 106, 1175–1192. {% If revealing beliefs about games, and then playing games, and then paying for both, income effects can arise. The method widely used to avoid income effects, the RIS, can obviously also be used in the case just mentioned. This is what this paper proposes and tests. They find that with repeated payments, income effects do arise. %} Blanco, Mariana, Dirk Engelmann, Alexander K. Koch, & Hans-Theo Normann (2010) “Belief Elicitation in Experiments: Is there a Hedging Problem?,” Experimental Economics 13, 412–438. {% equity-versus-efficiency: describes situations in which equity is not much at the cost of efficiency. If equity is at the cost of efficiency, this is called the “leacky bucket effect.” %} Blank, Rebecca M. (2002) “Can Equity and Efficiency Complement Each Other?,” Labour Economics 9, 451–468. {% %} Blaschke, Wilhelm (1928) “Topologische Fragen der Differentialgeometrie, I,” Mathematische Zeitschrift 28, 150–157. {% %} Blaschke, Wilhelm & Gerrit Bol (1938) “Geometrie der Gewebe.” Springer, Berlin. {% Jan. 18, 2002 I discussed this book with Mark Blaug. He said that he did not write things to express his opinions, but rather to provoke students and make them think. Ch. 8: “The marginal revolution.” §18.1, p. 278, on period following 1870, “For the first time, economics truly became the science that studies the relationship between given ends and given scarce means that have alternative uses for the achievement of those ends.” (Italics from original.) §8.4, p. 284, on philosophers emphasizing introspection as an instrument for economics and on hedonism in England in the 1850s. Blaug is negative on Mirowsky. Ch. 9: “Marshallian Economics: Utility and Demand” §9.2, p. 313, ascribes, as did Stigler (1950, §V), to Fisher the same way of measuring cardinal utility under additive decomposable MAU. Blaug, however, does not ascribe it to Fisher (1892) as did Stigler, but to Fisher (1927). I spent many hours checking both Fisher-works, and found that this idea of standard sequences simply is not there. Blaug (Feb. 12, 2002, personal communication) explained that he had taken the reference from Stigler (1950) without checking the original. §9.2, end (p. 316) seems to suggest that for utilitarian welfare evaluations the origin of utility must be determined?? §9.4, p. 320, deals with marginal utility derived from vNM utility and is awfully close to equating it with riskless utility, although the text immediately follows by saying that no one can measure the latter yet. §9.7, p. 330, mentions an observability problem of indifference, as follows, for two commodities x and y (say x are apples and y pears): “we do not presume that he can say how much more y would be equivalent to a unit reduction in x. To make that presumption is to suppose that the individual can compare increments and decrements of marginal utility, which would imply cardinal measurement of utility.” That is, Blaug confuses, for instance, marginal rates of substitution with cardinal utility. §9.10, p. 332 seems to (re)state the observability problem of indifference (we can never be sure from an observed choice whether or not the agent was indifference), but claims that, in the absence of introspection, indifference is as unobservable as strength of preference. It immediately gives one solution, indifference can be observed statistically. Another is that indifference can be observed approximately (every improvement determines a strict preference). P. 333 l. 1 then goes on to suggest that avoidance of this indifference problem, together with unobservability of strength of preference, were the main motivations for Samuelson to develop the revealed preference approach. I don’t think that the indifference problem played such a role, neither that it is in the same league as the unobservability of strength of preference. P. 337, §9.12, seems to identify the difference between Benthamite utility and choice-based utility with a normative-descriptive difference, and then criticizes others for not having grasped this difference. P. 338, bottom line, seems to equate violations of revealed preference axioms with changing tastes. Ch. 17, “A Methodological Postscript,” is on empirical status, formal status, and falsifiability. P. 695, §17.3: “… theories are overthrown by better theories, not simply by contradictory facts.” P. 698, §17.4, “After a serious of attacks on utilitarian welfare economics, a new Paretian welfare economics was erected in the 1930s that purported to avoid interpersonal comparisons of utility.” End of §17.4, p. 700, points out that welfare economics must involve value judgments. %} Blaug, Mark (1962) “Economic Theory in Retrospect.” Cambridge University Press, Cambridge. (5th edn. 1997). {% Eq. 2 is a clever way of approximating PT with a power function p for w(p). Then with U(x) = x, PT of the St. Petersburg paradox prospect is finite iff < . The author considers this to be a problem for PT. Refers to Tversky & Bar-Hillel (1983) who actually predicted risk seeking in the St. Petersburg paradox, if properly truncated to get empirical realism. %} Blavatskyy, Pavlo R. (2005) “Back to the St. Petersburg Paradox?,” Management Science 51, 677–678. {% Urn contains one white and one black ball. Random drawing with replacement, white ball delivers $1. Then another black ball is added, again random drawing with replacing, with $1 if white; etc. So, the subject receives (1/2:$1) + (1/3:$1) + (1/4:$1) + (1/5:$1) + … etc. Probability that total payment is below x is zero for every real x, so, with probability 1 it yields infinite much. Yet subjects pay only finite amount for it. So, it is a variation of the St. Petersburg paradox, one that falsifies every existing theory. %} Blavatskyy, Pavlo R. (2006) “Harmonic Sequence Paradox,” Economic Theory 28, 221–226. {% You choose between two prospects by seeing which has the higher probability of giving a better outcome. This simple heuristic is tested descriptively. %} Blavatskyy, Pavlo R. (2006) “Axiomatization of a Preference for Most Probable Winner,” Theory and Decision 60, 17–33. {% Tradeoff method; Assume that first Wakker & Deneffe’s (1996) Tradeoff method is used to elicit a sequence x0, … , x k of outcomes equally spaced in utility units. They can be given utilities U(xj) = j/k. Then xj ~ xkpjx0) implies that w(pj) = j/k for probability weighting w. This method was used by Abdellaoui (2000). We can continue and use the elicited weights to refine the utilities measured. We can for instance consider indifferences yi ~x1pix0 to conclude that U(yi) = j/k*1/k = j/k2. The author considers a three-stage approach of this kind, considers response-errors, and analyzes which of the adaptive method has the smallest overall errors. %} Blavatskyy, Pavlo R. (2006) “Error Propagation in the Elicitation of Utility and Probability Weighting Functions,” Theory and Decision 60, 315–334. {% Assumes EU with error theory. Says that purported violations of betweenness found empirically may be due to errors in choice rather than being genuine violations of betweenness. %} Blavatskyy, Pavlo R. (2006) “Violations of Betweenness or Random Errors?,” Economics Letters 91, 34–38. {% Reanalyzes existing data sets using stochastic choice theories; concave utility for gains, convex utility for losses: p. 271; P. 271 finds lower error for losses than for gains. This agrees with findings of Yechiam, Retzer, Telpaz, & Hochman (2015). error theory for risky choice %} Blavatskyy, Pavlo R. (2007) “Stochastic Expected Utility Theory,” Journal of Risk and Uncertainty 34, 259–286. {% A theoretical paper deriving a stochastic choice result from preference assumptions about stochastic choice. %} Blavatskyy, Pavlo R. (2008) “Stochastic Utility Theorem,” Journal of Mathematical Economics 44, 1049–1056. {% N=48 subjects answered 19 general knowledge questions. Then they could choose to either gamble on one of their answers, or on an objective probability, of getting a prize. The objective probability was taken equal to the percentage of correct answers for each subject. So, the two options are indifferent. Although the paper does not write it explicitly, I assume that the subjects were NOT informed about how the probability had been chosen. Most subjects preferred to gamble on the known probability, which can be interpreted as underconfidence. %} Blavatskyy, Pavlo R. (2009) “Betting on Own Knowledge: Experimental Test of Overconfidence,” Journal of Risk and Uncertainty 38, 39–49. {% Shows that preference reversals, with more common than uncommon ones, can follow from merely errors in choice, using a probabilistic choice model that avoids violations of stochastic dominance. %} Blavatskyy, Pavlo R. (2009) “Preference Reversals and Probabilistic Decisions,” Journal of Risk and Uncertainty 39, 237–250. {% Köbberling & Wakker (2003) defined, for PT with monetary outcomes, a more loss averse concept that implies the same risk attitudes for gains and for losses, in other words, that can only be used if the same risk attitudes for gains and for losses. It means that same basic utility and same weighting functions, but stronger kink. This paper generalizes the condition to general, nonmonetary, outcomes and splits the condition up into two. The first half, called more loss averse, imposes the condition only on mixed prospects that are preferred to the reference point. The second half, called less gain prone, imposes it only on mixed prospects worse than the reference point. It does not formulate the conditions for PT but only for RDU and, preceding that, for the special case of EU. It also gives a probabilistic extension. Kõbberling & Wakker’s (1993) preference conditions compare mixed prospects only to unnmixed sure outcomes, and not to unmixed general prospects as does this paper. Because K&W have a continuum of outcomes, and because the two decision makers compared have the same preferences over nonmixed prospects, this difference does not matter. I prefer a terminology where less gain seeking means just the same as more risk averse, as this has been done in other papers, and in the same way as less risk seeking is the same as more risk averse. So in this sense I would have preferred a different terminology for this paper. Köbberling & Wakker (2003) defined comparative loss aversion also under the restriction of same risk attitudes, and presented this as a restriction to be generalized in the future. This author proceeds differently. He argues that this restriction is intuitive and good and is how it should be. See his text below Proposition 1, p. 130: “Thus, to have a meaningful concept of comparative loss aversion, we need to consider individuals with identical preferences over the set of loss-free lotteries.” It reminds me of people who, for subjective expected utility, use the particular Yaari-type more-risk-averse-than condition, notice that it implies the same subjective probabilities so that Yaari’s method only works for the special case of identical subjective probabilities, and then start arguing that this is a law of nature and that we should never try to compare risk attitudes if different subjective probabilities; a common misunderstanding in the field. %} Blavatskyy, Pavlo (2010) “Loss Aversion,” Economic Theory 46, 127–148. {% biseparable utility %} Blavatskyy, Pavlo (2010) “Modifying the Mean-Variance Approach to Avoid Violations of Stochastic Dominance,” Management Science 56, 2050–2057. {% real incentives: RIS. PT falsified Obtains systematic examples of reversed common ratio. If to choose between sure outcome and prospect with considerably higher EV, most choose the latter, risky, option. If then the probabilities of nonzero outcomes are scaled down by a common factor, many switch to a safe choice. For example, 60 1003/40 (64.9%) but 601/30 1001/40 (67.1%). I wondered if some error theory could account for it, with simply more errors in the latter choice because then the options are more indifferent. But this does not work well because the paradoxical choices are majority choices. The finding 601/30 1001/40 (67.1%) is amazing and puzzling. The paper considers some error theories but they cannot account for the finding. These findings violate every existing theory. %} Blavatskyy, Pavlo R. (2010) “Reverse Common Ratio Effect,” Journal of Risk and Uncertainty 40, 219–241. {% %} Blavatskyy, Pavlo (2011) “Probabilistic Risk Aversion with an Arbitrary Outcome Set,” Economics Letters 112, 34–37. {% The version of March 2011 lets 38 subjects choose between all prospects generated by the probabilities j/4 and amounts €5, €20, €25, €40. Tests virtually all presently existing theories. RDU and EU do well, quadratic utility and Chew’s betweenness do bad. Best is the heuristic of first minimizing probability of worst outcome and then maximizing probability of best outcome. This fits well with extreme inverse-S and neoadditive. %} Blavatskyy, Pavlo R. (2011) “Which Decision Theory? {% biseparable utility: violated because the model is very general, with functions phi depending on pairs of states. %} Blavatskyy, Pavlo R. (2011) “Modeling Ambiguity Aversion as Aversion to Utility Dispersion Caused by Ambiguous Events,” Dept. of Economics, University of Innsbrück, working paper. {% Probabilistic choice with an error theory that, however, is never allowed to violate stochastic dominance. Theoretical derivation using preference conditions is given, and it is fit to data. The papers Blavatskyy (2011 Management Science) and Blavatskyy (2012 Economic Theory) are very close, with the same model, but, inappropriately, have no proper cross references. The 2012 ET paper does not cite the 2011 MS paper. The 2011 MS paper does cite the 2012 ET paper (as forthcoming) but only in the appendix for technical steps in the proof, and in no way explains the overlap. This MS paper more discusses empirical implications, and implications for consumer choice, and the ET paper more does the mathematical proof. This MS paper also gives the representation theorem but only sketches the proof. %} Blavatskyy, Pavlo R. (2011) “A Model of Probabilistic Choice Satisfying First-Order Stochastic Dominance,” Management Science 57, 542–548. {% Probabilistic choice with an error theory that, however, is never allowed to violate stochastic dominance. Theoretical derivation using preference conditions is given. The papers Blavatskyy (2011 Management Science) and Blavatskyy (2012 Economic Theory) are very close, with the same model, , but, inappropriately, have no proper cross references. The 2012 ET paper does not cite the 2011 MS paper. The 2011 MS paper does cite the 2012 ET paper (as forthcoming) but only in the appendix for technical steps in the proof, and in no way explains the overlap. This ET paper more does the mathematical proof, and the MS paper more discusses empirical implications, and implications for consumer choice. %} Blavatskyy, Pavlo R. (2012) “Probabilistic Choice and Stochastic Dominance,” Economic Theory 50, 59–83. {% A pretty test of the multiplicative model (p:x, 1-p:0) -->w(p)U(x) by testing what in fact is the Thomsen condition. I informed the author that his condition is the Thomsen condition around 2009. I regret that he does not cite the Thomsen condition but inappropriately continues to claim novelty. Other than this, the empirical demonstration is pretty. %} Blavatskyy, Pavlo R. (2012) “The Troika Paradox,” Economics Letters 115, 236–239. {% Characterizes a probabilistic generalization of the subjective-mixture SEU axiomatization by Ghirardato et al. (2003, Econometrica). It shares the drawback with the result by Ghirardato et al. that the endogenous mixture operation is not observable by finitely many observations. Using it in preference axioms is the same as using utility as an input in preference axiomatizations. I did not understand in the proof of Proposition 1 why different outcomes cannot be indifferent, and why this would contradict Axiom 4. %} Blavatskyy, Pavlo R. (2012) “Probabilistic Subjective Expected Utility,” Journal of Mathematical Economics 48, 47–50. {% %} Blavatskyy, Pavlo R. (2013) “The Reverse Allais Paradox,” Economic Letters 119, 60–64. {% Tradeoff method: very interestingly, this paper weakens my tradeoff consistency condition which generalizes the Reidemeister condition by considering inter-attribute difference comparisons. It does not turn it into a consistency for endogenous mipoints (which would generalize the hexagon condition by considering inter-attribute comparisons), and for which it has been an open question since my youth whether it gives SEU for more than two states. It does something in between. On one coordinates it uses differences, as does tradeoff consistency, but on the other it considers endogenous mipoints. Still the condition is strong enough to imply SEU. The difficult step in this is to show that the condition implies joint independence (separability), but the author succeeds in doing it. %} Blavatskyy, Pavlo R. (2013) “The Simplest Behavioral Characterization of Subjective Expected Utility Theory Using the Connected Topology Approach,” Operations Research 61, 932–940. {% %} Blavatskyy, Pavlo R. (2014) “Stronger Utility,” Theory and Decision 76, 265–286. {% In common discounted utility, time separability is problematic. It implies that splitting $2 today up into $1 today and $1 tomorrow is favorable if utility is sufficiently concave. This paper takes a discounted sum, but not of separate amounts received today, but of all cumulated payments received up to a timepoint. It avoids the above monotonicity violations and relaxes time separability. It reminds me of Scholten, Read, & Sanborn (2016) who also consider weighted sums of cumulative payoffs. %} Blavatskyy, Pavlo R. (2016) “A Monotone Model of Intertemporal Choice,” Economic Theory 62, 785–812. {% Do a truncated BDM (Becker-DeGroot-Marschak), with upper/lower bound, and use error theory to analyze. Give a multistage explanation with nonEU and each price set a new stage. For p > 0.5 the restricted BDM gives higher prices than the unrestricted, for p < 0.5 it is the other way around. %} Blavatskyy, Pavlo R. & Wolfgang R. Köhler (2009) “Range Effects and Lottery Pricing,” Experimental Economics 12, 332–349. {% survey on nonEU: on the Allais paradox, to be precise. %} Blavatskyy, Pavlo & Andreas Ortmann (2012) “The Allais Paradox: Perception and Evidence,” working paper. {% %} Blavatskyy, Pavlo, Andreas Ortmann, & Valentyn Panchenko (2015) “Now You See It, now You Don’t: How to Make the Allais Paradox Appear, Disappear, or Reverse,” working paper. {% Best core theory depends on error theory: find that. In particular, best fitting parameters within one theory depend on the error theory. Thus, when fitting EU with CRRA, they find risk seeking convex U for a random utility model, risk neutrality for a tremble model, and risk aversion for a Fechner model. They find inverse-S probability weighting confirmed for all error models except Fechner. In Fechner error component does similar things as inverse-S so takes over. They find that log-power (CRRA) utility fits worse than expo-power. Probably because both very small and very large amounts are involved. %} Blavatskyy, Pavlo & Ganna Pogrebna (2010) “Models of Stochastic Choice and Decision Theory: Why Both Are Important for Analyzing Decisions,” Journal of Applied Econometrics 25, 963–986. {% In the deal-or-no-deal show, the authors make the questionable assumption that in a choice between the offer of the bank (a sure option) and a prospect, a choice for the prospect entails a violation of loss aversion. %} Blavatskyy, Pavlo & Ganna Pogrebna (2006) “Loss Aversion? Not with Half-a-Million on the Table!,” IEW WP # 274. {% People can gamble on 20% price or 80% price but exhibit similar risk aversion in a deal or no deal context. %} Blavatskyy, Pavlo & Ganna Pogrebna (2008) “Risk Aversion when Gains Are Likely and Unlikely: Evidence from a Natural Experiment with Large Stakes,” Theory and Decision 64, 395–420. {% %} Bleichrodt, Han (1995) “QALYs and HYEs: Under What Conditions Are They Equivalent?,” Journal of Health Economics 14, 17–37. {% %} Bleichrodt, Han (1996) “Applications of Utility Theory in the Economic Evaluation of Health Care.” Ph.D. dissertation, iMTA, Erasmus University, Rotterdam, the Netherlands. {% %} Bleichrodt, Han (1997) “Health Utility Indices and Equity Considerations,” Journal of Health Economics 16, 65–91. {% %} Bleichrodt, Han (1998) “Health Utility Indices and Equity Considerations.” In Morris.L. Barer, Tom E. Getzen, & Greg L. Stoddart (eds.) Health, Health Care and Health Economics, 331–362, Wiley, Chichester. {% %} Bleichrodt, Han (2000) “Rational Risk Policy by W. Kip Viscusi,” Journal of Economic Literature 38, 127–128. {% %} Bleichrodt, Han (2000) “De Waardering van Gezondheidsbaten.” In Robert Spreeuw & Diederik Stapel (eds.) Over de Grenzen van het Weten, 25–29, KNAW, Amsterdam (in Dutch). {% Compares utilities measured through adaptive SG to utilities measured through nonadaptive SG, all with two-outcome gambles. Under classical elicitation assumption (doing calculations assuming EU descriptively), discrepancies arise, falsifying EU. If a correction is carried out for probability weighting using inverse-S within RDU, the discrepancies only increase. This is counterevidence against RDU. Earlier counterevidence, by Wakker, Erev, & Weber (1994), Birnbaum & McIntosh (1996), and Birnbaum & Navarrete (1998), always concerned three-outcome gambles, this paper has two-outcome gambles. The author suggests that loss aversion and framing can explain the findings. %} Bleichrodt, Han (2001) “Probability Weighting in Choice under Risk: An Empirical Test,” Journal of Risk and Uncertainty 23, 185–198. {% %} Bleichrodt, Han, (2001) “Utility of Gains and Losses by R. Duncan Luce,” Journal of Economic Literature 39, 130–131. {% SG doesn’t do well; SG higher than CE Biases in SG utility measurements all go in the same direction (upwards); biases in the TTO go in different directions. Scale compatibility and loss aversion give bias upwards, utility curvature a bias downwards. Hence, TTO may not be so bad on average. My guess is that the two upwards biases are stronger than the one downward bias, suggesting that on average TTO comes out too high. Also contributes to CE bias towards EV %} Bleichrodt, Han (2002) “A New Explanation for the Difference between SG and TTO Utilities,” Health Economics 11, 447–456. {% %} Bleichrodt, Han (2002) “Het Dilemma van de Minister van Volksgezondheid.” In Harry van Dalen & Frank Kalshoven (eds.) Meesters van de Welvaart: Topeconomen over Nederland. Balans, 201–211, Amsterdam (in Dutch). {% Tradeoff method is used. Paper assumes choices from choice sets where one of the elements in the choice set is the reference point. It means that the preference relation given each reference point, as derivable using revealed preference techniques, cannot compare options worse than the reference point (they are never chosen because rather the reference point is chosen). This is a very realistic assumption. Sugden (2003) assumed such preferences observable which is unconvincing. Thus, reference dependence leads to incomplete preference (or, put another way in this case, to complete preference on a subset). The author develops additive representations for this case. This paper is the first to illustrate that reference dependence makes completeness more questionable and adds to the desirability to study weakenings of completeness. %} Bleichrodt, Han (2007) “Reference-Dependent Utility with Shifting Reference Points and Incomplete Preferences,” Journal of Mathematical Psychology 51, 266–276. {% %} Bleichrodt, Han (2009) “Reference-Dependent Expected Utility with Incomplete Preferences,” Journal of Mathematical Psychology 53, 287–293. {% SG higher than others: seem to show that SG results are too high. %} Bleichrodt, Han, Jose Maria Abellán, José Luis Pinto, & Ildefonso Mendez-Martinez (2007) “Resolving Inconsistencies in Utility Measurement under Risk: Tests of Generalizations of Expected Utility,” Management Science 53, 469–482. {% %} Bleichrodt, Han & Werner B.F. Brouwer (1999) “Disconteren.” In Maureen P.M.H. Rutten-van Mölken, Jan J. van Busschbach, & Frans F.H. Rutten (eds.) Van Kosten tot Effecten: Een Handleiding voor Evaluatiestudies in de Gezondheidszorg, 123–129, Elsevier, Maarssen (in Dutch). {% Tradeoff method The first paper to actually measure the regret theory functional quantitatively. This has not been done before, probably, because people thought that something as strange as a nontransitive functional can never be measured in any sensible way. This paper shows it can. Confirms the main empirical hypothesis that Loomes & Sugden put up in the 1980s, that people are disproportionally averse to large regrets. This is even after controlling for event splitting. (In later papers, after the 1980s, Loomes, Sugden, and others conjectured that their original findings may have been just due to event splitting.) Under regret theory, we have x > y iff p1Q(U(x1) - U(y1)) + … + pnQ(U(xn) - U(yn)) > 0 where xi (yi) is the outcome of act x (y) at state i, and pi the subjective probability of that state. The tradeoff method with indifferences j+1ix ~ jiy for many j still implies that the j's are equally spaced in utility units. (It, first, implies that Q(j+1,j) is the same for all j. This then implies the same U(j+1) U(j) for all j. That is, the tradeoff method is robust not only against probability weighting as shown many times before, but also against violations of transitivity. This paper, thus, measures U. Then, with U available, it derives Q from PE questions. Download 7.23 Mb. Share with your friends:
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