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| §7 considers variable dimension, with all finite-dimensional subspaces. It points out the omission in Blackorby, Primont, & Russel (1977) of not imposing consistency across different dimensions so as to ensure the same utility function there (following Proposition 20). It points out that one gets all rational-probability prospects this way. It also tries to extend to nonrational-probability prospects by taking limits, but then from Eqs. 150-152 implicitly uses that the functional is continuous in probability (the continuity it refers to is of the EU functional, and not of the functional considered and yet to be proved to be EU).
The paper throughout gives generalizations to implicit (betweenness) functionals as studied primarily by Chew. It heavily leans on Chew & Epstein (1989), a paper that unfortunately has several mathematical problems. %} Diewert, Walter E.(1993) “Symmetric Means and Choice under Uncertainty.” In Walter E. Diewert & Alice O. Nakamura, Elsevier, (eds.) Essays in Index Number Theory, 355–441, Elsevier, Amsterdam. {% Discovering new particle in physics requires p-value of 1/(3.5 106). Reason is that apparently H0 and H1 were not specified well a priori. This is called the problem of multiple comparisons, or, in popular press, the look-elsewhere effect. %} Dijkgraaf, Robert (2015) Column in NRC, December 19, 2015. {% intuitive versus analytical decisions; In simple situations, conscious deliberation gives best decisions. In complex situations, unconscious thought does better. Abstract l. 2 writes that the authors use recent insights into …, so as to suggest novelty. The novelty viz-a-viz many preceding studies into analytic versus intuitive decision making seems to be that these authors put forward some explanation about unconscious, but this is speculation and other explanations as in Wilson & Schooler (1991) work as well. P. 1005 middle column write: “the idea that conscious deliberation is the ideal (if not always attainable) way to approach a decision forms the backbone of classic (4, 5) as well as contemporary perspectives on decision making (6,7) …” I disagree. Also decision theorists including me and many others know that in most decision situations decision theory has absolutely no help to offer. Only if very particular conditions are met (such as completeness of preferences over a rather rich set of prospects), it can be of some use. During my work in health this happened for 1 out of 1000 diseases. (Many decision theorists, unfortunately, oversell their theories by making the mistake, common in any science, to pretend that they cover everything in life.) One of the many problems for the studies is that the evaluation of what is the best option is weak in each study. In the car studies (studies 1 and 2) the criterion taken is that the car is to be best that is best on MOST attributes (described as “normative” on p. 1006 middle column). But very obviously, different individuals weigh the attributes differently. (P. 1006 2nd column end of 1st para qualifies this as normative.) Maybe the unconscious subjects just went by majority-attribute rule as a heuristic. Maybe in study 2 they just reported bigger evaluation differences because of lack of nuance. In studies 3 and 4, the outcomes of deliberate choice need not be worse, but instead there may be an error in the evaluation of the outcomes of nondeliberate choice being that people here haven’t thought enough about the drawbacks of their choice so that their evaluation as given is too optimistic, and there then is more space for instance for cognitive dissonance. Also, people may think more, or less (which may depend on complexity) BECAUSE they like it less. There are too many interactions between selection criterion and dependent variable of how much they like it. Wilson & Schooler (1991) in a thorough study on the same topic, write (p. 182 2nd column penultimate para): “evaluating a stimulus on several different dimensions causes people to moderate their evaluations.” They claim, p. 1005 top of 3rd column, that scientists have investigated the pros of unconscious decisions “infrequently” and that they are going to show the opposite, suggesting novelty on this point. But there have been dozens of solid studies doing and showing it before, as the key word intuitive versus analytical decisions in this bibliography shows. To not only claim this novelty for the superficial readers, but also defend against closer readers that they do not claim this novelty and that they do credit predecessors, the next para lists a number of predecessors. P. 1005 3rd column middle writes “Two reasons why conscious deliberation sometimes leads to poor decisions have been identified” but there are many similar biases. P. 1006 claims: “Unconscious thought does not suffer from low capacity,” citing a paper by one of the authors for this unqualified claim. P. 1007 2nd column 3rd para is typical of psychology: for each study alone one can raise doubts, but the studies together are so many that they support the general hypothesis. The last para suggests, optimistically and based on a “there is no reason that not” argument, that the findings of this study, studied only for consumers, will not hold for politicians, managers, and, may I add, why not for all of mankind? Nieuwenstein et al. (2015) does a meta-analysis on the Deliberation-without-Attention Effect with a negative conclusion. %} Dijksterhuis, Ap, Maarten W. Bos, Loran F. Nordgren, & Rick B. van Baaren (2006) “On Making the Right Choice: The Deliberation-without-Attention Effect,” Science 311, February 17 2006, 1005–1007. {% proper scoring rules; Paper discusses scoring rules that have the special purpose of best fitting only in a particular region, relating it to conditioning and censoring, and deriving properness results. P. 217 1st column: under proper scoring rules, it may be better to deliberately not take the best statistical model if it incorporates as yet unknown parameters and those are easier to guess approximately from a wrong model. P. 218: the authors like logarithmic scoring rules because those have nice properties, close to likelihood ratios. %} Diks, Cees, Valentyn Panchenko, & Dick van Dijk (2011) “Likelihood-Based Scoring Rules for Comparing Density Forecasts in Tails,” Journal of Econometrics 163, 215–230. {% Considers recursive expected utility. Considers preference for one-shot resolution of uncertainty (PORU) versus gradual, and other things. So not preference for early or late, but, as written. All kinds of conditions are then equivalent to all kinds of static preference conditions. Proposition 1 shows that the certainty effect (NCI, negative certainty independence; p. 1980) is equivalent to PORU. PORU is also equivalent to preference for perfect info (Proposition 2, p. 1984). NCI and rank dependence imply EU (Proposition 3, p. 1986). Also smoothness can imply EU (Proposition 5, p. 1989). %} Dillenberger, David (2010) “Preferences for One-Shot Resolution of Uncertainty and Allais-Type Behavior,” Econometrica 78, 1973–2004. {% A well known characterization of EU for risk with continuous utility function, that has to be bounded, can through isomorfisms be used in other structures. Pity for me that this paper does not cite Spinu & Wakker (2013, JME) in the same journal. The literature discussion in §5 is misleading. The penultimate para on p. 146 says that Fishburn (1975) “must necessarily be silent about the continuity of the vN-M utility u.” However, approaches of Fishburn (1975) and Wakker (1993) need not commit to continuity and have it optional. They can very easily get it by adding a continuity axiom. The last para writes that “the above works [including Fishburn 1975] implicitly recover a growth condition on the utility function” but I do not understand this. They suggest it is growth function as in their approach but then write “growth condition” and keep it vague. %} Dillenberger, David & R. Vijay Krishna (2014) “Expected Utility without Bounds—A Simple Proof,” Journal of Mathematical Economics 52, 143–147. {% %} Dillenberger, David, Andrew Postlewaite, & Kareen Rozen (2012) “Optimism and Pessimism with Expected Utility,” {% Risk aversion depends on whether preceding resolutions of risk were favorable or unfavorable, where unfavorable outcomes enhance risk aversion. This is different than Köszegi & Rabin (2006), where only future expectations matter. It entails a violation of consequentialism (forgone-event independence) because counterfactual events, what could have happened but did not happen, matters. %} Dillenberger, David & Kareen Rozen (2015) “History-Dependent Risk Attitude,” Journal of Economic Theory 157, 445–477. {% Consider two-outcome prospects, where there is a 2nd order distribution over the probability of getting the best outcome. A noise decision model is proposed. The last section of the paper points out that the model can accommodate ambiguity seeking for small likelihood gains. %} Dillenberger, David & Uzi Segal (2017) “Skewed Noise,” Journal of Economic Theory 169, 344–364. {% %} Dimitri, Nicola (1995) “On the Notion of Independence between Events with Non-Additive Probabilities.” {% dynamic consistency %} Dimitri, Nicola (2009) “Dynamic Consistency in Extensive Form Decision Problems,” Theory and Decision 66, 345–354. {% %} Dimmock, Stephen G. & Roy Kouwenberg (2010) “Loss-Aversion and Household Portfolio Choice,” Journal of Empirical Finance 17, 441–459. {% After their paper in the Journal of Financial Economics, this is the second follow-up paper after Dimmock, Kouwenberg, & Wakker (2016 MS; DKW). This one is richer, using the same data set as the first follow-up paper, with same points of why not controled for suspicion and so on. But now it also uses the likely (p = 0.9) and unlikely (p = 0.1) urns. Further, for the fifty-fifty urns it also does hypothetical loss. The ambiguity aversion in these four questions will all be positively correlated. The authors explain (p. 222 footnote 3), and I agree, that hypothetical is better than paying from prior endowment. (losses from prior endowment mechanism) ambiguity seeking for losses: they find it (p. 228 last sentence). ambiguity seeking for unlikely: they find it. reflection at individual level for ambiguity: ambiguity aversion for gains and losses is positively related (p. 229 penultimate sentence of first para) The authors use the -maxmin model to analyze things. They take an -contaminated set of priors. For the stimuli considered, with only two-outcome prospects, and with EU for risk, it is equivalent to the source method of Dimmock, Kouwenberg, & Wakker (2016 MS; DKW) with a neo-additive source function, as shown by Chateauneuf, Eichberger, & Grant (2007), and as pointed out by the authors. But a restriction is that their model assumes EU for risk whereas DKW do not need that restriction. The authors propose an index that they interpret as perceived ambiguity, and then the index of ambiguity aversion. As they point out in their footnote 20 (p. 231), their indexes , are transformations of the a-insensitivity index a and the ambiguity aversion index b of DKW. More precisely, their perception index is identical to the insensitivity index a and for their aversion index we have = (b/ + 1)/2. The linear rescaling b/ (b/ + 1)/2 is immaterial. But the division of b by means that their index gives ambiguity aversion per unit of perceived ambiguity , whereas b of DKW is an index of absolute ambiguity aversion. Which is more convenient depends on context. The important thing is that the two pairs of indexes are equivalent. This relation between the two index pairs was first pointed out by Baillon, Aurélien, Han Bleichrodt, Umut Keskin, Olivier L’Haridon, & Chen Li (2015) “Learning under Ambiguity: An Experiment Using Initial Public Offerings on a Stock Market,” working paper; first version August 2013, end of §2 there). As regards their findings, in the neo-additive terminology of Chateauneuf et al., their (ambiguity aversion) is 0.56 and their (confidence in probability, = 1a-insensitivity) = 0.60 (p. 221 l. -5). They test a number of less interesting sets of priors but those all perform poorly. P. 241 2nd para: ambiguity aversion is positively related to being male, old, and, strangely enough, college-educated. P. 241 3rd para: confirms the Fox-Tversky finding that ambiguity aversion is higher if the ambiguous option is presented after the risky one, than when before. Ambiguity aversion is positively related to being male, old, and, P. 241 4th para: a-insensitivity (or level of perceived ambiguity) is positively related to being male, white, and, again strangely enough, college-educated (vs. high school), going against some cognitive hypotheses. (cognitive ability related to risk/ambiguity aversion) correlation risk & ambiguity attitude: positive but weak (p. 222 2nd para), both for gains and losses. Correlation risk aversion and a-insensitivity: not significant (p. 222 2nd para). P. 241 last para of §4 repeats it, saying that it is plausible if perceived ambiguity is formed independently from risk preferences. Pp. 239-240: the authors make the assumption that perceived ambiguity is the same for gains and losses, which is plausible if this is cognitive. They assume that a-insensitivity is the same for gains and losses, citing Baillon & Bleichrodt (2015) for it. It is plausible because a-insensitivity is cognitive. Ambiguity aversion is stronger for subjects who first get the risk aversion question, confirming the contrast effect of Fox & Tversky (1995). P. 242 argues against universal ambiguity aversion. reflection at individual level for ambiguity: seems that AA0.5 and AA0.5 are positively correlated (0.25), going against reflection at the individual level. %} Dimmock, Stephen G., Roy Kouwenberg, Olivia S. Mitchell, & Kim Peijnenburg (2015) “Estimating Ambiguity Preferences and Perceptions in Multiple Prior Models: Evidence from the Field,” Journal of Risk and Uncertainty 51, 219–244. {% Data set: publicly available from the RAND American Life Panel (ALP) website, as survey number 243: https://alpdata.rand.org/ The authors were so kind to provide me with their questionnaire. Abstract: “In this paper we test the relation between ambiguity aversion and five household portfolio choice puzzles: nonparticipation in equities, low allocations to equity, home-bias, own-company stock ownership, and portfolio under-diversification. In a representative US household survey, we measure ambiguity preferences using custom-designed questions based on Ellsberg urns. As theory predicts, ambiguity aversion is negatively associated with stock market participation, the fraction of financial assets in stocks, and foreign stock ownership, but it is positively related to own-company stock ownership. Conditional on stock ownership, ambiguity aversion is related to portfolio under-diversification, and during the financial crisis, ambiguity-averse respondents were more likely to sell stocks.” correlation risk & ambiguity attitude: find positive relation. suspicion under ambiguity: in the end of §2, p. 563, the authors carefully explain, with good arguments, that they deliberately do not control for suspicion. This paper is a follow-up on Dimmock, Kouwenberg, & Wakker (2016 MS; DKW hereafter). DKW used some 1935 subjects from the Dutch population of which only half were incentivized (paying €7650 in total). This study has 3258 subjects from the US that are all incentivized, paying $23,850 real incentives (!; p. 560 3rd para), and measuring way more of their financial decisions. It focuses on ambiguity aversion and uses only the fifty-fifty likelihoods, with the standard known and unknown Ellsberg urns. DKW did not find significant relations between ambiguity aversion and financial decisions (but did for a-insensitivity), and gave as a possible explanation that their standard measurement had only considered gains, whereas for financial decisions also (ambiguity attitude for) losses is relevant. This study does find significant relations between ambiguity aversion and financial decisions, possibly because of more subjects. Because it has rich financial data, it finds many relations, a.o. with home bias, showing that ambiguity aversion is important for finance. Ambiguity aversion is negatively related to stock market participation, fraction of financial assets in stocks, foreign stock ownership. It is positively related to homebias, own-company stock ownership, portfolio-underdiversification, and selling stocks during financial crisis. Also to being male, college educated (vs. high school), and young. They confirm many common things, with 52% ambiguity averse, 10% neutral, and 38% seeking. The intro, p. 561 2nd column 3rd para, misleadingly writes that DKW would use a theory, the source method, which would differ from models used in the finance literature. However, the theory used in the present paper is identical to that in DKW, and is just an equivalent rewriting (details below). The authors further write that, hence, DKW’s predictions do not align with the theoretical predictions in the literature. However, this paper rejects H0 and DKW do not reject H0, but this may be just because DKW have less power. The findings of these two papers are not inconsistent. Thinking they are is misinterpretation 17 of Greenland et al. (2016). Details on identity of models used: the model used by DKW (biseparable utility) is, for the stimuli considered (gambles with no more than two outcomes), equivalent to the maxmin model that this paper uses. Because this paper satisfies the axioms of Chew & Sagi (2006, 2008) as can be seen, it is in fact a special case of the source method used by DKW (having within-source probabilistic sophistication), and therefore is not different after all. The ambiguity aversion index used in this paper is equivalent to the one used by DKW. Further, the ambiguity perception index used in the JRU follow-up paper by these authors is equivalent to the a-insensitivity index used by DKW, as the authors point out there in their footnote 20 there. These relations between the two index pairs were first pointed out by Baillon, Aurélien, Han Bleichrodt, Umut Keskin, Olivier L’Haridon, & Chen Li (first version 2013) “Learning under Ambiguity: An Experiment Using Initial Public Offerings on a Stock Market,” working paper. Hence the decision theory and index in this paper are not different than DKW, but are identical. This paper finds a significant relation between ambiguity aversion and financial decisions whereas DKW found H0 there, i.e., no significance (but DKW found that their other index of ambiguity attitude, a-insensitivity, was significantly related, so they also found a relation between ambiguity attitude and financial decisions). This can just be a matter of power (this paper had many more subjects) and the results of these wo papers are not inconsistent. Hence the suggestion that DKW would, unlike this paper, not align with predictions in the literature is misleading. cognitive ability related to risk/ambiguity aversion: This paper relates cognitive ability with ambiguity aversion but finds no relation. It does, surprisingly, find higher ambiguity aversion among higher educated than lower educated. §2 nicely explains in words that matching probabilities are so nice to measure ambiguity attitudes because everything of risk attitude drops. %} Dimmock, Stephen G., Roy Kouwenberg, Olivia S. Mitchell, & Kim Peijnenburg (2016) “Ambiguity Aversion and Household Portfolio Choice Puzzles: Empirical Evidence,” Journal of Financial Economics 119, 559–577. {% DOI http://pubsonline.informs.org/doi//pdf/10.1287/mnsc.2015.2198 correlation risk & ambiguity attitude: risk aversion is negatively related to ambiguity aversion and a-insensitivity %} Dimmock, Stephen G., Roy Kouwenberg, & Peter P. Wakker (2016) “Ambiguity Attitudes in a Large Representative Sample,” Management Science 62, 1363–1380. Link to paper
Ding, Min (2007) “An Incentive-Aligned Mechanism for Conjoint Analysis,” Journal of Marketing Research 44, 214-223. {% Z&Z %} Dionne, Georges & Scott E. Harrington (1992, eds.) “Foundations of Insurance Economics: Readings in Economics and Finance.” Kluwer, Dordrecht. {% Z&Z; two-period insurance where there can be renegotiation or precommitment; the efficiencies and inefficiencies of that %} Dionne, Georges & Neil A. Doherty (1994) “Adverse Selection, Commitment, and Renegotiation: Extension to and Evidence from Insurance Markets,” Journal of Political Economy 102, 209–235. {% Z&Z %} Dionne, Georges & Christian Gouriéroux, & Charles Vanasse (2001) “Testing for Evidence of Adverse Selection in the Automobile Insurance Market: A Comment,” Journal of Political Economy 109, 444–453. {% Assume EU with differentiable utility. Assume you face a small risk that, however, is correlated with a big background risk. Then the small risk itself can have big implications as a signal of what the background risk is. So in this sense it can give first-order risk aversion. I guess that this underlies the result of this paper. Section 6 considers RDU but, unfortunately, does bottom-up integration rather than top-down as is nowadays common. P. 4517 1st para: they equate risk aversion with concave (so convex if top-down integration) probability weighting, which deviates from usual definitions of preference for EV over prospect although, if I could change the world and history the way I wanted, the term risk aversion would not involve any utility and would be this. %} Dionne, Georges & Jingyuan Li (2014) “When Can Expected Utility Handle First-Order Risk Aversion?,” Journal of Economic Theory 154, 403–422. {% probability elicitation; with feedback etc. children are taught to express probabilities through scoring rules. %} Dirkzwager, Arie (1996) “Testing with Personal Probabilities: 11-Year-Olds Can Correctly Estimate Their Personal Probabilities,” Educational and Psychological Measurement 56, 957–971. {% probability elicitation: using de Finetti scoring rules etc. as alternative to multiple choice. %} Dirkzwager, Arie (2000) “A Bayesian Testing Paradigm: Multiple Evaluation, a Feasible Alternative for Multiple Choice,” University of Twente. {% %} Dirkzwager, Arie (2001) “Consensus Measurement in Multi-Participant Conversations,” Kybernetes 30, 573–588. {% Shows that adding loss aversion can better explain observed contracts of 595 CEOs in a principal-agent model than if it is done using only utility curvature. It can also explain an observed convexity of the shape of optimal contracts. %} Dittmann, Ingolf, Ernst Maug, & Oliver Spalt (2010) “Sticks or Carrots? Optimal CEO Compensation when Managers are Loss Averse,” Journal of Finance 65, 2015–2050. {% Loss aversion explains bidding behavior, and is also relevant for non-rare events. %} Dittrich, Dennis A. Werner Güth, Martin G. Kocher, & Paul Pezanis-Christou (2012) “Loss Aversion and Learning to Bid,” Economica 79, 226–257. {% ISBN 0-393-31035-3 %} Dixit, Avinash K. & Barry J. Nalebuff (1993) “Thinking Strategically.” Norton, New York. {% %} Dixit, Avinash K. & Jörgen W. Weibull (2007) “Political Polarization,” Proceedings of the National Academy of Sciences 104, 7351–7356. {% bisection > matching: Seems that they introduced bisection, called the staircase method, in psychophysics, shortly after von Békésy (1947), so as to avoid biases in top-bottom or -bottom-up methods such as choice lists. The latter methods are called limiting methods, and were already used by Fechner (1860). %} Dixon, W. J., & A.M. Mood (1948) “A Method for Obtaining and Analyzing Sensitivity Data,” Journal of the American Statistical Association 43, 109–126. {% biseparable utility violated; event/utility driven ambiguity model: utility-driven §III describes an experiment for the three-color Ellsberg urn. For gains the great majority of participants is ambiguity averse, for losses about as many are ambiguity seeking as averse. So, mixed evidence on ambiguity seeking for losses. second-order probabilities to model ambiguity: models ambiguity through subjective second-order probabilities with recursive expected utility. This is very similar to the recursive (smooth) ambiguity model of KMM. But it is different. It is as follows: imagine an act a that can give n outcomes x1,…,xn. There is a random variable = (1,…,n) reflecting a subjective first-order probability distribution over the n outcomes generated by act a. itself is a random variable, reflecting subjective uncertainty about the first-order probabilities. (p1,…,pn) is the first-order distribution that results by averaging out the s. The author denotes by the expected utility of a w.r.t. (p1,…,pn) but I think that it plays no particular role here. Anyway, after an outcome xj results, the decision maker can update the second-order distribution of the s using Bayes formula. He can recalculate the updated (p1,…,pn)j here. He can then calculate the updated EU of act a under the updated (p1,…,pn)j, which we write as EUj(a). Now he uses a utility-transformation , much like of KMM, and evaluates a by j=1;n pj(EUj(a)). If is the identity then we just get , concave gives something smaller (ambiguity aversion), and convex gives something bigger. One may wonder why a decision maker, after receiving xj, would bother to re-evaluate the whole act a. The author argues for an ex-ante regret-like psychology. He also argues that this is just a way to capture ambiguity using tools similar to usual EU studies of risk, and that it does not need to resort to nonadditive or transformed probabilities (p. 435 2nd para and before). This he also shares with the smooth model. The author puts reflection central, with ambiguity seeking for losses, which he can model by being convex for losses. This is indeed where he beats non-reference dependent nonadditive models. The smooth model can also handle sign-dependence this way. P. 424 penultimate para: his functional generates overweighting of unlikely events/outcomes (for the RDU workers: unlikely is not the same as extreme). P. 420 2nd para writes that getting 2nd-order probabilities will be harder than getting 1st order ones, an argument also advanced by Lindley (1996). Dobbs counters that much knowledge of the 2nd order distribution is not needed for his analysis, only some general characteristics. (p. 421 top: all we need are mean values and a covariance matrix of 2nd order probabilities). Nicely, the model is tested with an experiment on Ellsberg 3-color, both with gains and losses within subjects. Subjects can choose neutral if they like. Hence there are 34 = 81 choice patterns. 5 of those fit with the author’s theory (neutral, and the four combinations of amb. av. or seeking for gains and losses; the author only allows neutral for both gains and losses, apparently). reflection at individual level for ambiguity: the data in Table 2, p. 428, give nrs. of observations for the five most interesting choice patterns. Unfortunately, there is almost no ambiguity seeking for gains in these five patters and, hence, we cannot asses reflection at the individual level. Would have been possible if more data on deviating patterns had been provided, but it isn’t. Roughly, of the ambiguity averse people for gains as many are ambiguity averse for losses as ambiguity seeking. P. 430 2nd para points out (admits I would say when it is beyond sign dependence) that in this model ambiguity attitudes depend not only on the probabilities but also on the outcomes. The author’s writing here and in general is mature. %} Dobbs, Ian M. (1991) “A Bayesian Approach to Decision-Making under Ambiguity,” Economica 58, 417–440. {% conservation of influence: self-aware agents must possess self-directed goals. Can virtual animals be considered situated and embodied? %} Dobbyn, Chris & Susan Stuart (2003) “The Self as an Embedded Agent,” Minds and Machines 13, 187–201. {% Two-dimensional tradeoffs where one dimension is waiting time for biosurveillance info and other is value of info. %} Doctor, Jason N., Janet G. Baseman, William B. Lober, Jac Davies, John Kobayashi, Bryant T. Karras, & Sherrilynne Fuller (2008) “Time-Tradeoff Utilities for Identifying and Evaluating a Minimum Data Set for Time-Critical Biosurveillance,” Medical Decision Making 28, 351–358. {% SG higher than others: meta-analysis of rating scale (RS) versus TTO and SG. RS and TTO were not significantly different, but SG was significantly higher if analyzed the usual (EU) way. If analyzed using prospect theory, SG is no longer different than the others. %} Doctor, Jason N., Han Bleichrodt, & Jill H. Lin (2010) “Health Utility Bias: A Meta-Analytic Evaluation,” Medical Decision Making 30, 58–67. {% Characterize person tradeoffs evaluations, using Fishburn’s (1966) marginal independence and an additivity condition about adding unaffected people. Give a rank-dependent extension. Test some conditions and they do not fare very well. Find that probability 0.5 is some underweighted. %} Doctor, Jason N., John Miyamoto, & Han Bleichrodt (2009) “When Are Person Tradeoffs Valid?,” Journal of Health Economics 28, 1018–1027. {% Subjects are risk averse w.r.t. life duration in impaired health states, suggesting concave utility under nonexpected utility. However, the risk aversion can also be explained by probability transformation, after which the null hypothesis of linear utility for life duration is no longer rejected. This is confirmed in an experiment where invariance w.r.t. unit and level of outcomes (which characterizes linear utility) is tested. %} Doctor, Jason N., Han Bleichrodt, John M. Miyamoto, Nancy R. Temkin, & Sureyya Dikmen (2004) “A New and More Robust Test of QALYs,” Journal of Health Econonomics 23, 353–367. {% Shows that constant proportional tradeoffs can simplify other aspects of axiomatizations. %} Doctor, Jason N. & John M. Miyamoto (2003) “Deriving Quality-Adjusted Life Years (QALYs) from Constant Proportional Time Tradeoff and Risk Posture Conditions,” Journal of Mathematical Psychology 47, 557–567. {% foundations of probability: Joyce (2005) has argued that our beliefs should be modeled by sets of probability measures (advocates of multiple prior models in decision theory will like this), being all that are compatible with the info we have. Roger Wite provided a counterargument. This paper provides a counter-counter argument. %} Dodd, Dylan (2013) “Roger White’s Argument against Imprecise Credences,” British Journal for the Philosophy of Science 64, 66–77. {% They have data from a long continuous period from Germany and the Nehterlands, where risk aversion is measured each year, not from revealed preferences but from introspective questions. They study how risk aversion depends on age. The big challenge is of course how to correct for other factors related to historical events. The main contribution of the paper is handling this. They find that people’s risk aversion increases linearly with age until age 65, after which it becomes flatter. %} Dohmen, Thomas, Armin Falk, Bart H.H. Golsteyn, David Huffman, & Uwe Sunde (2017) “Risk Attitudes across the Life Course,” Economic Journal 127, F95–F116. {% cognitive ability related to risk/ambiguity aversion %} Dohmen, Thomas, Armin Falk, David Huffman, & Uwe Sunde (2010) “Are Risk Aversion and Impatience Related to Cognitive Ability?,” American Economic Review 100, 1238–1260. {% Use a 2004 representative sample in Germany. Risk and trust attitudes are measured using purely introspective questions of the type: “How much do you like to take risks.” Find that risk attitudes of children are associated with those of their parents. %} Dohmen, Thomas, Armin Falk, David Huffman, & Uwe Sunde (2012) “The Intergenerational Transmission of Risk and Trust Attitudes,” Review of Economic Studies 79, 645–677. {% Impressive sample of 22,019 (from 11,803 families) in the 2004 wave of the Socio-economic panel (SOEP), representative of the German population (later the paper restricts this to adult Germans). In addition, 450 people, representative for the 22,019, are visited at their home and interviewed. Asked to the 22,000 people and also the 450 people, on 11-point scale (0-10), to indicate how much they were willing to take risk, (0) in general (1); car driving; (2) financial matters; (3) sports and leisure; (4) career; (5) health. Then they ask other questions about risky behavior from such domains, such as about smoking etc. From the 450 people they also revealed an indifference of the prospect 3000.50 by measuring the switching value for increasing sequence of sure amounts, with random incentive system paying one of every seven subjects (p. 532: doing a 1/7 chance for every subject, rather than select one from every seven; as so often, subjects could not verify this randomization. This is why I prefer selecting in class rooms one of every 7 subjects, visible for all.) (between-random incentive system). That’s an average payment of about €25 per subject. Subjects were not paid cash on the spot, but by check sent by mail. Their CEs (certainty equivalents) ranged from 0 to 190, so did not allow for much risk seeking as the authors explain on p. 532). 87% (= 78%+9%) was risk averse (pp. 533-534) and 13% (4% + 9%) was risk seeking. The correlation between introspective general risk attitude and CE of 3000.50 is about 0.5 (Table 2), correcting for some variables, and is significant (p 0.01). Relate it to demographic variables, where risk aversion is enhanced by being female (gender differences in risk attitudes), being old, having low education and, remarkably, being small. They obtain natural and intuitively plausible results: the willingness-to-take risk question are all positively related to the real-incentive choice (see above, regarding the 450 subjects). The general question best correlates with the whole of the others. Domain-specific question better correlate with questions specific to their domain, e.g. health-risk willingness better correlating with smoking. As the authors point out, the general attitude questions, in contrast to the prospect-choice questions, comprise not only risk attitude, but also risk perception and risk exposure. A person with a good job does not take career risks, not because he is risk averse, but because he has little to gain and much to lose. P. 538, end of 2nd para, when discussing a correlation, precedes it with: “The answer to these questions is of obvious importance from both a methodological and a practical point of view.” Positive relations found are described as “economically significant.” real incentives/hypothetical choice: p. 543 is positive about asking hypothetical questions: “In light of these findings, the usual practice of only eliciting risk attitudes in the context of hypothetical financial lotteries would be expected to have benefits for predicting financial decisions, but be a less effective approach for providing a summary statistic of risk attitudes across other nonfinancial contexts.” P. 523 advanced another argument against real incentives: they are very expensive, and also cumbersome, to implement in large samples such as 22,000 subjects. To those subjects a hypothetical risky choice was asked, not reported but briefly discussed on p. 543, that correlates well with things. %} Dohmen, Thomas, Armin Falk, David Huffman, Uwe Sunde, Jürgen Schupp, & Gert G. Wagner (2011) “Individual Risk Attitudes: Measurement, Determinants, and Behavioral Consequences,” Journal of the European Economic Association 9, 522–550. {% Seems that they define a bi-order between sets and that that is very close to triple cancellation etc. %} Doignon, Jean-Paul, André Ducamp & Jean-Claude Falmagne (1984) “On Realizable Biorders and the Biorder Dimension of a Relation,” Journal of Mathematical Psychology 28, 73–109. {% %} Doignon, Jean-Paul & Jean-Claude Falmagne (1974) “Difference Measurement and Simple Scalability with Restricted Solvability,” Journal of Mathematical Psychology 11, 473–499. {% AHP %} Dolan, James G. (1990) “Can Decision Analysis Adequately Represent Clinical Problems?,” Journal of Clinical Epidemiolog 43, 277–284. {% AHP; uses example of dogbite with risk of rabies to illustrate. %} Dolan, James G., Bernard J. Isselhardt, Joseph D. Cappuccio (1989) “The Analytic Hierarchy Process in Medical Decision Making: A Tutorial,” Medical Decision Making 9, 40–50. {% questionnaire versus choice utility: seems that, for each EQ-5D state, a general population “tarif” value is proposed. Is recommended by the UK’s National Institute for Clinical Excellence for use in cost-utility studies. %} Dolan, Paul (1997) “Modeling Valuations for EuroQol Health States,” Medical Care 11, 1095–1108. {% Indicates that HYE s have theoretical problems but still treat it throughout as if a serious idea. Seems to argue that time separability is the most problematic assumption of the QALY model. risky utility u = strength of preference v (or other riskless cardinal utility, often called value): p. 1735 says that “in general” utility is an index of strength of preference. P. 1732 suggests that for policy decisions utilities should be elicited from the general public; i.e., the unfortunate viewpoint of Gold et al. (1996). P. 1739 says that for intervention for particular group better only that group is asked. intertemporal separability criticized: p. 1743 (quality of life depends on past and future health) SG doesn’t do well: p. 1745; SG higher than TTO: §3.2.3 gives refs. P. 1746 and p. 1748: people who experience health state, value it higher. P. 1747: converting VAS to SG/TTO does not work well. P. 1753-1754 pleas for more intense interviews of fewer subjects. %} Dolan, Paul (2000) “The Measurement of Health-Related Quality of Life for Use in Resource Allocation Decisions in Health Care.” In Antony J. Culyer & Joseph P. Newhouse (eds.) Handbook of Health Economics, 1723–1760, Elsevier, Amsterdam. {% N=1173 internet and telephone survey TTO questions capture relevant aspects of health evaluation not captured by other measurements. %} Dolan, Paul (2011) “Thinking about It: Thoughts about Health and Valuing QALYs,” Health Economics 20, 1407–1416. {% Study spillover effects of policy recommendations. “No behavior sits in a vacuum” the authors write some times. %} Dolan, Paul & Matteo M. Galizzi (2015) “Like Ripples on a Pond: Behavioral Spillovers and Their Implications for Research and Policy,” Journal of Economic Psychology 47, 1–16. {% %} Dolan, Paul & Claire Gudex (1995) “Time Preference, Duration and Health State Valuations,” Health Economics 4, 289–299. {% %} Dolan, Paul, Claire Gudex, Paul Kind, & Alan Williams (1996) “The Time Trade-Off Method: Results from a General Population Study,” Health Economics 5, 141–154. {% P. 1735: SG doesn’t do well. Find, remarkably, that SG gives lower values than TTO. Find that ping-pong and top-down give different results. %} Dolan, Paul, Claire Gudex, Paul Kind, & Alan Williams (1996) “Valuing Health States: A Comparison of Methods,” Journal of Health Economics 15, 209–231. {% A very interesting study, nicely investigating central topics of prospect theory about source preference and source sensitivity. Both the ambiguity that is objective in the terminology of this paper, and that is subjective, combines objective (lack of) info about choice stimuli with preference conditions. What they call objective is comparing probability intervals with their midpoints (the latter as known, objective), what they call subjective is source preference (each part of a partition dominates its counterpart). Fig 1, p. 285, is winv(W), so it is the belief index of my ’04 Psych. Rev. paper. P. 286 mentions that the “subjective” approach of this paper cannot elicit source sensitivity (“venture-theory relationship” in the terminology of this paper). In my Psych. Rev. paper it is shown how it can be done. P. 287: unfortunately, in the ambiguous choice subjects cannot choose the color for which they win, so that they have extra reason to be suspicious (suspicion under ambiguity) and the data will have extra ambiguity aversion. P. 288, subjects get vague info about experimenter choosing proportions “arbitrarily.” P. 290, adding complementary values (for 5% and 95%, etc.) leads to a test of source preference and not of source sensitivity. ambiguity seeking for unlikely: p. 293: ambiguity aversion for moderate and high likelihood, ambiguity neutrality for low likelihood (5% and 10%). For the comparative ignorance hypothesis, they do not find it, with not more prudence in comparative situation than in noncomparative. All ambiguous high likelihoods had the explicit possibility that the unknown probability was 1, increasing attractiveness, and going against ambiguity aversion and subadditivity. All ambiguous low likelihoods had the explicit possibility that the unknown propbability was zero, decreasing attractiveness, and reinforcing ambiguity aversion but going against subadditivity. %} Dolan, Paul & Martin Jones (2004) “Explaining Attitudes towards Ambiguity: An Experimental Test of the Comparative Ignorance Hypothesis,” Scottish Journal of Political Economy 51, 281–301. {% %} Dolan, Paul & Michael W. Jones-Lee (1997) “The Time Trade-off: A Note on the Effect of Lifetime Reallocation of Consumption and Discounting,” Journal of Health Economics 16, 731–739. {% Plead for experienced against decision utility for health measurements in an unqualified manner; P. 215 l. -1 writes that economists use hypothetical choice to elicit utility! Gold et al. (1996) argued that QALYs should be measured from the general public and not from patients, and I disagree with their arguments. The approach of this paper goes in the opposite direction, as the authors point out (p. 230 3rd para). Paper does not very consciously distinguish between intertemporal tradeoffs, risky tradeoffs, and so on. The hedonimeter of Edgworth (p. 215 1st para) and the adaptation (§1 opening para) concern merely intertemporal aggregation. When discussing rationality on p. 215 2nd para the authors suddenly switch to risky tradeoffs, consider the assumption of expected utility as rational (without committing to it), which merely concerns risky tradeoffs. As an aside, Tversky considered expected utility to be rational and so did the early papers by Kahneman & Tversky, but in several later papers Kahneman argued that deviations are rational. P. 217 3rd para, in the context of general utility, suddenly turns to only intertemporal aggregation through the reference to streams in “the fundamental problem with such utilities, which is that they do not accurately represent the utility streams associated with different health states.” P. 227 last line again connects to EU and risky tradeoffs, probably because they connect to rationality. QALY overestimated when ill: p. 218 cites studies for and against it through adaptation. P. 223 top gives further references, arguing that most find that ill overestimate. intertemporal separability criticized: p. 228 l. 2-3. %} Dolan, Paul & Daniel Kahneman (2008) “Interpretations of Utility and Their Implications for the Valuation of Health,” Economic Journal 118, 215–234. {% %} Dolan, Paul & Paul Kind (1996) “Inconsistency and Health State Valuations,” Social Science and Medicine 42, 609–615. {% questionnaire versus choice utility: relate the two empirically. P. 578 writes, and references, for one thing that QALY measurements from the general public are preferred to those from people who are in the health state: “In the United Kingdom, the National Institute for Health and Clinical Excellence (NICE) recommends that “the value of changes in patients’ health related quality of life should be based on public preferences using a choice-based method . . . [and] the EQ-5D is the preferred measure of HRQL in adults.” %} Dolan, Paul & Robert Metcalfe (2012) “Valuing Health: A Brief Report on Subjective Well-Being versus Preferences,” Medical Decision Making 32, 578–582. {% If an unequal division of health is taken as status quo, then loss aversion may work opposite to equity preference. They find this empirically. %} Dolan, Paul & Angela Robinson (2001) “The Measurement of Preferences over the Distribution of Benefits: The Importance of the Reference Point,” European Economic Review 45, 1697–1709. {% %} Dolan, Paul & Peep Stalmeier (2003) “The Validity of Time Trade-Off Values in Calculating QALYs: Constant Proportional Time Trade-Off versus the Proportional Heuristic,” Journal of Health Economics 22, 445–458. {% An extremely useful job that should have been done long before, so good that these authors did it. As usual in meta-analyses, many “dirty” decisions have to be taken. For TTO they found that usually patient-preferences (preference is often used in the meaning of utility in this field, and I will do so too) are lower, not higher as commonly thought, than population (hypothetical) preferences. For VAS and EQ-5D is was the other way around. I did not read enough to know how they did a statistical analysis, and if they took every study as just one observation or did something different. %} Dolders, Maria G.T., Maurice P.A. Zeegers, Wim Groot, & André Ament (2006) “A Meta-Analysis Demonstrates No Significant Differences between Patient and Population Preferences,” Journal of Clinical Epidemiology 59, 653–664. {% %} Dolmas, Jim (1995) “Time-Additive Representations of Preferences when Consumption Grows without Bound,” Economics Letters 47, 317–325. {% %} Domar, Evsey D. & Richard A. Musgrave (1944) “Proportional Income Taxation and Risk-Taking,” Quarterly Journal of Economics 58, 388–422. {% Coefficients of relative risk aversion well over 100, for instance, it is 2 = 656 in Table 1.B and 2 = 165 in Table 3.B. %} Dominguez, Kathryn M. & Jeffrey A. Frankel (1993) “Does Foreign-Exchange Intervention Matter? The Portfolio Effect,” American Economic Review 83, 1356–1369. {% In reaction to Lo (1991), shows that iterated Choquet integrals (recursive CEU that should be CEU again) can exist if and only the partitions involved to not affect each others decision weights. %} Dominiak, Adam (2012) “Iterated Choquet Expectations,” working paper. {% Implement traditional Ellsberg both as a game against an opponent, instead of nature, with common interests (coordination game) and with opposite (zero-sum game) interests. In the former case of common interests people are less ambiguity averse, and traditional ambiguity aversion is like the opposite interest game. %} Dominiak, Adam & Peter Duersch (2015) “Benevolent and Malevolent Ellsberg Games,” working paper. {% updating; dynamic consistency: this paper defines the subtle concepts of dynamic consistency and consequentialism for uncertainty correctly. It assumes collapse independence throughout; see p. 626 footnote 1. It studies various updatings in ambiguity, for Ellsberg 3-color. Unfortunately, they do not use Ellsberg’s colors, but different ones. The subjects rather dropped dynamic consincy empirically than forgone event independence (Result 1, p. 630). They confirm and extend findings of Cohen et al. (2000). %} Dominiak, Adam, Peter Duersch, & Jean-Philippe Lefort (2012) “A Dynamic Ellsberg Urn Experiment,” Games and Economic Behavior 75, 625–638. {% Study agreeable trade and bet for uncertainty and rank dependence, where they allow nonconvex weighting functions, including neo-additive. %} Dominiak, Adam, Jürgen Eichberger, & Jean-Philippe Lefort (2012) “Agreeable Trade with Optimism and Pessimism,” Mathematical Social Sciences 64, 119–126. {% dynamic consistency; updating; defines consequentialism, DC (dynamic consistency), with conditioning on events, and derives that they imply the sure-thing principle, but has no explicit event-invariance (RCLA). It is not yet clear to me how these concepts are related to Machina (1989). It considers various updatings under RDU (CEU). It takes a fixed filtration (finer and finer partitions, more and more info) and shows that dynamic principles imply that last-stage events have EU maximization. Uses Nehring-definition of unambiguous meaning that decision weight is independent of rank. %} Dominiak, Adam & Jean-Philippe Lefort (2011) “Unambiguous Events and Dynamic Choquet Preferences,” Economic Theory 46, 401–425. {% Extend Aumann’s agreement theorem to neo-additive weighting functions. This involves using an updating rule. (updating) %} Dominiak, Adam & Jean-Philippe Lefort (2013) “Agreement Theorem for Neo-Additive Beliefs,” Economic Theory 52, 1–13. {% Uncertainty aversion in Anscombe-Aumann setting suggests preference for randomization. They test both usual Ellsberg ambiguity aversion and preference for randomization (as per Schmeidler’s uncertainty aversion) in an Anscombe-Aumann setting. Most subjects are neutral towards randomization, even slightly more are averse to it, and preference for randomization is unrelated to Ellsberg ambiguity aversion. So, this is bad news for the Anscombe-Aumann approach! %} Dominiak, Adam & Wendelin Schnedler (2011) “Attitudes toward Uncertainty and Randomization: An Experimental Study,” Economic Theory 48, 289–312. {% %} Domotor, Zoltan (1978) “Axiomatization of Jeffrey Utilities,” Synthese 39, 165–210. {% Harsanyi’s aggregation: %} Domotor, Zoltan (1979) “Ordered Sum and Tensor Product of Linear Utility Structures,” Theory and Decision 11, 375–399. {% %} Donaldson, David & John A. Weymark (1980) “A Single-Parameter Generalization of the Gini Indices of Inequality,” Journal of Economic Theory 22, 67–86. {% PT: data on probability weighting; panel-data, many participants, 2593!; inverse-S: find that 56% of their 2593 participants prefer (.01, 6000) to (.02, 3000). No real incentives possible. decreasing ARA/increasing RRA: find decreasing absolute risk aversion, in other words richer people are less risk averse. In general, men (gender differences in risk/ambiguity attitude), young people, rich people, and people with high education are less risk averse. %} Donkers, A.C.D., Bertrand Melenberg, & Arthur H.O. van Soest (2001) “Estimating Risk Attitudes Using Lotteries; A Large Sample Approach,” Journal of Risk and Uncertainty 22, 165–195. {% updating of nonadditive measures, deriving mathematical results. %} Doria, Serena (2012) “Characterization of a Coherent Upper Conditional Prevision as the Choquet Integral with Respect to Its Associated Hausdorff Outer Measure,” Annals of Operations Research 195, 33–48. {% How a modified version of Hintzman’s memory model can account for many biases (availability etc.). The model used thee parameters. %} Dougherty, Michael R.P., Charles F. Getty, & Eve E. Ogden (1999) “MINERVA-DM: A Memory Processes Model for Judgments of Likelihood,” Psychological Review 106, 180–209. {% %} Dougherty, Michael R.P. & Jennifer Hunter (2003) “Hypothesis Generation, Probability Judgment, and Individual Differences in Working Memory Capacity,” Acta Psychologica 113, 263–282. {% inverse-S: seem to show that subadditivity in probability estimates can emerge from limited working memory capacity. %} Dougherty, Michael R.P. & Jennifer Hunter (2003) “Probability Judgment and Subadditivity: The Role of Working Memory Capacity and Constraining Retrieval,” Memory & Cognition 31, 962–982. {% %} Dow, James, Vincente Madrigal, & Sérgio R.C. Werlang (1990) “Preferences, Common Knowledge, and Speculative Trade,” London Business School. {% equilibrium under nonEU?; presence of uncertainty and the agent’s aversion to it. Def. 3.1: they define 1 v(A) v(Ac) as measure of uncertainty aversion. Don’t seem to make intuitive mistakes. %} Dow, James & Sérgio R.C. Werlang (1992) “Uncertainty Aversion, Risk Aversion and the Optimal Choice of Portfolio,” Econometrica 60, 197–204. {% PT, applications: nonadditive measures, excess volatility in security markets %} Dow, James & Sérgio R.C. Werlang (1992) “Excess Volatility of Stock Prices and Knightian Uncertainty,” European Economic Review 36, 631–638. {% %} Dow, James & Sérgio R.C. Werlang (1992) “Learning under Knightian Uncertainty: The Law of Large Numbers for Non-Additive Probabilities,” London School of Business. {% equilibrium under nonEU %} Dow, James & Sérgio R.C. Werlang (1994) “Nash Equilibrium under Knightian Uncertainty: Breaking Down Backward Induction,” Journal of Economic Theory 64, 304–324. {% Shows that voting for sole the purpose of influencing the outcome is not rational given the very small probability that one vote will decide. %} Downs, Anthony (1957) “An Economic Theory of Democracy.” Harper and Row, New York. {% Investigates relations of neurochemical systems to risk taking, discounting, and learning. %} Doya, Kenji (2008) “Modulators of Decision Making,” Nature Neuroscience 11, 410–416. {% Theoretical survey of different discount models. P. 117 end of 2nd para points out that there have been no empirical comparisons of different discount models. Pp. 120/122 is strange. The author favors working with a rate parameter rather than with NPV (net present value) and then starts arguing that NPV is a recent discovery and is non-obvious, citing Rubinstein (2003) who however shows that NPV was continuously used from the very beginning (de Wit 1671). Download 7.23 Mb. Share with your friends:
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