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Utility of gambling: p. 259 argues that comparing risky to riskles gambles induces biases (due to utility or disutility of gambling) P. 260 argues for CE (certainty equivalent) method and against PE method because participants may not fully understand concept of probability (SG doesn’t do well) P. 263: “By keeping the number of participants small and by casting the study in a realistic and important decision context, we found it possible to evaluate the hypotheses of the study in greater depth.” P. 264, footnote 3: “Any obviously inconsistent answers were returned to the subject and ... were usually corrected” P. 268, Table 2, gives five utility functions measured through PE (probability equivalents), CE, and SP (strength of preference), on interval [0, 3500]. These numbers are costs, not gains. The authors don’t analyze it much. When I did, I found: PE higher than others: 1st subject: UPE: inconsistent (decreasing after 2000). UCE: convex; USP: concave 2nd subject: UPE: linear. UCE: linear; USP: concave 3rd subject: UPE: convex. UCE: concave; USP: convex on [0,1800] and concave on[1800,3500] (I drew the graph) 4th d subject: UPE: concave. UCE: convex; USP: concave 5th subject: UPE: concave-convex. UCE: convex; USP: convex; after normalization, UPE dominates UCE almost everywhere (on [0, 3100], except near 3500. %} Officer, Robert R. & Alfred N. Halter (1968) “Utility Analysis in a Practical Setting,” American Journal of Agricultural Economics 50, 257–277. {% Adapts Schmeidler (1989) by basing additive probabilities on Savage axioms. %} Oginuma, Takashi (1994) “A Theory of Expected Utility with Nonadditive Probability,” Journal of Mathematical Economics 23, 451–473. {% %} Ok, Efe A. (1994) “On the Approximation of Fuzzy Preferences by Exact Relations,” Fuzzy Sets and Systems 67, 173–179. {% %} Ok, Efe A. (1995) “Fuzzy Income Inequality Measurement: A Class of Fuzzy Inequality Measures,” Social Choice and Welfare 12, 111–136. {% %} Ok, Efe A. (1995) “On the Principle of Equal Sacrifice in Income Taxation,” Journal of Public Economics 58, 453–467. {% %} Ok, Efe A. (1996) “Fuzzy Measurement of Income Inequality: Some Possibility Results on the Fuzzification of the Lorenz Ordering,” Economic Theory 7, 513–530. {% %} Ok, Efe A. (1997) “A Note on the Existence of Progressive Tax Structures,” Social Choice and Welfare 14, 527–543. {% %} Ok, Efe A. (1997) “On Opportunity Inequality Measurement,” Journal of Economic Theory 77, 300–329. {% %} Ok, Efe A. (1997) “Inequality Averse Collective Choice,” Journal of Mathematical Economics 30, 301–321. {% completeness-criticisms; Preference representations for one-dimensional utility with incomplete preferences; incompleteness is because of indecisiveness. %} Ok, Efe A. (2002) “Utility Representation of an Incomplete Preference Relation,” Journal of Economic Theory 104, 429–449. {% %} Ok, Efe A. & Levent Koçkesen (2000) “Negatively Interdependent Preferences,” Social Choice and Welfare 17, 533–558. {% %} Ok, Efe A., Levent Koçkesen, & Rajiv Sethi (2000) “Evolution of Interdependent Preferences in Aggregative Games,” Games and Economic Behavior 31, 303–310. {% %} Ok, Efe A. & Laurence Kranich (1998) “The Measurement of Opportunity Inequality: A Cardinality-Based Approach,” Social Choice and Welfare 15, 263–287. {% %} Ok, Efe A. & Peter J. Lambert (1999) “On Evaluating Social Welfare by Sequential Generalized Lorenz Dominance,” Economics Letters 63, 45–53. {% time preference; Pp. 216-217 gives an example where, even if a priori choice between some alternative consumption paths are not determined if intransitivity, the choices are determined if it can be done using backward induction where at each time point there are only two choice options. However, the authors suggest that this may mean that intransitivity in general is no problem in case of backward induction. They axiomatize (x,t) > (y,s) iff U(x) > eta(s,t)U(y). This allows intransitivities. They do this by imposing the Reidemeister condition on the 2nd coordinate while giving up transitivity. Their domain is in Re x Re, so it is real-valued. They interpret the first coordinate as money and the second as time. Such intransitive additive representability reminds me of Vind’s work. %} Ok, Efe A. & Yusufcan Masatlioglu (2007) “A Theory of (Relative) Discounting,” Journal of Economic Theory 137, 214–245. {% revealed preference: a choice function is given on a general set of choice alternatives. The authors formulate revealed preference conditions (mostly acyclity conditions) that hold if and only if there exist a reference dependent model as follows: for each choice set, either one of the choice alternatives serves as reference point, or not. If not, then a utility function is maximized. If yes, then the utility function is only maximized over the choice alternatives that dominate the reference point for every attribute. Here both the reference point and the attributes (can also take as utility functions) are derived endogenously. The paper is targeted to/motivated by the attraction effect, where adding a dominated choice alternative makes the dominating choice alternative more attractive (the other one is ruled out here by taking the added alternative as reference point), and it reviews the literature on it. The paper confines attention to two-point interactions, where the value of an alternative x chosen is increased by the presence in the choice-menu of one other alternative z (z is a potential reference for x), and not by bigger sets of other alternatives through multiple interaction. The possibility to define attributes endogenously joint with the lexicographic processing gives much flexibility. If we want to rule out one alternative everywhere then we introduce an extra attribute where this alternative has value 0, all others in the set have value 1, and some proper reference point is chosen if needed. Contrary to what p. 301 l. -1 writes, this is not parsimonious but increases fit rather than parsimonity. It reminds me of Suck (1990) who also derived attributes endogenously, and Epstein, Marinacci, & Seo (2007), who derive a state space endogenously. %} Ok, Efe A., Pietro Ortoleva, & Gil Riella (2015) “Revealed (P)Reference Theory,” American Economic Review 105, 299–231. {% A nice unification of two forms of incompleteness: Bewley kind with set of probability measures and preference only if unanymous EU, and Dubra-Maccheroni-Ok kind with set of utility functions and preference only if unanymous EU. The idea is that at the beginning, with your first preference, you are just free to choose indecisiveness one way or the other and they are on the same footing. However, once chosen indecisiveness one way you can no more have any in the other direction because the mix of the two will violate the independence-like axiom imposed. Do it in an Anscombe-Aumann setup. P. 1794 concisely presents Bewley’s theorem, with indecisiveness in beliefs. P. 1795 has the Dubra, Maccheroni, & Ok (2004) dual, of indecisiveness in tastes (Theorem 1). The main axiom is reduction: it is a kind of local probabilistic sophistication, where the subjective probability can depend on the act. P. 1796 Theorem 2 is the main result, with weak reduction as the main axiom. Now there need not exists act-dependent probabilistic sophistication yielding indifference, but only weak preference. %} Ok, Efe A., Pietro Ortoleva, & Gil Riella (2012) “Incomplete Preferences under Uncertainty: Indecisiveness in Beliefs versus Tastes,” Econometrica 80, 1791–1808. {% %} Ok, Efe A. & Fernando Vega-Redondo (2001) “On the Evolution of Individualistic Preferences: Complete versus Incomplete Information Scenarios,” Journal of Economic Theory 97, 231–254. {% %} Ok, Efe A. & Lin Zhou (1999) “Revealed Group Preferences on Non-Convex Choice Problems,” Economic Theory 13, 671–687. {% %} Ok, Efe A. & Lin Zhou (2000) “The Choquet Bargaining Solutions,” Games and Economic Behavior 33, 249–264. {% DOI: 10.1017/S0266267115000346 utility = representational?: nice text on p. 421, intended only for descriptive applications: “Though Savage insisted on the behaviouristic interpretation, from a modern vantage point this looks untenable. Almost all sciences introduce theoretical posits that go beyond, and are meant to explain, the data; few philosophers today are tempted by an instrumentalist or fictionalist attitude towards such posits. This is as true in psychology as anywhere else; since the ‘first cognitive revolution’, psychologists have been happy to posit unobservable mental states and processes, many of them inaccessible to consciousness, that are meant to explain behaviour. And in philosophy of mind, it is a commonplace to regard an agent’s intentional attitudes, such as beliefs and desires, as internal causes of the agent’s behaviour. ” own little expertise = meaning of life: in the opening the paper, nicely, points out that many philosophers equate all of decision theory with EU: “Indeed many philosophers appearto use `decision theory’ simply to mean EU theory.” (p. 410 ll. 2-3) The author favors the mentalist approach, as I do, for descriptive applications. For me it is the same normatively, but for the author it is not and for normative he favors the behaviourist/representational view. This is because he, while he like me assumes that EU axioms are necessary for rationality, he, unlike me, also assumes that they are sufficient. After working 8 years in a hospital I have come to understand that there is more to rationality and the EU axioms. Anyway, this makes the author strongly criticize any author who does not leave the choice of utility completely free. P.425 2nd para: “But it is quite wrong to view the normative content of the theory as saying that an agent should maximize expected utility relative to a psychologically real utility and credence function.” P. 429 ll. 1-3: “It is evident that Briggs construes decision theory as telling the agent to maximize expected utility with respect to some independently defined utility function; which as I have argued is a misconception.” p. 421 pnultimate para: “psychologist have been happy to posit unobservable mental states and processes, many of them inaccessible to consciousness, that are meant to explain behaviour.” P. 422 1st para about as if calculations: “but this is quite standard in cognitive psychology.” %} Okasha, Samir (2016) “On the Interpretation of Decision Theory,” Economics and Philosophy 32, 409–433. {% A problem in the famous Asian disease example of Tversky & Kahneman (1981) is that, with nr. of people dying given, it may not be clear how many then survive, and that this is meant to be all others. This study makes the latter explicit and then the framing effect disappears. %} Okder, Hidetaka (2012) “The Illusion of the Framing Effect in Risky Decision Making,” Journal of Behavioral Decision Making 25: 63–73. {% DC = stationarity: does not happen here, and the authors state the point carefully: “Present bias may lead to violations of dynamic consistency when choices at later points in time are also part of the analysis;” (p. 1450-1451). Tradeoff method: P. 1459 Axiom 11 is the tradeoff consistency axiom, that I introduced in Wakker (1984) and used in 2/3 of my papers, e.g. Köbberling & Wakker (2003), where my later papers also used that name tradeoff consistency. But, , they do not cite me there. Fortunately, they do cite way more of my papers () than the average researcher does today so I am still in a good mood. The technique of measuring discounting without measuring utility by subjectively matching time intervals, used in this paper to identify and , was introduced by Attema, Bleichrodt, & Wakker (2012 MDM) for the general measurement of discounting (from a different field; not cited) and was also used by Attema, Bleichrodt, Gao, Huang, & Wakker (2016 AER p. 1490). P. 1462 footnote 9 cites Ramsey on pointing out a relation between time and belief. Ramsey apparently wrote: “the degree of belief is like a time interval; it has no precise meaning unless we specify how it is to be measured.” But I conjecture that Ramsey did not think of subjective discounting here, but only of time as objective unit, and the analogy only concerned measurement of equal sets in general. Attema, Bleichrodt, & Wakker (2012 MDM p. 585) did point out the analogy between measuring subjective discounting without involving utility through matching time intervals and measuring subjective probabilities, a point reiterared by Attema, Bleichrodt, Gao, Huang, & Wakker (2016 AER p. 1490). %} Olea, José Luis Montiel & Tomasz Strzalecki (2014) “Axiomatization and Measurement of Quasi-Hyperbolic Discounting,” Quarterly Journal of Economics 129, 1449–1499. {% %} Oleay, José Luis Montiel & Tomasz Strzalecki (2011) A Simple Axiomatization of Quasi-Hyperbolic Discounting,” working paper. {% concave utility for gains, convex utility for losses: do this w.r.t. nr. of human lives lost in tragic events, showing diminishing sensitivity. The authors use the decision-by-sampling model by Neil Stewart and others. They argue, in my terminology, that it is more numerical perception than intrinsic value that drives judgement. The more one’s country has large catastrophes, the more one can “handle” large numbers and the less the diminishing sensitivity/convexity are. %} Olivola, Christpoher Y. & Namika Sagara (2009) “Distributions of Observed Death Tolls Govern Sensitivity to Human Fatalities,” Proceedings of the National Academy of Sciences 106, 22151–22156. {% correct for probability distortion Modifies the SG, similar to Bleichrodt, Pinto, & Wakker. Finds that loss aversion increases the internal consistency of the SG, probability transformation does not. %} Oliver, Adam J. (2003) “The Internal Consistency of the Standard Gamble: Tests after Adjusting for Prospect Theory,” Journal of Health Economics 22, 659–674. {% %} Oliver, Adam J. (2003) “A Quantitative and Qualitative Test of the Allais Paradox Using Health Outcomes,” Journal of Economic Psychology 24, 35–48. {% utility measurement: correct for probability distortion %} Oliver, Adam J. (2005) “Testing the Internal Consistency of the Lottery Equivalents Method Using Health Outcomes,” Health Economics 14, 149–159. {% Shows that ranking can reduce preference reversals. %} Oliver, Adam J. (2006) “Further Evidence of Preference Reversals: Choice, Valuation and Ranking over Distributions of Life Expectancy,” Journal of Health Economics 25, 803–820. {% Finds usual preference reversals but now for health stimuli. Although not very systematic direction (although still sgnificant), about 35% reversals. The intro nicely summarizes the main findings on preference reversals. Last para of §1.2: Thus, to sum up current thinking on the causes of preference reversals, based on two [three] decades of research, we can say that the rate of preference reversal is hardly affected by the payoff scheme and therefore cannot be attributed to a failure of independence, that intransitivity accounts for quite a small proportion of preference reversals, and that the principal cause of the phenomenon is a failure of procedural invariance, particularly the overpricing of the $-bet in the valuation task, which in turn suggests that preferences are often constructed, not fixed. The second experiment uses real incentives, but not the health states given to the subjects. Instead subjects are told that the heath states will be converted to money, but they are not told how. %} Oliver, Adam J. (2013) “Testing Procedural Invariance in the Context of Health,” Health Economics 22, 272–288. {% Short comment arguing that behavioral economics may be used to improve behavior also if it cannot be along the lines of nudge, and it cannot be libertarian. %} Oliver, Adam J. (2013) “Should Behavioural Economic Policy Be Anti-Regulatory?,” Health Economics 22, 373–375. {% doi: 10.1111/padm.12165 Argues that nudging, with no coercion used, often is not enough, and discusses work of British nudge dept. BIT and others. %} Oliver, Adam J. (2015) “Nudging, Shoving, and Budgeting: Behavioural Economic-Informed Policy,” Public Administration 93, 700–714. {% Do SG for life duration (N=30) and find risk aversion, in agreement with many preceding studies. Surprisingly, the lottery equivalent (N=40) does not reduce the risk aversion. %} Oliver, Adam & Richard Cookson (2010) “Analysing Risk Attitudes to Time,” Health Economics 19, 644–655. {% time preference: finds that discounting is not constant. %} Olsen, Jan A. (1993) “Time Preference for Health Gains: An Empirical Investigation,” Health Economics 2, 257–265. {% That discounting of money must be equally strong as discounting of health states. %} Olsen, Jan A. (1993) “On What Basis Should Health Be Discounted,” Journal of Health Economics 12, 39–53. {% %} Olsen, Jan A. (1994) “Person vs Years: Two Ways of Eliciting Implicit Weights,” Health Economics 3, 39–46. {% The term “common curency” in the title nicely expresses that we should not have QALY depending on everything, like the context-dependence that psychologists like so much, but we should get some measures that can be compared across different contexts. EQ-5D-5L from Canada, Englan, Netherlands, Spain are very similar, e.g. regarding importance weights of dimensions and utility decrements. A common scale is developed. %} Olsen, Jan Abel, Admassu N. Lamu, & John Cairns (2018) “In Search of a Common Currency: A Comparison of Seven EQ‐5D‐5L Value Sets,” Health Economics 27, 39–49. {% P. 20 DC = stationarity? Person prefers consuming 4/5 of his possession today, 3/25th tomorrow, 2/25 third day. He exhibits time inconsistency if myopic; Distinguish between diminishing marginal utility and pure time preference; P. 1: “the case for positive time preference is absolutely compelling.” Several things they write are debatable P. 13: one need not have a “what-has-posterity-ever-done-for-me” attitude. %} Olson, Mancur & Martin J. Bailey (1981) “Positive Time Preference,” Journal of Political Economy 89, 1–25. {% Risk averse for gains, risk seeking for losses: surveys among professional investors confirms loss aversion, risk aversion for gains, and risk seeking for losses. %} Olsen, Robert A. (1997) “Prospect Theory as an Explanation of Risky Choice by Professional Investors: Some Evidence,” Review of Financial Economics 6, 225–232. {% utility = representational?: argues against coherentism. Coherentism means that internal coherence of a set of beliefs is the only criterion for truth. There is no debatable link with external reality otherwise. %} Olsson, Erik (2005) “Against Coherence. Truth, Probability and Justification.” Oxford University Press, Oxford. {% biseparable utility violated; ordering of subsets; Preferences over sets of lotteries, where nature next chooses one, but does so in a nonprobabilized manner: ambiguity à la Jaffray (cited by the author) and others. As in Jaffray’s model, the evaluation is through a mixture of the inf and sup of the utility (which is EU here) of the prospects. Axioms include a set-version of the independence condition, and set-continuity. If set A c B, decision maker 1 prefers A to B more than decision maker 2 does, whereas they have same (EU) preference over singletons, then decision maker 1 is more ambiguity averse. (Seems to use betweenness-like axioms.) Holds (Corollary 2, p. 575) iff the mixture-weight of the inf is bigger for decision maker 1. %} Olszewski, Wojciech (2007) “Preferences over Sets of Lotteries,” Review of Economic Studies 74, 567–595. {% Assume a fixed prize, and t the time at which you receive it. This paper considers the case where, with the prize fixed, t is uncertain. Under the classical discounted EU, the commonly found convex discounting function would imply risk seeking w.r.t. t. Empirically, however, we find risk aversion. (The authors show it systematically, citing Chesson & Viscusi 2003 as the first finding of this kind.) As the authors point out, their finding gives nice evidence for risk aversion not being outcome driven but probability driven. An original idea! The finding supports rank-dependent utility. An alternative explanation is that the discounting function would be concave, with increasing rather than the commonly assumed decreasing impatience, but the authors do not favor this explanation. The authors cite Kacelnik & Bateson (1996) who find risk seeking instead for animal foraging behavior. Redelmeier & Heller (1993 MDM) also find risk aversion in an experiment very similar to the one here, but with aversive health outcomes instead of money. Then convex discounting is multiplied by a negative outcome meaning that the resulting function is concave, and common positive discounting gives risk aversion. Hence what Redelmeier & Heller find is in agreement with common findings and not the paradox that this paper provides. %} Onay, Selçuk & Ayse Öncüler (2007) “Intertemporal Choice under Timing Risk: An Experimental Approach,” Journal of Risk and Uncertainty 34, 99–121. {% DOI: http://dx.doi.org/10.1002/bdm.1763 Ambiguity attitudes for future payments. Distinguish ambiguity about probabilities from ambiguity about outcomes. Table 1 cites many papers making the same distinction (ambiguous outcomes vs. ambiguous probabilities). Refer to construal level theory, from which they derive the prediction that the future moderates ambiguity attitudes towards probabilities but amplifies them towards outcomes. They find that future moderates ambiguity aversion for probabilities and amplifies ambiguity seeking towards outcomes. %} Onay, Selcuk, Dolchai La-Ornual, & Ayse Öncüler (2013) “The Effect of Temporal Distance on Attitudes toward Imprecise Probabilities and Imprecise Outcomes,” Journal of Behavioral Decision Making 26, 362–374.
Ontario Ministry of Health (1991) “Guidelines for the Preparation of Economic Analysis to Be Included in Submission to Drug Programs Branch for Listing in the Ontario Drug Benefit Formulary/Comparative Drug Index,” Ministry of Health, Toronto. {% %} Oostenbrink, Rianne, Ronald de Groot, & Henriette A. Moll (1999) “Het Jonge Kind met Koorts zonder Focus; Diagnostiek en Beleid,” Nederlands Tijdschrift voor de Geneeskunde 23, 185–190. {% %} Oosterbeek, Hessel, Randolph Sloof, & Gijs van der Kuilen (2004) “Cultural Differences in Ultimatum Game Experiments: Evidence from a Meta-Analysis,” Experimental Economics 7, 171–188. {% special issue, dedicated to decision analysis. %} Operations Research 28, no. 1. {% %} Opp, Marcus M. & John Y. Zhu (2015): “Impatience vs. Incentives,” Econometrica 83, 1601–1617. {% %} Oresme, Nicolas (1968) “Tractatus de Configurationibus Qualitatum et Motuum.” In Marshall Clagett (ed.) Nicole Oresme and the Medieval Geometry of Qualities and Motions, University of Wisconsin Press, Madison. {% %} Orlovski, Sergei A. (1994) “Calculus of Decomposable Properties, Fuzzy Sets, and Decisions.” Allerton Press, New York. {% %} Ordonez, Lisa & Lehman Benson (1997) “Decisions under Time Pressure: How Time Constraint Affects Risky Decision Making,” Organizational Behavior and Human Decision Processes 71, 121–140. {% A review of Plotts work. It is negative on the biases and heuristics literature by Kahneman and others, with very critical remarks on Rabin for instance on p. 569. It, accordingly, argues that, besides Smith, Plott rather than Kahneman should have gotten the Nobel prize. %} Ortmann, Andreas (2003) “Charles R. Plott’s Collected Papers on the Experimental Foundations of Economic and Political Science,” Journal of Economic Psychology 24, 555–575. {% foundations of statistics Discusses controversies about hypothesis testing in organization studies (OS) which, according to the abstract, refers to all management-related journals and disciplines, including but not limited to organizational behavior, strategy, human resource management, and organization theory. %} Orlitzky, Marc (2012) “How Can Significance Tests Be Deinstitutionalized?,” Organizational Research Methods 15, 199–228. {% In an Anscombe-Aumann model, assumes a preference relation 0 if there is no status quo, and for all acts f a preference relation f which is preference if f is status quo. f is such that there is a set of priors such that only acts g are f preferred to f if they are so unanimously for the whole set of priors. Among those acts preferences f are as 0, so as if there was no status quo. So the status quo does not affect preference between acts preferred to the status quo. Other than that 0 can be anything in Theorem 1. Theorem 2 adds axioms that make 0 maxmin. %} Ortoleva, Pietro (2010) “Status Quo Bias, Multiple Priors and Uncertainty Aversion,” Games and Economic Behavior 69, 411–424. {% updating: in the Anscombe-Aumann model, the author imposes standard Anscombe-Aumann axioms (continuity, weak ordering, independence). Further he considers updating and assumes consequentialism, event-collapsing (implicitly), and a weakened version of dynamic consistency: dynamic coherence. The latter means that if a set of events is informationally equivalent in the sense that given one, the complement of any other is null, then their updated preferences should be identical. He proves that these axioms hold iff: Bayesian updating for all events whose subjective probability exceeds a threshold . An observation less likely than is not trusted. Then the decision maker imposes a second-order probability distribution on his priors, updates that, and takes the most likely prior as new prior. How restrictive the last part, of maximizing likelihood, is, depends on how restricted the choice of prior is. What it is beyond preserving null I did not study. Remarkable that AER took this purely axiomatic paper. %} Ortoleva, Pietro (2012) “Modeling the Change of Paradigm: Non-Bayesian Reactions to Unexpected News,” American Economic Review 102, 2410–2436. {% Abstract: “Overconfidence is a substantively and statistically important predictor of ideological extremeness, voter turnout, and partisan identification.” P. 507: “This work contributes to the emerging literature on behavioral political economy, which applies findings from behavioral economics to understand the causes and consequences of political behavior. This approach promises to allow political economists to integrate the insights of a half-century of psychology-based political behavior studies.” Derive their conclusion from a dataset nationwide of over 3000 adults. P. 505: “Citizens passively learn about a state variable through their experiences (signals). however, to varying degrees, citizens underestimate how correlated these experiences are, and thus, have different levels of overconfidence about their information. This underestimation—which we call correlational neglect” Thus the authors give a behavioral interpretation to data and derive new insights from that. %} Ortoleva, Pietro & Erik Snowberg (2015) “Overconfidence in Political Behavior,” American Economic Review 105, 504–535. {% %} Ortona, Guido (1994) “Examining Risk Preferences under High Monetary Incentives: Comment,” American Economic Review 84, 1104. {% %} Osborne, Martin J. & Ariel Rubinstein (1994) “A Course in Game Theory.” MIT Press, Cambridge, MA. {% paternalism/Humean-view-of-preference: they propose heuristic but clever manner for correcting quantitatively for incoherencies in probability judgments. P. 1 and 2 give many refs to people trying to correct for incoherencies in probability judgments. They ask participants for judgments of probabilities of elementary statements and the set E of their logical combinations. These contain, obviously, incoherencies. They then take state space S with 10 equally probable states. Stage 1. They stretch all probabilities of elementary statements by a random factor towards, randomly chosen, either 0 or 1. Stage 2. To each elementary statement they assign a, randomly chosen, subset E of S with ||E||/10 as close as possible to the “stretched” probability of the elementary statement. Thus, a probability distribution over E results. Stage 3. They calculate the absolute deviation between the probability over E of stage 2 and the direct judgments of probability Stage 4. They do the whole above process 30 times, and of these 30 times choose the one that has the minimal distance in Stage 3. The probability distributions obtained like this better fit to objective probabilities, known to experimenters but not to participants, than the direct judgements do. %} Osherson, Daniel, Eldar Shafir, David H. Krantz, & Edward E. Smith (1997) “Probability Bootstrapping: Improving Prediction by Fitting Extensional Models to Knowledgeable but Incoherent Probability Judgments,” Organizational Behavior and Human Decision Processes 69, 1–8. {% Best known study showing overconfidence %} Oskamp, Stuart (1965) “Overconfidence in Case-Study Judgments,” Journal of Consulting Psychology 29, 261–265. {% Adolescents take more risks because they are worse at learning from experience. %} Osmont, Anaïs, Sylvain Moutier, Grégory Simon, Lison Bouhours, Olivier Houdé, & Mathieu Cassotti (2017) “How Does Explicit Versus Implicit Risk Information Influence Adolescent Risk-Taking Engagement?,” Journal of Behavioral Decision Making 30, 1093–1103. {% CBDT; Students repeatedly guess colors from balls drawn from urns with unknown compositions, where they learn from repeated drawings. Get points, the total sum of which is turned into money later. CBDT is implemented with particular similarity functions, and utility linear. It accommodates observations better than maxmin, maxmax, maxmin, and some learning models. Subjects got points and were paid, besides €5 showup fee, €0.05 per point if the nr. of points was positive, but did not have to pay if the sum was negative. %} Ossadnik, Wolfgang, Dirk Wilmsmann, & Benedikt Niemann (2013) “Experimental Evidence on Case-Based Decision Theory,” Theory and Decision 75, 211–232. {% Hypothetical choice. Consider choice between a sure gain and a gain-loss prospect, and between a sure loss and a gain-loss prospect. Seem to assume linear utility, and fit probability weighting using the Goldstein & Einhorn (1987) transformation family. Investigate interactions between payments and probability weighting (probability weighting depends on outcomes). Do not refer to prospect theory or the vast risky-choice literature, but only to intertemporal choice as analog of risky choice. %} Ostaszewski, Pawel & Wojciech Bialaszek (2010) “Probabilistic Discounting in “Certain Gain–Uncertain Loss” and “Certain Loss–Uncertain Gain” Conditions,” Behavioural Processes 83, 344–348. {% Independently obtained the Goldstein & Einhorn (1987, Eqs. 2224) family by applying a hyperbolic function—often used in intertemporal choice—to the odds ratio p/(1p). %} Ostaszewski, Pawel, Leonard Green, & Joel Myerson (1998) “Effects of Inflation on the Subjective Value of Delayed and Probabilistic Rewards,” Psychonomic Bulletin & Review 5, 324–333. {% information aversion: %} Oster, Emily, Ira Shoulson, & E. Ray Dorsey (2013) “Optimal Expectations and Limited Medical Testing: Evidence from Huntington Disease,” American Economic Review 103, 804–830. {% The paper considers evaluations of (a1,t1,..., an,tn). There are n individuals, and this is health state ai (abstract, with dead as worst and perfect heath as best) during time ti (positive reals) for individual i. The paper assumes separability giving evaluation V1(a1,t1) + ... + Vn(an,tn) and then adds axioms to give linearity in t, power functions in t, and particular multiplicative decompositions that follow mostly from utility independence. An important step in proofs is to replace pairs (ai,ti) by an equivalent (a*,ti*), where a* is perfect health and (a*,ti*) is the healthy years equivalent. %} Østerdal, Lars-Peter, Jens Hougard, & Juan Moreno-Ternero (2012) “A New Axiomatic Approach to the Evaluation of Population Health,” working paper. {% free-will/determinism %} Otterström, Göran Duus (2009) “Almost Pregnant: On Probabilism and its Moral Uses in the Social Sciences,” Philosophy of the Social Sciences 39, 572–594. {% probability communication: %} Oudhoff, Jurriaan P. & Daniëlle R. M. Timmermans (2015) “The Effect of Different Graphical and Numerical Likelihood Formats on Perception of Likelihood and Choice,” Medical Decision Making 35, 487–500. {% Theorem A.1, presented as an elaboration of an exercise of Bourbaki, gives a topological version of Hölder’s lemma, with a connected topology. %} Ovchinnikov, Sergei (2001) “On Ordered Structures of Scale Type (N,N),” Journal of Mathematical Psychology 45, 913–916. {% Seems to point out that randomization is only to let opponent be uncertain about which (possibly pure) strategy is chosen. %} Owen, Guillermo (1974) “A Discussion of Minimax,” Management Science 20, 1316–1317. {% A theoretical model on how in ambiguity learning affects/converges to risk aversion %} Oyarzun, Carlos & Rajiv Sarin (2013) “Learning and Risk Aversion,” Journal of Economic Theory 148, 196–225. {% Theorems on generalized quasilinear means and other topics. There are results on information aversion in §5, relating it to low sensitivity to probabilities. Iterated integrals are analogous to associativity and axiomatize the implicit means that are in fact quasilinear. %} Ozaki, Hiroyuki (2009) “Conditional Implicit Mean and the Law of Iterated Integrals,” Journal of Mathematical Economics 45, 1–15. {% conservation of influence: paper is about something different, being unknown states of nature. But many of its sentences, especially in the beginning, suggest related thoughts. Reading this paper gives good feelings. Nice conclusion: “There are occasions when even if an alternative has a high priority relative to other alternatives that priority is questionable because there may be other criteria that need to be identified and used that can change the ranks obtained for the alternatives. In that case “other” would not be of help. One needs to be fairly sure that all the important criteria have been used and the priorities of the alternatives are close, in which case “other” would be useful to determine the stability of the best alternative.” %} Ozdemir, Mujgan S. & Thomas L. Saaty (2006) “The Unknown in Decision Making: What to Do about It,” European Journal of Operational Research 174, 349–359. {% %} Ozdenoren, Emre (2002) “Completing the State Space with Subjective States,” Journal of Economic Theory 105, 531–539. {% dynamic consistency; Consider, for instance, Ellsberg 3-color with conditioning and the paradoxical implications of ambiguity aversion. %} Ozdenoren, Emre & James Peck (2008) “Ambiguity Aversion, Games against Nature, and Dynamic Consistency,” Games and Economic Behavior 62, 106–115. {% N = 1047 subjects from the US and Germany answered hypothetical choice questions. There were affect-poor choices (lotteries over money) and affect-rich choices (lotteries over medical outcomes). Numeracy measures of the subjects were available. High numeracy and US give more EV maximization. (cognitive ability related to risk/ambiguity aversion) Remarkably, although the Americans on average had lower numeracy scores, they still did more EV maximization. Study 2 (N = 118 from Germany) shows that with affect-rich outcomes there is more neglect of probability (I guess, then more inverse-S). %} Pachur, Thorsten & Mirta Galesic (2013) “Strategy Selection in Risky Choice: The Impact of Numeracy, Affect, and Cross-Cultural Differences,” Journal of Behavioral Decision Making 26, 260–271. {% violation of objective probability = one source: they investigate this. Several studies have shown that affectrich outcomes can affect probability weighting, the electric shocks versus moviestar kisses of Hsee & Rottenstreich being most well known. This paper shows the effect very thoroughly, also within-subject, and is the first to do so. The main finding is that affect-rich outcomes make people less, or even completely, insensitive to probabilities. Process data with eye tracking support this claim. The authors interpret disregarding probabilities as something fundamentally different than bigger insensitivity (p. 75 last para of 1st column and p. 76 2nd column 2nd para), and follow that same interpretation in other papers. I disagree. It is an extreme case of insensitivity. Thus, what the authors take as evidence against inverse-S, in my opinion is strong support. %} Pachur, Thorsten, Ralph Hertwig, & Roland Wolkewitz (2014) “The Affect Gap in Risky Choice: Affect-Rich Outcomes Attenuate Attention to Probability Information,” Decision 1, 64–78. {% loss aversion: erroneously thinking it is reflection: Reanalyze data of Glöckner & Pachur (2012), considering various parametric families of PT. Remarkably, sign-dependence of probability weighting captures more variance in data than loss aversion. %} Pachur, Thorsten & David Kellen (2013) “Modeling Gain-Loss Asymmetries in Risky Choice: The Critical Role of Probability Weighting,” working paper. {% cognitive ability related to risk/ambiguity aversion: The measure PT and used real incentives. Subjects with high probabilistic insensitivity pay little time looking at probabilities, supporing the cognitive interpretation of inverse-S. P. 148: “Arguably the most influential descriptive model in the expectation tradition is cumulative prospect theory (CPT; Kahneman & Tversky, 1979; Tversky & Kahneman, 1992).” They assume power utility with the same power for gains and losses, which, as explained by Wakker (2010, end of §9.6.1): “Thus, there is no clear way to define loss aversion for power utility unless the powers for gains and losses agree. Tversky & Kahneman (1992) coincidentally found such an agreement.” Table 1 shows a strange finding: < 1, gain seeking. P. 155: “CPT has a previously overlooked capacity to reflect aspects of the cognitive processing of specific attribute information.” Experiment 2 manipulates attention to gains and losses, and, unsurprisingly, more attention to losses increases loss aversion. %} Pachur, Thorsten, Michael Schulte-Mecklenbeck, Ryan O. Murphy, & Ralph Hertwig (2018) “Prospect Theory Reflects Selective Allocation of Attention,” Journal of Experimental Psychology: General 147, 147–169. {% Consider how PT can accommodate five heuristics: maxmin (maximize minimal outcome; the authors call it minimax), maxmax (maximize maximal outcome), least likely (identify the worst outcome of each prospect; take the one that assigns the lowest probability to its worst outcome; so (0.1: 107, 0.9:106) is preferred to 106 because the latter assigns probability 1 to its worst outcome, and the former only probability 0.1), most likely (equate each prospect with its most likely outcome, and choose according to those, which also readily leads to violations of stochastic dominance), and the priority heuristic (described in my comments to the Brandstätter, Gigerenzer, & Hertwig 2006 paper). A nice attempt at reconciliation! They do not solve the problem mathematically, but by taking the parametric families of T&K92 and fitting those to two-, three-, and five-outcome prospects. Here are my mathematical speculations: for gains, maxmin (or maxmax) can be perfectly accommodated by a weighting function that is 0 (or 1) everywhere outside 0 (or 1), see my Wakker (2010) book Exercise 10.4.3. For losses this goes dually. Least likely and most likely are so far from any traditional theory satisfying stochastic dominance that it will depend entirely on the data set considered. The priority heuristic is more interesting but also more involved. Its overweighting of worst gain and best loss, and ignorance of intermediate outcomes supports pessimism + inverse-S for gains and optimism + inverse-S for losses. I did not find clearly what stimuli were used in the simulations and experiments. The authors consider hypothetical risky choices with monetary outcomes and with health outcomes. With health the probability weighting is more pessimistic and also more inverse-S. The heuristics models all have a context dependence that means they will violate transitivity. All the ones considered here are non-cmpensatory. Although algebraic models could be equipped with speculations on underlying cognitive processes and heuristics could be used without, mostly it is the other way around and this the authors write. The abstract takes diminishing sensitivity to outcomes and probabilities as psychophysical and not as cognitive. I like to take insensitivity (inverse-S) probability weighting as (also) cognitive. The abstract calls risk aversion “and loss aversion” psychological. P. 62 §8.1.1: “Algebraic models, with their focus on describing preference patterns, are mute about the cognitive processes underlying choice.” P. 62 §8.1.2: “Prospect theory has psychophysical roots that Kahneman and Tversky (1979) highlighted, for instance, in the context of diminishing sensitivity” Again, the case of probability weighting, I like to take that as (also) cognitive. I emailed with Thorsten Pachur on 23Feb.2018 and I think we converged on the following: the term prospect theory is used in different senses in the literature. Some economists prefer to take it Friedman-style purely as revealed-preference without any interpretation. Their claim of muteness refers to those. However, others, including Kahneman, Tversky, Rich Gonzalez (I would like to join in this group), like do speculate on cognitive interpretations and are not mute. Nice is that the paper tries to relate and compare PT and heuristics in neutral terms. %} Pachur, Thorsten, Renata Suter, & Ralph Hertwig (2017) “How the Twain Can Meet: Prospect Theory and Models of Heuristics in Risky Choice,” Cognitive Psychology 93, 44–73. {% ratio bias %} Pacini, Rosemary & Seymour Epstein (1999) “The Relation of Rational and Experiental Information Processing Styles to Personality, Basic Beliefs, and the Ratio-Bias Phenomenon, Journal of Personality and Social Psychology 76, 972–987. {% measure of similarity %} Paclík, Pavel, Jana Novovicová, & Robert P. W. Duin (2006) “Building Road-Sign Classifiers Using a Trainable Similarity Measure,” IEEE Transactions on Intelligent Transportation Systems 7, 309–321. {% Voice means that victims may speak in court. Students in lab are told hypothetically how much time they get and then scale it introspectively for fairness. The resulting function has a shape like the value function of prospect theory. %} Paddock, E. Layne, Jaewon Ko, Russell Cropanzano, Jessica Bagger, Assâad El Akremi, Julie Camerman, Gary J. Greguras, Antonio Mladinic, Carolina Moliner, Kidok Nam, Kjell Törnblom and Kees Van den Bos (2015) “Voice and Culture: A Prospect Theory Approach,” Journal of Behavioral Decision Making 28, 167–175. {% utility = representational?: neurons in the OFC (orbitofrontal cortex) are proposed as a good “candidate network” for economic value (so, utility). %} Padoa-Schioppa, Camillo & John A. Assad (2006) “Neurons in the Orbitofroonal Cortex Encode Economic Value,” Nature 441, 11 May 06, 223–226. {% %} Page, Frank H. Jr. (1996) “Arbitrage and Asset Prices,” Mathematical Social Sciences 31, 183–208. {% %} Page, Lionel & Robert T. Clemen (2013) “Do Prediction Markets Produce well Calibrated Probability Forecasts?,” Economic Journal 491–513. {% doi:10.1038/544161d Download 7.23 Mb. Share with your friends:
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