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ambiguity seeking for unlikely
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ambiguity seeking for unlikely: if interpreted as ambiguity study, this paper finds considerable risk seeking for positively-skewed 2nd -order distributions, so it is again evidence against the assumption of universal ambiguity aversion. However, I interpret it differently. First, the 2nd -order probabilities are so explicit and simple that I rather consider this to be a study of RCLA than of ambiguity. Second, I think that the subjects have simply treated the first-order probabilities as outcomes, somewhat as in Selten, Reinhard, Abdolkarim Sadrieh, & Klaus Abbink (1999). Much in this paper enhances such processing, e.g. the manager-is-blamed-for-bad-1st -order-probability-interpretation on p. 136 (did author express such explanations to participants, MBA students who had had decision theory?). The interpretations of the author in many places and in the theoretical model take 1st order probabilities as outcomes. Then the findings of this paper are simply explained as an overweighting of small second-order probabilities. %} Boiney, Lindsley G. (1993) “The Effects of Skewed Probability on Decision Making under Ambiguity,” Organizational Behavior and Human Decision Processes 56, 134–148. {% %} BolaÑos, Manuel J., Maria T. Lamata, & Serafin Moral (1988) “Decision Making Problems in a General Environment,” Fuzzy Sets and Systems 25, 135–144. {% Too much economics for me to understand. %} Boldrin, Michele & Aldo Rustichini (1994) “Growth and Indeterminancy in Dynamic Models with Externalities,” Econometrica 62, 323–342. {% Argue for equal weighting in expert aggregation. %} Bolger, Fergus & Gene Rowe (2015) “The Aggregation of Expert Judgment: Do Good Things Come to Those Who Weight?,” Risk Analysis 35, 5–11. {% R.C. Jeffrey model %} Bolker, Ethan D. (1966) “Functions Resembling Quotients of Measures,” Transactions of the American Mathematical Society 124, 292–312. {% R.C. Jeffrey model %} Bolker, Ethan D. (1967) “A Simultaneous Axiomatization of Utility and Subjective Probability,” Philosophy of Science 34, 333–340. {% between-random incentive system (paying only some subjects): analyzes it theoretically, and tests it, in an ultimatum game. Finds that paying all or doing this incentive system gives the same result, which is good news for the random incentive system. A Sefton (1992) paper will find differences. %} Bolle, Friedel (1990) “High Reward Experiments without High Expenditure for the Experimenter,” Journal of Economic Psychology 11, 157–167. {% %} Bolotin, David (1989) “The Concerns of Odysseus: An Introduction to the Odyssee,” Interpretation 17, 41–57. {% crowding-out: government subsidies seem to crowd-out private donations and charitable contributions. %} Bolton, Gary E. & Elena Katok (1998) “An Experimental Test of the Crowding Hypothesis: The Nature of Beneficient Behavior,” Journal of Economic Behavior and Organization 37, 315–331. {% conservation of influence: on partial influence. People only do partial influence, leaving future influences for crossing that bridge when we come to it (also contingent on state of nature), where such decisions are postponed based on a cost-of-decision calculation. Have results such as Proposition 3 (p. 1218): a reduction of uncertainty reduces the attractiveness of both complete planning and of complete nonplanning, and favors a step-by-step approach. %} Bolton, Patrick & Antoine Faure-Grimaud (2009) “Thinking Ahead: The Decision Problem,” Review of Economic Studies 76, 1205–1238. {% equity-versus-efficiency %} Bolton, Gary E. & Axel Ockenfels (2006) “Inequality Aversion, Efficiency, and Maximin Preferences in Simple Distribution Experiments: Comment,” American Economic Review 96, 1906–1911. {% Groups are more risk averse than individuals because of social responsibility (enhancing caution and blaming for bad outcomes). Conformity has no directional effect because it can as well be conformity with more risk averse as with more risk seeking others. Preference for distributional fairness has no effect either. The authors used the stimuli of Holt & Laury (2002) to measure risk attitude. %} Bolton, Gary E., Axel Ockenfels, & Julia Stauf (2015) “Social Responsibility Promotes Conservative Risk Behavior,” European Economic Review 74, 109–127. {% P. 152: “general aversion to gambling with one’s health, a “gambling aversion” which must be distinguished from the “risk aversion” familiar to student of decision analysis.” Relates SG to TTO %} Bombardier, Claire, A.D. Wolfson, A.J. Sinclair, & A. McGreer (1982) “Comparison of Three Preference Measurement Methodologies in the Evaluation of a Functional Status Index.” In Raisa B. Deber & Gail G. Thompson (eds.) Choices in Health Care: Decision Making and Evaluation of Effectiveness, University of Toronto. {% They observe choices of contestants in an Italian tv show (is is deal or no deal) and find that logarithmic utility fits the data well both for small and large states. NonEU does not improve, and they suggest that they do not find Rabin’s discrepancy. However, their stimuli set may not be well suited to detect violations of EU. Further, logarithmic utility gives extreme risk aversion if the status quo is incorporated and given utility ln(0) = . The biggest problem in this study is that at each stage the authors model the decision not to accept (so, to continue playing) simply as the probability distribution over the remaining sums of money. In reality, continuing is more attractive because later new information will be received and relatively better bank offers will come. Many studies of these shows have shown that the bank offers at the beginning are indeed relatively more unfavorable than later. Hence, the authors take subjects as more risk seeking than they really are, especially at the beginning of the show when the offers still concern relatively low amounts of money. A second problem is that subjects who face low offers have been unlucky so far and will be in a frame of mind of facing losses and wanting to make up (as losing gamblers in a casino do not take their losses but go for ruin), wanting to break even, and increasing their risk seeking (as found by Post et al. 2008). Because of this complication, I disagree with the authors’ discussions of Rabin’s paradox and do not think that they provided counterevidence. Another problem, and this one the authors do signal and analyze, is that the bank offers constitute a complex game. But an extra complication here is that not so much the real bank strategy, but rather the subject’s perception of it, is relevant. %} Bombardini, Matilde & Francesco Trebbi (2012) “Risk Aversion and Expected Utility Theory: An Experiment with Large and Small Stakes,” Journal of the European Economic Association 10, 1348–1399. {% decreasing/increasing impatience: provides theoretical arguments for the possibility of increasing impatience. %} Bommier, Antoine (2006) “Uncertain Lifetime and Intertemporal Choice: Risk Aversion as a Rationale for Time Discounting,” International Economic Review 47, 1223–1246. {% criticism of monotonicity in Anscombe-Aumann (1963) for ambiguity: criticizes separability of single states in Anscombe-Aumann (AA) model. A similar criticism is in Wakker (2010 Section 10.7.3). Considers the AA model, but does not assume EU, or AA monotonicity, and only assumes monotonicity w.r.t. stochastic dominance; replacing, conditional on a horse, a lottery by a stochastically dominating lottery is preferred. Then, in the horse-state contingent model imposes the comonotonic sure-thing principle, giving the Green-Jullien-Chew-Wakker type representation there. Part of the analysis consists of replacing a horse-race contingent act by an equivalent objective lottery that has all cumulative events equivalent, in the spirit of cumulative dominance of Sarin & Wakker (1992). It can be considered to be a generalized version of matching probabilities. %} Bommier, Antoine (2017) “A Dual Approach to Ambiguity Aversion,” Journal of Mathematical Economics 71, 104–118. {% Consider Yaari’s (1969) more risk averse than relation, which refers to certainty equivalents, but also generalizations with richer more-risky-than relations between prospects than only riskless-risky. Their theorems focus on when the distributions cross only once. Characterize more-risk-averse than for various theories, including EU (called Kihlstrom-Mirman) and Quiggin’s rank dependence (RDU). The Epstein-Zin model gives no clear results. In the general definition of RDU they assume general, nonlinear utility (Definition 1, u2 there). But in the sufficiency proofs of Results 2 and 3, where convexity of w (they denote ) is derived, they take utility linear. P. 1617 takes vNM utility as additively separable not if it is a strictly increasing transform of an additively decomposable function, but only if it is that function itself. P. 1616, as do many, cites Kihlstrom & Mirman (1974) on the strange claim that more risk averse comparison is possible only under the prior restriction of same ordering of riskless outcomes. Peters & Wakker (1987) show … see my annotations of the K&M paper. Many results are first presented for fifty-fifty lotteries (§3.2), e.g. regarding w(0.5) in RDU, and next for general lotteries (§3.3). P. 1626 points out that we should acknowledge, rather than ignore by arbitrary choice, the problem that there is no unique definition of more-risk-averse-than, and then choose a definition of single crossing over of distribution functions (“simple spreads”). %} Bommier, Antoine, Arnold Chassagnon, & François Le Grand (2012) “Comparative Risk Aversion: A Formal Approach with Applications to Saving Behavior,” Journal of Economic Theory 147, 1614–1641. {% Consider decisions with both risk and time involved, with infinite horizon. Study recursive preferences that satisfy monotonicity. Here monotonicity means that, given each state of nature, we have a preferred time profile. So, it first integrates over time and only then over uncertainty. They argue that this assumption is nontrivial, and in Footnote 7, p. 1438, points out that monotonicity in Anscombe-Aumann is nontrivial. (criticism of monotonicity in Anscombe-Aumann (1963) for ambiguity) I would favor the term separability for such conditions iso monotonicity. Epstein-Zin preferences are not included. They characterize some functional forms that specify their conditions, where Chew & Epstein 1990 papers are important. P. 1437: Stationarity and the slightly weak history independence are considered. %} Bommier, Antoine, Asen Kochov, & François le Grand (2017) “On Monotone Recursive Preferences,” Econometrica 85, 1433–1466. {% Consider a dynamic setup with time consistency, consequentialism, and the restrictions they impose on inequality comparisons. %} Bommier, Antoine & Stéphane Zuber (2012) “The Pareto Principle of Optimal Inequality,” International Economic Review 53, 593–608. {% %} Bonanno, Giacomo & Klaus D.O. Nehring (1998) “Assessing the Truth Axiom under Incomplete Information,” Mathematical Social Sciences 36, 3–29. {% Law of maturity means that unlikely events will be more likely to occur in the future. Seems like the law of small numbers. Violates exchangeability. The authors reconcile it with a finite version of exchangeability. %} Bonassi, Fernando V., Rafael B. Stern, Cláudia M. Peixoto, & Sergio Wechsler (2015) “Exchangeability and the Law of Maturity,” Theory and Decision 78, 603–615. {% %} Bond, Gary & Bernard Wonder (1980) “Risk Attitudes amongst Australian Farmers,” Australian Journal of Agricultural Economics 24, 16–34. {% %} Bondareva, Olga N. (1963) “Some Applications of Linear Programming Methods to the Theory of Cooperative Games” (in Russian), Problemy Kibernet 10, 119–139. {% %} Bone, John, John Hey, & John Suckling (1999) “Are Groups More (or Less) Consistent than Individuals?,” Journal of Risk and Uncertainty 18, 63–81. {% A nice paradox: a person can choose between UP or DOWN, and then between UP1 or UP2, or between DOWN1 and DOWN2. UP1 stochastically dominates all others, so UP and then UP1 should be it. However, UP2 is extremely unfavorable, and people erroneously seem to take the UP option as something like a 50-50 choice between UP1 and UP2, because of which they prefer to go DOWN. They confuse their influence with randomness (conservation of influence). Nice! The authors interpret this finding as evidence that people do not plan. The conclusion is vague and broad, and I guess that more can be gotten from the paradox. %} Bone, John, John D. Hey, & John Suckling (2009) “Do People Plan?,” Experimental Economics 12, 12–25. {% %} Bonferroni, Carlo Emilio (1924) “La Media Esponenziale in Matematica Finanziaria,” Annuario del Regio Istituto Superiore di Scienze Economiche e Commerciali di Bari AA 23-24, 1–14. {% real incentives/hypothetical choice; Tables 3-4 seem to show that real incentives mostly have no effect on performance. %} Bonner, Sarah E.S., Mark Young, & Reid Hastie (1996) “Financial Incentives and Performance in Laboratory Tasks: The Effects of Task Type and Incentive Scheme Type,” Department of Accounting, University of Southern California, Los Angeles, CA. {% %} Bontempo, Robert N. (1990) “Cultural Differences in Decision Making,” Commentary: Special Issue on Judgement and Decision Making, published by the National University of Singapore. {% %} Boogaards, Erik & Peter P. Wakker (2009) “Doe de Polis-Check (en Bespaar Geld),” Plus Magazine 20 no. 11, 28-29. {% gender differences in risk attitudes: find that women are more risk averse than men. Because this study, unlike most other studies, separates utility curvature, probability weighting, and loss aversion, it can show that it is loss aversion where women are more extreme than men. Tradeoff method %} Booij, Adam.S. & Gijs van de Kuilen (2009) “A Parameter-Free Analysis of the Utility of Money for the General Population under Prospect Theory,” Journal of Economic Psychology 30, 651–666. {% Ask hypothetical WTP questions about payments with both risks and delays to a large sample representative of the working class of the Dutch population. Estimate average relative risk aversion (if no initial wealth assumed) to be 2, and discounting 6% per month. Typical thing of this study is that risk aversion and discounting are estimated jointly. Seem to find negative relation between discounting and risk aversion. %} Booij, Adam S. & Bernard M.S. Van Praag (2009) “A Simultaneous Approach to the Estimation of Risk Aversion and the Subjective Time Discount Rate,” Journal of Economic Behavior and Organization 70, 374–388. {% Tradeoff method; inverse-S: confirm it using the Goldstein & Einhorn and Prelec 2-parameter families. Reanalyze the data of Booij & van de Kuilen (2009) but now use parametric fitting, and add to it that they also estimate probability weighting; confirm all the findings of the earlier paper and find inverse-S. Find loss aversion = 1.58. %} Booij, Adam S., Bernard M.S. Van Praag, & Gijs van de Kuilen (2010) “A Parametric Analysis of Prospect Theory's Functionals,” Theory and Decision 68, 115–148. {% %} Booker, Lashon B., Naveen Hota, & Connie L. Ramsey (1990) “BaRT: A Bayesian Reasoning Tool for Knowledge Based Systems.” In Max Henrion, Ross D. Shachter, Laveen N. Kanal, & John F. Lemmer (eds.) “Uncertainty in Artificial Intelligence 5,” 271–282, North-Holland, Amsterdam. {% Jack Stecher pointed out to me April 2015: Seems to have discussed a coin with unknown probability of landing heads. Argued that it would be incorrect to give p a "definite value" of 1/2. Instead, he thought it should receive an indefinite value of 0/0. %} Boole, George (1854/2003) “The Laws of Thought.” Facsimile of 1854 edn., with an introduction by J. Corcoran. Buffalo: Prometheus Books (2003). (Reviewed by James van Evra (2004) Philosophy in Review 24, 167–169.) {% The following was pointed out to me by Jack Stecher (15Dec2017): For events with no observations the probability is 0/0, i.e., undefined. P. 252: “Hence in the present theory the numerical expression for the probability of an event about which we are totally ignorant is not ½, but c [indeterminate].” Here c is a constant that can be anything between 0 and 1. A footnote on p. 251 cites Bishop Terrot, who seems to have had similar ideas before. Also Keynes (1921) p. 46 seems to cite Boole and Terrot for it. %} Boole, George (1862) “On the Theory of Probabilities,” Philosophical Transactions of the Royal Society of London 152, 225–252. {% Show that SEU in the Anscombe-Aumann framework can be characterized by restricting axioms to a subset of acts, which contains all lottery acts, all act preferences with identity except for one horse. Then authors impose separability only for such acts. %} Borah, Abhinash & Christopher Kops (2016) “The Anscombe–Aumann Representation and the Independence Axiom: A Reconsideration,” Theory and Decision 80, 211–226. {% Seems to argue that sure-thing principle is normative for all who think about it. %} Borch, Karl H. (1968) “The Allais Paradox: A Comment,” Behavioral Science 13, 488–489. {% Relates moments approaches (mean-variance etc.) to EU, showing that usually mean-variance really violates EU. He seems to also have shown here that mean-variance violates stochastic dominance. %} Borch, Karl H. (1969) “A Note on Uncertainty and Indifference Curves,” Review of Economic Studies 36, 1–4. {% Maths for econ students. %} Borch, Karl H. (1974) “The Mathematical Theory of Insurance.” Lexington Books, Lexington, MA. {% %} Borcherding, Katrin, Thomas Eppel, & Detlof von Winterfeldt (1991) “Comparison of Weighting Judgments in Multiattribute Utility Measurement,” Management Science 37, 1603–1619. {% Review of descriptive studies of behavioral influences on attribute weighting in MAUT. Swing-method of determining decision weights qualitative strategies (e.g. letting most important dimension decide) is more likeley to be employed in qualitative method of choice; quantitative strategy such as making tradeoffs between dimensions is more likely to be employed in the quantitative method of matching. %} Borcherding, Katrin, Stefanie Schmeer, & Martin Weber (1995) “Biases in Multiattribute Weight Elicitation.” In Jean-Paul Caverni, Maya Bar-Hillel, Francis Hutton Barron, & Helmut Jungermann (eds.) Contributions to Decision Making I, 3–28, Elsevier, Amsterdam. {% The paper is based on a very good and new intuition, but the modeling is still problematic. There is a fundamental problem: the model is essentially intransitive (in same way as regret theory is), making it unsuited for most applications in economics and finance. There is also a theoretical problem that needs further fixing: the model as written is too general with too many parameters. Before discussing more, here is the basic idea of the model. ==================== BASIC IDEA (1) Assume states of nature that have objective probabilities (as with regret theory, although the latter also allows for subjective probabilities); (2) consider only binary choices between two prospects, say x,y; (3) let x and y have outcomes xi and yi for state si, and define the salience function (xi,yi), specifying how salient state si is due to the outcome difference. “Ordering”: it is increasing in the max of {xi, yi} and decreasing in the min, as with difference xiyi. (4) Transform decision weights of states in a somewhat complex way: give states salience rank number (so salience is only used ordinally; note that this ranking part is independent of the probability of the state, which will generate discontinuities under convergence to null), then adjust odds of all state pairs (si,sj) by a factor (rirj) where 0 < 1 and ri is the salience ranking of state si, with rj similar. = 1 means classical EU with no overweightings, and the smaller the more sensitivity to salience. (The formula is sound in the sense that readjusting the odds of si and sj, and then of sj and sk, gives the right adjustment of si and sk. Getting this soundness in is nontrivial. It is reminiscent of Birnbaum’s RAM and TAX models, where probability weights are moved from some states to others as terms.) In this way we can overweigh the salient states. It also works so that small probabilities are more overweighted than large ones can be (which could hardly be otherwise numerically; here a weighting of goodnews probabilities, as in rank dependence, would be worthwhile). (5) There is a reference point, and salience becomes less as outcomes, in absolute sense, move farther away from the reference point. Hence the paper favors, in examples, not using the difference xiyi , but rather | xi yi|/(|xi| + |yi|), to assess salience. For this, the reference point is crucial. ====================== THE GOOD INTUITION As regards the very good intuition of salience theory, prospect theory assumes that the state (of nature event) generating the largest outcome, and the state generating the lowest outcome, are overweighted; they are salient. It is just as plausible that, when comparing two prospects, the state with the largest DIFFERENCE in outcomes (or a variation of difference) is salient and gets extra weight. The idea that people directly compare outcomes of a prospect to outcomes of the competing prospect before any aggregation of the prospect's value is not new (regret theory has it too, and other theories have it also; it is the basis of the tradeoff concept that I used in many papers). To let this lead to overweighting of large differences is not new either (regret theory has this too, again, and it is central in regret theory). But to model these things through state weighting rather than through utility is new. It makes salience theory an interesting counterpart to regret theory. Salience theory modifies prospect theory as regret theory modified expected utility. Modeling the extra weighting through event weights, as salience theory does, seems more natural to me than modeling it through outcomes and utility as regret theory does. Hence salience theory can turn into an improved version of regret theory. Moderating this pro: it is also plausible that people sometimes UNDERweight states with big differences, in something like diminishing sensitivity with respect to difference. If one prospect yields €1 more in 5 states, and €5 less in one state, then being better five out of six times may decide. Similarly, later studies in regret theory found no clear empirical evidence for its original hypotheses of overweighting of big differences. Salience theory can easily accommodate these things by allowing their to exceed 1, and I recommend using this generalization. FIRST PROBLEM (INTRANSITIVITY) The essence of transitivity is that each prospect is evaluated on its own, independently of the other prospects it is competing with. To wit, if transitivity holds, then there exists a function V such that, for all prospects x,y, we have x > y if and only if V(x) > V(y). It means that when evaluating x by V(x), we do not even look at its competitor y. This excludes anything like salience. The essence of salience theory (and the above very good intuition) is that the evaluation of a prospect does depend on the one it is competing with (only binary choice is treated). Here salience theory is like regret theory. The essence of salience is violating transitivity, and it doesn’t bring any novelty otherwise. Problem 1a: intransitivity entails irrationality at a basic level. For most work in economics and finance such irrationalities are of no interest. Salience theory can, therefore, only be of use in psychologically oriented applications, such as understanding behavior of subjects in labs, and in marketing for instance where such irrationalities are also important. Problem1b: intransitive models are intractable. It is not clear how to choose from more than two prospects (the web appendix has suggestions but their dependence on whole choice set is too general to be tractable). It even is not clear how to define optimality. Thus quantitative assessments are hard to imagine, as it is with regret theory. For these reasons, regret theory hasn't been used in quantitative applications, and with salience theory it will be the same. The only paper that every measured regret theory quantitatively is Bleichrodt, Cillo, & Diecidue (2010 Management Science), using my tradeoff technique (), and this may also work for measuring the salience function. SECOND PROBLEM To explain the second problem, expected utility has one one-variate function, utility of money, as parameter. Prospect theory has two such one-variate functions, with probability weighting in addition (and one more number, loss aversion; I assume the reference point fixed, here as with salience theory). Salience theory has a two-variable function, the salience (x,y) as function. This is much larger generality, and it is something like infinitely many univariate functions. (There is also one more number, being ; I assume loss aversion is also good to add). This is way too general. Good subfamilies with fewer parameters will have to be developed. Eq. 5, p. 1250, gives a tractable subfamily, but it will take more to prove its value. Regret theory faced the same problem, with two-variable U(xi,xj) too general. They quickly went for the special case ((U(xi)U(xj)) with a nonlinear univariate function. Salience theory may go for (|xixj|/(|xi|+|xj|), similar to their Eq. 5 (p. 1250). Related to the second problem, there is no preference foundation (properly mentioned as an open problem on p. 1259 end of §III), and no verification of natural conditions such as continuity (will fail for probabilities tending to 0 for instance) or some kinds of monotonicity with respect to outcomes; or, for that matter, transitivity. The editing operations generate discontinuities and suggest other anomalies. There also is no way to measure/calibrate the functions, as in describe-predict. It is not discussed if they are at all identifiable. There are no quantitative assessments, which I think will be very hard at the present stage, and there are hardly ways to falsify the general theory (mostly the sure-thing principle is; see below). The theory does add some qualitative assumptions, and all tests and predictions concern those qualitative assumptions rather than the theory itself. It is as if setting up some complex weird theory that has a utility function in it, conjecturing decreasing concavity of utility and have that imply decreasing risk aversion, and then only testing the latter, which says almost nothing about the complex weird theory itself. On the positive side, the two qualitative assumptions are plausible and they very well predict right directions in the many examples chosen. It is obvious that the theory captures something substantial. Because of its many parameters, salience theory can accommodate almost everything, and the paper gives many examples, but it is almost impossible to falsify the theory. This second problem, concerning the theoretical problems, can be fixed if specific subfamilies are developed, and possibly some changes are made to the decision model itself. The only clearly restictive (so falsifiable, which is desirable) implication that I see (explained on pp. 1259 and 1267 for instance) is the sure-thing principle: states with the same outcome for both prospect have 0 salience and can be ignored, so that it does not matter if the common outcome is changed there. I add here that the sure-thing principle is not very restrictive under intransitivity. Under transitivity it amounts to completely excluding interactions between disjoint events, but here it need not. Tradeoffs between two states can be affected by a third state, that can interfere via the salience rankings I guess. DETAILS - Throughout, the authors do not make sufficiently clear, and do not sufficiently realize, that the essence of their theory lies in violating transitivity. They mention intransitivities once casually (p. 1246 l. -4). Near the bottom of p. 1259 they claim a positive result on transitivity (meaning their theory does not bring anything new there!). And at the bottom of p. 1273 they criticize intransitivity of regret theory. - The editing of the paper is not very good. Footnote 10 (p. 1255), referring to empirical measurements of probability weighting, an active field during the last two decades, cites only one 1996 paper, (nonincentivized and) 16 years old at the time of appearance (2012), and calls it “recent.” Pp. 1257-1258 out of the blue discuss contexts with apparently more than two choice options (whereas the paper restricts to binary choices), with vague claims and a vague consideration set (can be bigger than the choice set, but also smaller …). The idea about prospects that are permutations of each other at the bottom of p. 1257 is vague and ad hoc. (One problem: it matters much which of the permutations is randomly kept, because the correlation with other prospects matters.) When referring to “Both forms of editing” the paper means, besides the permutation idea, also the removal of dominated prospects. - The paper does not use the terms risk seeking (and risk aversion) the usual way, but risk seeking means choosing the riskier of two prospects. For example, a preference 1000.90 50 is called risk seeking. - I regret that the authors throughout use original 1979 prospect theory, and not the corrected 1992 version (e.g., footnote 2 on p. 1248 does not help). - The differences with regret theory listed on p. 1259 1st para are not important: adding framing, reference dependence, and reflection in the definition of regret theory can trivially be done; the non-trivial parts of these moves, maintaining tractability, is not done by salience theory either. Salience theory is a weighting-counterpart of utility-regret theory. But providing such a counterpart is interesting enough! P. 1259 2nd para is neither to the point. First, ordering and diminishing sensitivity do not make strong predictions, being only qualitative (although still good in their kind). Second, regret theory and the SSB theories by Fishburn (1982) also satisfy the sure-thing principle (although Fishburn 1982 concerns decision under risk and the analog there is bilinearity; other papers by him are directly for uncertainty and directly have the sure-thing principle there). As an aside, Vind (2003) provides advanced mathematics on intransitive preferences, where the sure-thing principle can still be satisfied. Third, the transitivity and dominance for independent prospects, suggested as a positive result, in fact means that salience theory has nothing new to offer there. P. 1264: the violation of prospect theory is not tight: the common view is that utility (value) becomes less concave as stakes increase, and then risk aversion may turn into risk seeking (risk seeking by w may start to dominate the concavity of utility for high stakes). Later the footnote only claims that the common calibrations of prospect theory do not accommodate, which is a weaker criticism. The more so as no common calibration of salience theory is available yet. P. 1267 ff. put forward as defence of salience theory, that the predicted sure-thing principle holds in framing that make the common consequence event clear. This is indeed a positive argument. It is weakened though because several people have argued that such independence of common consequence may reflect a heuristic that subjects use to simplify their task, rather than their preference. (This also weakens the, still positive, argument discussed on p. 1270, regarding what Kahneman & Tversky (1979) called the pseudo-certainty effect (term not used in this paper).) A psychological effect such as salience perception will not be restricted within a state but it will be global, generating violations of the sure-thing principle. P. 1276 claims as positive point that salience theory can explain the fourfold pattern while assuming linear utility, whereas prospect theory supposedly could not do this. This is not so. Prospect theory also predicts the fourfold pattern if utility is linear, where it then is generated by probability weighting. P. 1278 incorrectly writes: “In prospect theory, the main driver of risk attitudes is the curvature of the value function.” In PT, probability weighting is also a big driver or risk attitude (and also loss aversion, taking this “kink” not to be part of utility curvature). CONCLUSION. Positive: the basic intuition, that states with large differences of outcomes are overweighted, is very good. Modeling it through event weighting is good and more natural than regret theory’s modeling through outcome utility. The qualitative assumptions of ordering and diminishing sensitivity work well to accommodate many findings. Negative: biggest restriction is that intransitivity is the essence of the theory, limiting usefulness for economics and finance, and not well realized or presented by the authors. A problem that may be fixed (further work and creativity needed here) is that the model as is, especially with the bivariate salience function, is too general. There are no preference conditions to suggest that the model chosen is natural, and several aspects of it are not. Another problem is that the authors do not compare well with regret theory and prospect theory. Different fields should be able to exchange inputs and, therefore, this is not a serious problem. %} Bordalo, Pedro, Nicola Gennaioli, & Andrei Shleifer (2012) “Salience Theory of Choice under Risk,” Quarterly Journal of Economics 127, 1243–1285. {% Show that salience theory can accommodate the endowment effect. %} Bordalo, Pedro, Nicola Gennaioli, & Andrei Shleifer (2012) “Salience in Experimental Tests of the Endowment Effect,” American Economic Review, Papers and Proceedings 102, 41–46. {% Show that salience theory can accommodate may phenomena. Problem is that salience can accommodate too many phenomena. Again there is no discussion of the violations of transitivity. The conclusion compares with probability weighting of prospect theory and, incorrectly, claims that the overweighting of small probabilities would imply that risk aversion would increase in good times and decrease in bad times. Here is the sentence with the mistake: “In a recession, when the objective probability of left-tail payoffs increases, standard probability weighting would imply that the low payoff will be less overweighted than before.” If the probability increases from 0 (or something very small) to , the overweighting will INCREASE. Another problem for the authors, also underlying the preceding reasoning, can be inferred from the sentence in the conclusion where they try to separate salience theory from prospect theory: “In our model, extreme payoffs are overweighted not because they have small probabilities but because they are salient relative to the market payoff.” Here one sees, as in the other papers by the authors, being that they go by the outdated and incorrect 1979 version of prospect theory, and not by the updated and corrected version of 1992. In the latter, not the small probability of an outcome makes it being overweighted, but the extremity of being best or worst. Which is as close to salience as one can get without giving up transitivity. %} Bordalo, Pedro, Nicola Gennaioli, & Andrei Shleifer (2013) “Salience and Asset Pricing,” American Economic Review, Papers and Proceedings 103, 623–628. {% SIIA/IIIA %} Bordes, Georges & Nicolaus Tideman (1991) “Independence of Irrelevant Alternatives in the Theory of Voting,” Theory and Decision 30, 163–186. {% %} Border, Kim C. (1992) “Revealed Preference, Stochastic Dominance, and the Expected Utility Hypothesis,” Journal of Economic Theory 56, 20–42. {% Show that if P1,…,Pn are nonatomic countably additive probability measures on a measurable space S, A, where A is a sigma-algebra on S, then there is a subsigma algebra B of A on which all P’s agree, and such that every probability is generated on B. %} Border, Kim C., Paolo Ghirardato, & Uzi Segal (2008) “Unanimous Subjective Probabilities,” Economic Theory 34, 383–387. {% Many have alluded to strategic complications in the Dutch book game. The authors analyze these strategic complications formally by really considering the book making situation as a game. People can then deviate from Bayesianism. The results are enforced by the author’s 2002-JMP-paper. %} Border, Kim C. & Uzi Segal (1994) “Dutch Books and Conditional Probability,” Economic Journal 104, 71–75. {% Dutch book; p. 181-182 describes strange Dutch book; dynamic consistency %} Border, Kim C. & Uzi Segal (1994) “Dynamic Consistency Implies Approximately Expected Utility Preferences,” Journal of Economic Theory 63, 170–188. {% Nash bargaining solution %} Border, Kim C. & Uzi Segal (1997) “Preferences over Solutions to the Bargaining Problem,” Econometrica 65, 1–18. {% Follows up on their 1994 EJ paper and proves stronger results, where an equilibrium can necessitate the book maker to use nonadditive odds. %} Border, Kim C. & Uzi Segal (2002) “Coherent Odds and Subjective Probability,” Journal of Mathematical Psychology 46, 253–268. {% foundations of quantum mechanics %} Bordley, Robert F. (1995) “Relating Probability Amplitude Mechanics to Standard Statistical Models,” Physics Letters A 204, 26–32. {% %} Bordley, Robert F. (1998) “Quantum Mechanical and Human Violations of Compound Probability Principles: Toward a Generalized Heisenberg Uncertainty Principle,” Operations Research 46, 923–926. {% %} Bordley, Robert F. & Gorden B. Hazen (1991) “SSB and Weighted Linear Utility as Expected Utility with Suspicion,” Management Science 37, 396–408. {% Two different small worlds X and Y are two different partitions of the state space S. Their junction leads to receipt of two-dimensional outcomes (x,y). The utility assesments of these pairs can have all kinds of forms. If x and y are correlated, then . %} Bordley, Robert F. & Gorden B. Hazen (1992) “Nonlinear Utility Models Arising from Unmodelled Small World Intercorrelations,” Management Science 38, 1010–1017. {% P. 57 2nd para in Kyburg & Smokler (1964) discusses that subjective probabilities can be calibrated using matching probabilities. %} Borel, Émile (1924) “A Propos d’un Traité de Probabilités,” Revue Philosophique 98, 321–336. Reprinted as Note II in Émile Borel (1939) “Valeur Pratique et Philosophique des Probabilités.” Gauthier-Villars, Paris. Translated into English as “Apropos of a Treatise on Probability.” Reprinted in Henry E. Kyburg Jr. & Howard E. Smokler (1964, eds.) Studies in Subjective Probability, Wiley, New York (not reprinted in 2nd, 1980, edn. of the book). {% §39, p. 73 and §48, pp. 84-86, discuss that subjective probabilities can be calibrated through gambles on objective probabilities Pp. 60-66 discusses St. Petersburg paradox; %} Borel, Émile (1939) “Valeur Pratique et Philosophique des Probabilités.” Gauthier-Villars, Paris. {% Seem to argue that economic subjective attitude indexes such as risk aversion and discounting should be submitted to the same psychometric standards, e.g., test-retest reliability ( 0.7 correlation is desirable), like personality traits in psychology. %} Borghans, Lex, Angela L. Duckworth, James J. Heckman, & Bas ter Weel (2008) “The Economics and Psychology of Personality Traits,” Journal of Human Resources 43, 972–1059. {% real incentives: Cumulative payments, with income effects (subjects were informed about cumulative earnings throughout, p. 653). Average earning per subject is €21.30, average time of experiment 1.5 hour. N=347 high-school students aged 15/16. Tested 4 urns of 2 colors, first fifty-fifty so risk, then bit ambiguity (0.4 p 0.6, then more, 0.2 p 0.8, then all 0 p 1). P. 650 3rd para says these are Halevy urns, but this is not so. suspicion under ambiguity: ambiguity tests: subjects can guess color, which controls for suspicion (though maybe illusion of control). Women are more risk averse than men (gender differences in risk attitudes). Psychometric scales are related to risk attitude but not to ambiguity attitudes (p. 655, 657). Men are more ambiguity averse than women, which disappears after correcting for risk attitude (which I do not understand but did not read in detail). correlation risk & ambiguity attitude: although a central theme of the paper is that ambiguity is different than risk (their correlation is not 1), the actual correlation of these two is not reported. %} Borghans, Lex, Bart H.H. Golsteyn, James J. Heckman, Huub Meijers (2009) “Gender Differences in Risk Aversion and Ambiguity Aversion,” Journal of the European Economic Association 7, 649–658. {% Shows that s.th.pr. is implied by vNM independence, and the other way around if continuity %} Borglin, Anders (1993) “Conditional Preferences of a Savage Agent Who Satisfies Savage-Independence and Is Consistent with a von Neumann-Morgenstern Agent,” Institute of Economics, University of Copenhagen, Denmark. {% Apply not only SEU, but also the smooth model and maxmin (which can be taken as a limiting case of smooth) ambiguity models to some decision analysis problems, with decision trees. They connect well with the decision analysis literature and terminology, considering decision trees and referring to simulation techniques. They calculate risk and ambiguity premiums. In the smooth model, they seem to take the two-stage setup as exogenously given, although not very explicitly. Download 7.23 Mb. 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