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Pöyhönen, Mari & Raimo P. Hämäläinen (2000) “Notes on the Weighting Biases in Value Trees,” Journal of Behavioral Decision Making 11, 139–150. {% measure of similarity %} Prechelt, Lutz, Guido Malpohl, & Michael Philippsen (2002) “Finding Plagiarisms among a Set of Programs with JPlag,” Journal of Universal Computer Science 8, 1016–1038. {% %} Prasnikar, Vesna (1993) “Binary Lottery Payoffs: Do They Control Risk Aversion?,” Discussion Paper (Northwestern University, The Center for Mathematical Studies in Economics and Management Science) {% Multiple agents and multiple principals. Characterize pure-strategy equilibria and efficient equilibria. %} Prat, Andrea & Aldo Rustichini (2003) “Games Played through Agents,” Econometrica 71, 989–1026. {% foundations of statistics; p. 164 seems to write: …nevertheless NP theory is arbitrary, be it however ‘objective’, … %} Pratt, John W. (1961) Book Review of: Erich L. Lehmann (1959) “Testing Statistical Hypotheses,” Wiley, New York; Journal of the American Statistical Association 56, 153–156. {% %} Pratt, John W. (1964) “Risk Aversion in the Small and in the Large,” Econometrica 32, 122–136. {% “Few problems are important enough or self-contained enough to warrant a full-blown approach with honest prior distributions and utility functions, and I have been amazed by some people’s success in getting subjective expected utility used in practical situations. But to me, the clarification of thinking and discourse is much more important than any immediate practical application.” [Italics added here.] The italicized part is, I guess, a criticism of the strong (own little expertise = meaning of life) one finds in decision analysis. %} Pratt, John W. (2000) Interviewed by Thomas Eppel, Decision Analysis Newsletter 19, 4–5. {% The paper presents a very elementary and accessible derivation of subjective expected utility that, à la Anscombe-Aumann (1963), uses objective probabilities. Unfortunately, the authors, as do Anscombe-Aumann, use multistage prospects in a heavy manner. %} Pratt, John W., Howard Raiffa, & Robert O. Schlaifer (1964) “The Foundations of Decision under Uncertainty: An Elementary Exposition,” Journal of the American Statistical Association 59, 353–375. {% %} Pratt, John W., Howard Raiffa, & Robert O. Schlaifer (1965) “Introduction to Statistical Decision Theory.” McGraw-Hill, New York. {% Seem to have the ratio-difference principle %} Pratt, John W., David A. Wise, & Richard J. Zeckhauser (1979) “Price Differences in Almost Competitive Markets,” Quarterly Journal of Economics 93, 189–211. {% foundations of statistics %} Pratt, John W. & Robert O. Schlaifer (1988) “On the Interpretation and Observation of Laws.” In Omar F. Hamouda & J.C. Robin Rowley (1997, eds.) “Statistical Foundations for Econometrics.” Edward Elgar, Cheltenham. {% Modify the remarkably successful linear averaging aggregation rule for expert aggregation, by allowing for incompleteness and inconsistency, and doing something like best approximation. %} Predd, Joel B., Daniel N. Osheron, Sanjeev R. Kulkarni, & H. Vincent Poor (2008) “Aggregating Probabilistic Forecasts from Incoherent and Abstaining Experts,” Decision Analysis 5, 177–189. {% %} Prékopa, András & Gergely Mádi-Nagy (2008) “A Class of Multiattribute Utility Functions, Economic Theory 34, 591–602. {% %} Prelec, Drazen (1982) “Matching, Maximizing, and the Hyperbolic Reinforcement Feedback Function,” Psychological Review 89, 189–231. {% P. 27: ‘Two time intervals [t,s] and [t´,s´] have the same discount rate” is a beautiful way the author expresses (t:x) ~ (s:y) and (t´:x) ~ (s´:y). %} Prelec, Drazen (1989) “Decreasing Impatience,” working paper. {% %} Prelec, Drazen (1990) “A ‘Pseudo-Endowment’ Effect and Its Implications for Some Recent Nonexpected Utility Models,” Journal of Risk and Uncertainty 3, 247–260. {% inverse-S; Tradeoff method: in Appendix 1; Introduces some parametric families for probability transformations. Most interesting family I find the two-parameter CI. (compound invariance), w(p) = [exp((ln p))], 0 < < 1, > 0. Expected utility results for = = 1. The smaller the more inverse-S shaped it is, the higher the lower (more pessimistic) the curve. It satisfies subproportionality making it suited for very small probabilities, but also performs well, giving nice inverse-S shape, for not-very-small probabilities. Remarkably, this good empirical family also has a preference axiomatization! It also has other nice analytical properties. Unfortunately, Prelec promotes the one-parameter family with = 1. I think that the two-parameter family is the most important one. Definition 1 (compound invariance) should be restricted to nonzero outcomes and probabilities. x = y = x´ = 0 = p = q = r and y’= 1 = s and s = y´ = 1 provide a counterexample to the condition with 0 probabilities. (Restricting to only nonzero outcomes or to only nonzero probabilities will also work.) (First version: Prelec, Drazen (1989) “On the Shape of the Decision Weight Function,” Harvard Business School, Harvard University, Cambridge, MA, USA.) %} Prelec, Drazen (1998) “The Probability Weighting Function,” Econometrica 66, 497–527. {% DC = stationarity, p. 512 top, but bottom properly mentions the assumption of time invariance “and who resets the zero on the discount function when the next decision arrives” Footnote 1 p. 513 lists empirical violations of stationarity; p. 516 bottom: hybrid model. Considers Pratt-Arrow concavity of log of discount function as index of impatience. The paper throughout treats stationarity and dynamic consistency as if equivalent. P. 526, end of §VI, suggests that time perception may be driven by the numerosity effect. It does not use the term numerosity effect, and refers only to Rubinstein’s similarity model, but it is in fact a general argument for the numerosity effect. %} Prelec, Drazen (2004) “Decreasing Impatience: A Criterion for Non-Stationary Time Preference and “Hyperbolic” Discounting,” Scandinavian Journal of Economics 106, 511–532. {% Prelec (personal communication) credits Shane Frederick for having invented the term truth serum to describe proper scoring rules. probability elicitation. A large group of people all start from the same state of info (common prior à la Harsanyi 1988; logical view of probability à la Carnap). The only difference between people is which one of m possible signals each received. tri = 1 means that person r received signal i (so t can stand for True signal). Then trj = 0 for all j i. Each person is asked to report his signal, where they can lie if they want. xrj = 1 means that person r reports signal j. Then xri = 0 for all i j. x´k (denoted x_bark in paper, but here on internet I cannot implement the bar notation) is the portion of the group reporting signal k; i.e., it is the average of the xrk over r. Every person is also asked to report an estimate of the x´k. yrk is the estimate of person r of x´k. Every person is rewarded for the y anwers and for the x answers, in the following way, where I treat only the case of a=1 in Eq. 2 of Prelec. We will assume hereafter that the group is so large that a single-person’s answers do not influence the group averages. For the single-person optimization problems below, consequently, the group averages are treated as constants. Person 1 (and every other person alike) is rewarded for his y answers through the usual logarithmic proper-scoring rule reward: k x´kln(y1k). (*) (The ln’s are all negative, so he has to pay here.) Given that the x´k are the true population averages, it is well-known that the optimal result is obtained by setting y1k = x´k. Person 1 does not know x´k and must use subjective estimates. It is well known that the person (under subjective expected value maximization) best gives the true subjective estimates of the x´k’s. Person 1 also receives a positive constant amount: k x´kln(x´k). (**) Before we turn to the reward for person 1 for his x answer, first a notation: y´k is the geometric average of yrk over r. That is, ln(y´k) is the average of ln(yrk) over r. Now the reward for person 1 for his x answer is ln(x´k/y´k) where k indicates the answer given. (***) That is, x1k = 1 and x1j = 0 for all j k. The person should therefore seek to answer that k for which, in proportional terms, the population will mostly underestimate the true proportion. (Where they will be most surprised by the true proportion.) This paper assumes that person 1 expects the biggest underestimation by the population, so the biggest surprise x´k/y´k, at his true answer of true signal k. In other words, starting from the info that person 1 has about the others’ opinions, he assumes that his private signal moves closer to the truth. Then incentive compatibility trivially follows. The required assumptions are often not satisfied, (e.g., speaking for myself, if I like a politician then it usually is one that will receive only few votes), and this paper is to be applied only where they are. Often in case of violation something can be done such as embedding the question in more complex questions. Anyway, under the assumptions made you should honestly report your true signal. In total person 1 receives (*) + (***), plus also the constant (**). Because the y-answer of person 1 does not affect (***) and the x-answer does not affect (*), these constitute two independent optimization problems. The one for y-answers serves only to get the true y-answer estimates from each individual, to be used in (***). Several assumptions in this paper are questionable from the practical perspective. The assumption that apart from the private signal received and asked in the question, everything else is common knowledge and is the same for all people, is very very restrictive. But given that, the basic idea is impressive and valuable. The rewards make people tell the truth without requiring that the events in question become observable before payment takes place. This is an impressive achievement distinguishing this paper from traditional proper scoring rules or decision-based elicitations. In principle, we can observe everything of people this way, how happy they feel, and so on. Also, it does not require observability of any prior distribution, resolving a major restriction to the application of proper scoring rules. The paper achieves these things by assuming a group process for the signals and the corresponding subjective probabilities depending on the true beliefs that make the true beliefs observable after all, because the difference between the private signal and the assumed group average is assumed to be in the direction of the believed truth. The paper applies its technique not only to observable questions/signals, where the application is clear-cut, but also to questions such as what people think is “the” or “best” probability estimate, given all the info of mankind, that mankind will survive the coming century. Such concepts of probability are not easy to imagine or think about, so that the application is less clear-cut here. Johnson, Pratt, & Zeckhauser (1990) and others also study truth-revelation mechanisms, but a big difference seems to be that their mechanisms assume the common prior to be known, and Prelec does not need this info. %} Prelec, Drazen (2004) “A Bayesian Truth Serum for Subjective Data,” Science 306, October 2004, 462–466. {% %} Prelec, Drazen (2006) “Rebuilding the Boat while Staying Afloat: The Modeling Challenge for Behavioral Economics,” Journal of Marketing Research 43, 332–336. {% present value; time preference; they nicely list major empirical phenomena, found in several fields, here for time preference, such as decreasing absolute and inceasing proportional sensitivity, which correspond for instance to decreasing absolute (DARA) and increasing relative (IRRA) risk aversion of utility. intertemporal separability criticized; Point out discontinuity at 0 for discounting. %} Prelec, Drazen & George F. Loewenstein (1991) “Decision Making over Time and under Uncertainty: A Common Approach,” Management Science 37, 770–786. {% %} Prelec, Drazen & George F. Loewenstein (1997) “Beyond Time Discounting,” Marketing Letters, 97–108. {% %} Prelec, Drazen & George F. Loewenstein (1998) “The Red and the Black: Mental Accounting of Savings and Debt,” Marketing Science 17, 4–28. {% They reconsider the Prelec (Science, 2004) Bayesian truth serum. They consider now the answer k for which the people selecting that answer received the highest score. Under some assumptions about the relation between the true answer and how people develop their beliefs/probabilities, something like the true answer having a true group percentage most exceeding the estimated average, the method will then with high likelihood select the true answer. %} Prelec, Drazen & H. Sebastian Seung (2007) “An Algorithm That Finds Truth even if Most People Are Wrong,” {% %} Prelec, Drazen & Duncan Simester (2001) “Always Leave Home without It: A Further Investigation of the Credit-Card Effect on Willingness to Pay,” Marketing Letters 12, 5–12. {% %} Prelec, Drazen, Birger Wernerfelt, & Florian Zettelmeyer (1996) “The Role of Inference in Context Effects: Inferring What You Want from What is Available,” Journal of Consumer Research 24, 118–125. {% foundations of statistics %} Press, James (2003) “Subjective and Objective Bayesian Statistics, Principles, Models, and Applications.” Wiley, New York. {% crowding-out: p. 18 seems to question the crowding-out effect. %} Prendergast, Canice (1999) “The Provision of Incentives in Firms,” Journal of Economic Literature 37, 7–63. {% conservation of influence: through illusion of control. A meta-analysis. %} Presson, Paul K. & Victor A. Benassi (1996) “Illusion of Control: A Meta-Analytic Review,” Journal of Social Behavior and Personality 39, 104–113. {% inverse-S, intersecting diagonal at about .2 (for utility linear). Probability transformation seems to be .42 at .50! Certainty equivalents were obtained from bidding games, each time between two persons, where the highest bidder got the prospect. This, obviously, encourages subjects to bid less than the fair price and, hence, we get an overestimation of risk aversion, and strategic behavior as a horrible confound. The tendency to overbid, and winner’s curse, lead to biases that reduce risk aversion. questionnaire versus choice utility: p. 184 footnote 3: “also by purely social scientists (e.g. J. von Neumann and O. Morgenstern, Theory of Games and Economic Behavior, 1944, 1-641). … It is interesting to note that these writers appear to hold the understanding of economic phenomena without recourse to psychological theory as a worthwhile ideal (a familiar theme for those acquainted with the efforts in psychology to understand psychological phenomena without recourse to physiological theory).” Likelihood-sensitivity (inverse-S) ordering: unsophisticated men exhibit least, then sophisticated subjects, then women, in the sense that the first category has least overweighting of small probabilities and least underweighting of high probabilities (see Table II) (gender differences in risk attitudes). That sophisticated men deviate more from linearity than unsophisticated is strange, and deviates from the authors’ suggestion on pp. 191 line 1 (“while it may reduce them [effects]”). It makes me wonder if the unsophisticated-men and sophisticated-subects have been interchanged in Table II. linear utility for small stakes: they use linear utility. They justify this by pointing out that for small probabilities there is risk seeking, for large there is risk aversion, irrespective of what the prizes are (pp. 187-188; inverse-S). A strong argument deserving more attention also now, in 2015! %} Preston, Malcolm G. & Philip Baratta (1948) “An Experimental Study of the Auction Value of an Uncertain Outcome,” American Journal of Psychology 61, 183–193. {% cognitive ability related to risk/ambiguity aversion: has the data but does not seem to report this. correlation risk & ambiguity attitude: has the data but does not seem to report this. Follow-up on Abdellaoui, Klibanoff, & Placido (2015) and Halevy (2007). Better arithmetic test ==> better RCLA. Framing also affects relation RCLA and ambiguity aversion. No clear relation is found. Ambiguity is generated by starting from known composition, and then letting students randomly take out some things, unknown to all. This is in fact 2nd order probabilities. (second-order probabilities to model ambiguity). The thing it is to be related to. Use certainty equivalents (through choice list and RIS) to measure all attitudes. Ambiguity neutral likelihoods were always 0.5. Index of risk aversion is risk premium normalized by dividing by maximum outcome, and ambiguity aversion index is difference between that and its analog for ambiguity. So ambiguity aversion is indeed how much uncertainty deviates from risk, which is my preferred definition. For between-subject comparisons, the main purpose of this study, the indexes are OK. But they are not very well suited for comparisons to other studies, for one reason because dividing by the maximum outcome provides overcorrection, implementing local risk and ambiguity neutrality. Yet such measures are widely used in the literature. %} Prokosheva, Sasha (2017) “Comparing Decisions under Compound Risk and Ambiguity: The Importance of Cognitive Skills,” Journal of Behavioral and Experimental Economics 64, 94–105. {% P. 1383: that decision analysis is mostly used at group level. %} Protheroe, Joanne, Tom Fahey, Alan A. Montgomery, & Tim J. Peters (2000) “The Impact of Patients’ Preferences on the Treatment of Atrial Fibrillation: Observational Study of Patient Based Decision Analysis,” British Medical Journal 320, 1380–1384. {% conservation of influence; argue that intelligence is goal-oriented, and that getting this is the big problem in AI. %} Prudkov, Pavel N. (2010) “A View on Human Goal-Directed Activity and the Construction of Artificial Intelligence,” Minds & Machines 20, 363–383. {% Paradoxes of finite additivity and infinitesimals. %} Pruss, Alexander R. (2014) “Infinitesimals are too Small for Countably Infinite Fair Lotteries,” Synthese 191, 1051–1057. {% Used epicycles (midpoints of circles themselves circle around other midpoints) to explain planetary movements. Seems to have argued that this need not be going on physically, but it is only a mathematical model that happens to fit the planetary movements. So, that it was paramorph. %} Ptolemy, Claudius (150) “Almagest.” {% %} Puelz, Robert & Arthur Snow (1994) “Evidence on Adverse Selection: Equilibrium Signaling and Cross-Subsidization in the Insurance Market,” Journal of Political Economy 102, 236–257. {% SG correlated better with validation measures. %} Puhan, Milo A., Holger J. Schünemann, Eric Wong, Lauren Griffith, & Gordon H. Guyatt (2007) “The Standard Gamble Showed Better Construct Validity than the Time Trade-off,” Journal of Clinical Epidemiology 60, 1029–1033. {% Real incentives: not clear. P. 1082 describes instructions: “If you get a blue marble, you will be entered into a lottery draw with a cash prize.” I saw no other info on it. So I’m not sure if incentives are for real, and what the cash prize was or its probability. Footnote 1 p. 1084 refers to a nonpublished treatment with: between-random incentive system (paying only some subjects). The author writes precisely and accurately about concepts in a clear way that often is not psychologists’ strongest point. A pleasure to read! suspicion under ambiguity: the author does the Ellsberg experiment where subjects cannot choose the color to gamble on. However, here it is not a mistake as it is in so many sloppy experiments, but here it is done very deliberately so as to invest suspicion about rigging the balls. In one treatment ambiguity is nothing but second-stage probability and there is no reason to suspect the experimenter has rigged the balls except when the experimenter did outright lying (which often happens especially in psychology where it sometimes cannot be avoided). In the other treatment no info is given and there is more reason to suspect rigging of the balls. The author concludes (p. 1086, end of penultimate para): “Future researchers, using the two-colour Ellsberg urns task, with a specified target colour to be drawn, should also consider the issue of trust in the experimenter not to rig the urn, as this needs controlling for if pure ambiguity aversion is to be measured.” %} Pulford, Briony D. (2009) “Is Luck on My Side? Optimism, Pessimism, and Ambiguity Aversion,” Quarterly Journal of Experimental Psychology 62, 1079–1087. {% %} Pulford, Briony D. & Andrew M. Colman (2007) “Ambiguous Games: Evidence for Strategic Ambiguity Aversion,” Quarterly Journal of Experimental Physiology 60, 1083–1100. {% Subjects play lotteries, not knowing they are rigged. The subjects who were lucky (or thought so) became more ambiguity seeking. So, it is a spillover effect. This was in the first experiment. It did not replicate in four follow-up experiments. Men are more ambiguity averse for gains but not for losses. Ambiguity is generated by 2nd order probability. Not in the first, but in the 2nd experiment, subjects could choose the gaining color as control for suspicion. (suspicion under ambiguity) %} Pulford, Briony D. & Poonam Gill (2014) “Good Luck, Bad Luck, and Ambiguity Aversion,” Judgment and Decision Making 9, 159–166. {% questionnaire versus choice utility: derive utilities from discrete latent choice models, and from TTO, and investigate correlations (are big) and ways to transform one into the other. %} Pullenayegum, Eleanor & Feng Xie (2013) “Scoring the 5-Level EQ-5D: Can Latent Utilities Derived from a Discrete Choice Model Be Transformed to Health Utilities Derived from Time Tradeoff Tasks?,” Medical Decision Making 33, 567–578. {% Door Wenny gepresenteerd in referaat op 1 december 1993. %} Puma, John la & Edward F. Lawlor (1990) “Quality-Adjusted Life Years; Ethical Implications for Physicians and Policymakers,” JAMA 263, 2917–2921. {% Writes down the form of outcome dependent capacity; %} Puppe, Clemens (1990) “Preference Functionals with Prize-Dependent Distortion of Probabilities,” Economics Letters 33, 127–131. {% %} Puppe, Clemens (1990) “Distorted Probabilities and Choice under Risk,” Springer Lecture notes 363. Springer, Berlin. {% fuzzy sets %} Puppe, Clemens (1994) “Rational Choice Based on Vague Preferences,” Annals of Operations Research 52, 67–81. {% preference for flexibility %} Puppe, Clemens (1995) “Freedom of Choice and Rational Decisions,” Social Choice and Welfare 12, 137–153. {% preference for flexibility %} Puppe, Clemens (1996) “An Axiomatic Approach to “Preference for Freedom of Choice”,” Journal of Economic Theory 68, 174–199. {% Do Gilboa-Schmeidler minimax when outcome sets for different states need not be identical, but have sufficient overlap to do the scaling of priors and so on. %} Puppe, Clemens & Karl H. Schlag (2009) “Choice under Complete Uncertainty when Outcome Spaces Are State-Dependent,” Theory and Decision 66, 1–16. {% %} Puri, Manju, & David T. Robinson (2007) “Optimism and Economic Choice,” Journal of Financial Economics 86, 71–99. {% %} Puri, Manju, & David T. Robinson (2013) “The Economic Psychology of Entrepreneurship and Family Business,” Journal of Economics and Management Strategy 22, 423–444. {% Shows that intertemporal preferences have to reckon with subjective preferences if the market is not perfect, with different borrowing and lending rates. %} Pye, Gordon (1966) “Present Values for Imperfect Capital Markets,” Journal of Business 39, 45–51. {% Seems to describe wishful thinking: assigning higher likelihood to preferred outcome; (inverse-S (= likelihood insensitivity) related to emotions ?) %} Pyszczynski, Thomas A. (1982) “Cognitive Strategies for Coping with Uncertain Outcomes,” Journal of Research in Personality 16, 386–399. {% Generalize additive representations by imposing separability (they use Reidemeister condition) on subsets. First they derive a general additive representation V(x,z) + V(y,z) for (x,y) for each fixed level of z. Then they use that to generalize many results in the literature, such as Rohde’s (2010) preference foundation of the Fehr-Schmidt welfare model, rank-dependent utility, linear representations in mixture spaces, and other things. %} Qin, Wei-zhi & Hendrik Rommeswinkel (2017) “Conditionally Additive Utility Representations,” working paper. {% Tradeoff method: use it like Abdellaoui (2000), for gains. Replicate the Abdellaoui (2000) non-parametric measurement method with N=124. inverse-S: strangely enough, find convex w more than concave or inverse-S. It shows that probability weighting is rather volatile. (I would say that basic utility is most stable, then probability weighting is second, and loss aversion is the least.) A nice addition that this paper gives: even though conceptually and theoretically, probability weighting is a new component, it would not be very worthwhile if it was strongly related to utility curvature statistically. This paper finds that it is not strongly related, so that it does explain additional variance in the data. They also reanalyze the data of Bleichrodt & Pinto (2000), finding the same result. They could not reanalyze the data of Abdellaoui (2000) because those are lost. Utility deviates from linearity and is concave. %} Qiu, Jianying & Eva-Maria Steiger (2011) “Understanding the Two Components of Risk Attitudes: An Experimental Analysis,” Management Science 57, 193–199. {% correlation risk & ambiguity attitude: find a strong positive correlation %} Qiu, Jianying & Utz Weitzel (2012) “Reference Dependent Ambiguity Aversion: Theory and Experiment,” working paper. {% DOI 10.1007/s11166-016-9244-9 The authors measure multiple priors, but take the term in an unconventional sense. On the one hand it refers to two-stage probabilities, on the other hand to single priors entertained by other students in the experiment. The latter is equated, for an event, with its matching probability. They equate these two, calling this equation a leap of faith (p. 57), but giving arguments. Thus they get the two-stage structure of the smooth model. For the smooth model they allow using information about 2nd order distribution, but for maxmin not, and then smooth fits data better. %} Qiu, Jianying & Utz Weitzel (2016) “Experimental Evidence on Valuation with Multiple Priors,” Journal of Risk and Uncertainty 53, 55–74. {% %} Qiu, Jianying & Utz Weitzel (2016) “Reference Dependence and Aversion to Losses in Probabilities: Theory and Experiment of Ambiguity Attitudes," working paper, Radboud University, Nijmegen, the Netherlands. {% Provides arguments against libertarian paternalism typical of philosophers. It says that libertarian paternalists can’t be SURE that they maximize welfare and happiness, using “there is no reason that” claims, and being “potentially flawed,” and “it is not clear that,” “only imperfect guidance” So it questions everything but gives no alternatives. P. 656 end of 2nd para: only a few LP proposals would survive democratic debate. P. 657 adds that autonomy has a value of its own. Pp 657/658 argue that to do LP right, and to know welfare right, would require infinite calculative ability which is not available. %} Qizilbash, Mozaffar (2012) “Informed Desire and the Ambitions of Libertarian Paternalism,” Social Choice and Welfare 38, 647–658. {% probability elicitation: if we have an incentive compatible mechanism for measuring the subjective probability of one event E, then we can do if for a set of events by letting the subject report the subjective probability for each event in the set, then randomly selecting one, and applying the mechanism to that event. We use here a dynamic assumption such as backward induction. The author does this where the set of events concerns all cumulative events in a continuous probability distribution, and links it with Karni (2009). %} Qu, Xiangyu (2012) “A Mechanism for Eliciting a Probability Distribution,” Economic Letters 115, 399–400. {% Axiomatizes multiple priors in Anscombe-Aumann framework, like Gilboa & Schmeidler (1989), but adds a set of unambiguous events characterized by satisfying regular independence. %} Qu, Xiangyu (2013) “Maxmin Expected Utility with Additivity on Unambiguous Events,” Journal of Mathematical Economics 49, 245–249. {% Axiomatizes multiple priors, but adds a set of unambiguous events characterized by satisfying regular EU axion. This paper modifies Qu (2013 JME) by not using Anscombe-Aumann and instead using techniques of Alon & Schmeidler (2014). %} Qu, Xiangyu (2015) “Purely Subjective Extended Bayesian Models with Knightian Unambiguity,” Theory and Decision 79, 547–571. {% Defines more ambiguity averse as Yaari-type bigger preference for certainty equivalents through a hypothetical intermediate decision maker who has the same utility function as one decision maker and the same weighting function as the other. Ambiguity neutrality is probabilistic sophistication. Ambiguity aversion is being pointwise dominated by a probability measure (so, a Core element). More ambiguity averse amounts to pointwise dominance of the weighting function. The latter results are in the spirit of Epstein and Ghirardato & Marinacci. %} Qu, Xiangyu (2015) “A Belief-Based Definition of Ambiguity Aversion,” Theory and Decision 79, 15–30. {% A behavioral axiomatization of mean-variance maximization without assuming expected utility. The probabilities are subjective. I did not study the paper enough to understand how preference axioms such as strict quasi-concavity can use probabilities as input if those are subjective. %} Qu, Xiangyu (2017) “Subjective Mean–Variance Preferences without Expected Utility,” Mathematical Social Sciences 87, 31–39. {% Gives a necessary and sufficient condition for a demand function to be monotonic. Formulates it in terms of a condition that is invariance w.r.t. ordinal transformations of utility, and relates it to the Pratt-Arrow index of concavity of the vNM utility function (that is one of the members of the set of all ordinal utility functions). Seems to be that Pratt-Arrow measure in each direction of the commodity space should not vary by more than 4. %} Quah, John K.-H. (2003) “The Law of Demand and Risk Aversion,” Econometrica 71, 713–721. {% %} Quaid, Kimbery A. & Michael Morris (1993) “Reluctance to Undergo Predictive Testing for Huntington’s Disease,” American Journal of Medical Genetics 45, 41–45. {% %} Quattrone, George A. & Amos Tversky (1986) “Self-Deception and the Voter’s Illusion.” In John Elster (ed.) The Multiple Self, 35–58, Cambridge University Press, New York. {% P. 727, ratio-difference principle: “impact of any fixed positive difference between two positive amounts increases with their ratio.” As formulated, it describes concavity only. %} Quattrone, George A. & Amos Tversky (1988) “Contrasting Rational and Psychological Analyses of Political Choice,” American Political Science Review 82, 719–736. {% utility measurement: correct for probability distortion. First publication of anticipated utility (not Quiggin, 1982!), though it was written after Quiggin (1982). This is a nice paper, clear and accessible, with good ideas on utility measurement. inverse-S biseparable utility %} Quiggin, John (1981) “Risk Perception and Risk Aversion among Australian Farmers,” Australian Journal of Agricultural Economics 25, 160–169. {% Was published first as Bureau of Agricultural Economics working paper, 1980, and before that in 1979 as part of thesis for Honours degree. inverse-S: p. 326: “Typically events at extremes of the range of outcomes are likely to be overweighted.” biseparable utility %} Quiggin, John (1982) “A Theory of Anticipated Utility,” Journal of Economic Behaviour and Organization 3, 323–343. {% %} Quiggin, John (1982) “A Note on the Existence of a Competitive Optimum,” Economic Record 55, 174–176. {% %} Quiggin, John (1983) “Underwriting Agricultural Commodity Prices,” Australian Journal of Agricultural Economics 27, 200–211. {% %} Quiggin, John (1985) “Anticipated Utility, Subjectively Weighted Utility and the Allais Paradox,” Organisational Behavior and Human Performance 35, 94–101. {% %} Quiggin, John (1986) “Anticipated Utility: Some Developments in the Economic Theory of Uncertainty,” Ph.D. Thesis, University of New England, Australia. {% %} Quiggin, John (1987) “On the Nature of Probability Weighting: Response to Segal,” Journal of Economic Behavior and Organization 8, 641–645. {% %} Quiggin, John (1988) “Increasing Risk: Another Definition,” University of Sydney. {% %} Quiggin, John (1989) “Sure Things—Dominance and Independence Rules for Choice under Uncertainty,” Annals of Operations Research 19, 335–357. {% %} Quiggin, John (1990) “Stochastic Dominance in Regret Theory,” Review of Economic Studies 57, 503–511. {% Explains Friedman-Savage (1948) and gambling. %} Quiggin, John (1991) “On the Optimal Design of Lotteries,” Economica 58, 1–16. {% Seems to propose, for random variables X,Y, that X(s)Y(s) 0, i.e., that they are cosigned. %} Quiggin, John (1991) “Increasing Risk—Another Definition.” In Attila Chikàn et al. (eds.) Progress in Decision, Utility and Risk Theory, Kluwer Academic Publishers. {% P. 122: DC = stationarity Very unfortunately, the book applies the weighting function to badnews events and not, as is common nowadays, to goodnews events. So, concavity of the weighting function here is convexity in the modern literature, and so on. P. 76 footnnote 15 argues, and I agree, that it would be better to have the term risk aversion only refer to probabilistic attitude, independent of utility function. I proposed this terminology in early versions of Wakker (1994 Theory and Decision), but received so many criticisms that I gave up; it is too late. %} Quiggin, John (1993) “Generalized Expected Utility Theory - The Rank-Dependent Model.” Kluwer Academic Publishers, Dordrecht. {% %} Quiggin, John (1993) “Testing between Alternative Models of Choice under Uncertainty—Comment,” Journal of Risk and Uncertainty 6, 161–164. {% %} Quiggin, John (1994) “Regret Theory with General Choice Sets,” Journal of Risk and Uncertainty 8, 153–165. {% Background risk can “destroy” most of rank dependence, because the background risk mostly determines the ranking position of outcomes that can be all over the place. This paper shows a weaker result, being that background risk can reduce the risk premium under constant relative and constant absolute risk aversion. %} Quiggin, John (2003) “Background Risk in Generalized Expected Utility Theory,” Economic Theory 22, 607–611. {% Proposes value of info (about probabilities) as index of ambiguity (aversion), and shows that for Machina’s almost objective events it tends to 0 in the limit. %} Quiggin, John (2007) “Ambiguity and the Value of Information: An Almost-Objective Events Analysis,” Economic Theory 30, 409–414. {% Separates value of awareness and value of information, which sum to a constant. %} Quiggin, John (2016) “The Value of Information and the Value of Awareness,” Theory and Decision 80, 167–185. {% %} Quiggin, John & Jock R. Anderson (1981) “Price Bands and Buffer Funds,” Economic Record 57, 67–73. {% CARA (constant absolute risk aversion) and CRRA jointly are very restrictive. The authors propose a weakening. %} Quiggin, John & Robert G. Chambers (2004) “Invariant Risk Attitudes,” Journal of Economic Theory 117, 96–118. {% %} Quiggin, John & Peter P. Wakker (1994) “The Axiomatic Basis of Anticipated Utility; A Clarification,” Journal of Economic Theory 64, 486–499. Link to paper
Quine, Williard V. (1951) “Two Dogmas of Empiricism,” Philosophical Review 60, 20–43. Reprinted in From a Logical Point of View, 1953, Harvard University Press, Cambridge, MA. {% %} Quirk, James P. & Rubin Saposnik (1962) “Admissibility and Measurable Utility Functions,” Review of Economic Studies 29, 140–146. {% Discuss Binswanger (1981), and argue that Binswanger throughout assumed outcomes in terms of final wealth, and did not consider reference dependence. They discuss in particular for a study of relative risk aversion that one should compare U(w+x), with w initial wealth, to U(aw + ax) and not, as they argue, as Binswanger did, to U(w+ax). %} Quizon, Jaime, Hans P. Binswanger, & Mark J. Machina (1984) “Attitudes towards Risk: Further Remarks,” Economic Journal 94, 144–148. {% They recommend that one QALY should not take more than €80,000. %} Raad voor de Gezondheidszorg (2006, June 27) “Zinnige en Duurzame Zorg.” Report for Minister of Health. {% %} Raaij, W. Fred (1997) “The Life and Work of Amos Tversky,” Journal of Economic Psychology 14, 721–740. {% %} Rabin, Matthew (1990) “Communication between Rational Agents,” Journal of Economic Theory 51, 144–170. (Corrigendum 1992, Journal of Economic Theory 58, 110–111.) {% %} Rabin, Matthew (1993) “Information and the Control of Productive Assets,” Journal of Law, Economics, and Organization 9, 51–75. {% %} Rabin, Matthew (1993) “Incorporating Fairness into Game Theory and Economics,” American Economic Review 83, 1281–1302. {% %} Rabin, Matthew (1994) “Cognitive Dissonance and Social Change,” Journal of Economic Behavior and Organization 23, 177–194. {% %} Rabin, Matthew (1994) “Incorporating Behavioral Assumptions into Game Theory.” In James Friedman (ed.) Problems of Coordination in Economic Activity, Kluwer Academic Publishers, Norwell, MA. {% %} Rabin, Matthew (1994) “A Model of Pre-Game Communication,” Journal of Economic Theory 63, 370–391. {% %} Rabin, Matthew (1996) “Daniel Kahneman and Amos Tversky.” In Warren Samuels (ed.) American Economists of the Late Twentieth Century, 111–137, Edward Elgar Publishing Ltd, Cheltehem. {% %} Rabin, Matthew (1997) Review of Kenneth J. Arrow, Enrico Colombatto, Mark Perlman, & Christian Schmidt (eds.) The Rational Foundations of Economic Behaviour, MacMillan Press Ltd, 1996, Journal of Economic Literature 35, 2045–2046. {% Survey of many empirical psychological findings of deviations from standard classical economic assumptions on preference. %} Rabin, Matthew (1998) “Psychology and Economics,” Journal of Economic Literature 36, 11–46. {% %} Rabin, Matthew (1999) “Comment on ‘What Me Worry? A Psychological Perspective on Economic Aspects of Retirement,’ by George F. Loewenstein, Drazen Prelec, & Roberto Weber.” In Henry Aaron (ed.) Behavioral Dimensions of Retirement Economics, The Brookings Institution. {% %} Rabin, Matthew (2000) “Diminishing Marginal Utility of Wealth Cannot Explain Risk Aversion.” In Daniel Kahneman & Amos Tversky (eds.) Choices, Values, and Frames, Ch. 11, 202–208, Cambridge University Press, New York. {% The reasoning on p. 1282, 3rd para, is, for EU with concave utility: Assume expected utility with concave utility U, and consider the following ASSUMPTION. A person prefers a sure amount $M to a gamble (.5, $M+11; .5, $M10), for each level of wealth M. Then u´(M+11)/u´(M10) < 10/11 for all M. In other words, u´(x+21)/u´(x) < 10/11 for all x. Then u´(11)/u´(10) < 10/11, u´(32)/u´(11) < 10/11, etc. The assumption implies that U is very concave for large amounts of money, and is unsatisfactorily concave. For example, U´(x+21)/U´(x) is at most 10/11 and, therefore, U´(x+2100)/U´(x) is at most (10/11)100 = 0.00007; etc. Compare this with constant absolute risk averse (CARA) implying linear-exponential utility, which is also overly concave for large amounts. CARA is a condition of the kind “for all lotteries and all probabilities …”. That is, it is a mathematical condition whose empirical (un)reasonableness is not transparent. Rabin’s condition, imposing the invariance w.r.t. M only for one natural preference with moderate stakes, makes the empirical restrictiveness of the Assumption more tangible and shocking. In footnote 2, Rabin points out that the basic idea was presented before by Hansson (1988). Hansson’s presentation was, however, way less convincing. The conclusion is that expected utility advocates should abandon the displayed assumption. However, the Assumption can be restricted to bounded intervals for M where it is empirically convincing and still implies concavity of utility too extreme to be plausible. linear utility for small stakes: this is the basic message of this paper. It has been well known that utility is approximately linear for small stakes. This statement is a mathematical fact without much empirical relevance yet because “approximately” and “small” have no clear meaning. Rabin mentions concrete numbers and, thus, makes it clear that this point is empirically relevant. People who really want the displayed assumption, may want to adopt a nonEU theory. For example, prospect theory with M as status quo and then loss aversion may explain much of the empirical realism of the above assumption. risky utility u = strength of preference v (or other riskless cardinal utility, often called value): footnote 3, p. 1282, says that he finds the psychological interpreting of vNM utility the natural way to think about vNM utility. If the amounts 10 and 11 in the assumption are replaced by 10/ and 11/ for positive , then the concavity of U gets larger as gets larger and becomes infinite if goes to infinity (so the betting odds 10:11 are not accepted no matter how small the stake). That is, U then kind of explodes. EU advocates cannot have this. This point reflects that a concave U is almost everywhere differentiable so is approximately linear for small amounts of money. Empirically, it will matter a lot if people psychologically integrate M into the outcome (final wealth) as expected utility requires or do not in the Assumption. Prospect theory says they don’t and then loss aversion can explain the findings. Rabin recommends loss aversion as main factor to explain in the last para of the main text, pp. 1288-1289. The result can be reinforced by assuming that a person only declines this 50-50 +11 versus 10 gamble at the current state of wealth, but has concave utility and decreasing ARA (absolute risk aversion) so that he also declines the gamble for all smaller initial wealths. This point is alluded to on p. 1283-1284, with no mention of decreasing ARA, unfortunately. Kahneman & Tversky (1979, p. 277): “The certainty equivalent of the prospect (1,000, .50), for example, lies between 300 and 400 for most people, in a wide range of asset positions.” Christiane, Veronika & I: p. 1287 discusses relation between small-stakes and large-stakes risk attitudes. In particular, footnote 10 points out the related difficulties for the coefficient of relative risk aversion. Samuelson (1963) also showed that risk aversion in the small can imply implausible risk aversion in the large. Rabin’s argument is, however, more convincing. Its preference assumption is less extreme (rejecting 110.5(10) versus rejecting 2000.5(100)), its domain-assumption is less demanding (Samuelson needs invariance of his assumed preference over a large wealth range [10,000, +20,000]), and its conclusions are stronger (See Rabin’s footnote 11, p. 1288). %} Rabin, Matthew (2000) “Risk Aversion and Expected-Utility Theory: A Calibration Theorem,” Econometrica 68, 1281–1292. {% %} Rabin, Matthew (2002) “Inference by Believers in the Law of Small Numbers,” Quarterly Journal of Economics 117, 775–816. {% %} Rabin, Matthew (2002) “A Perspective on Psychology and Economics,” European Economic Review 46, 657–685. {% Discusses behavioral economics, that it brings in more psychological inputs, but should maintain precision and prediction. The journal gives the author the space to give many examples, where the author himself contributed much. %} Rabin, Matthew (2013) “Incorporating Limited Rationality into Economics,” Journal of Economic Literature 51, 528–543. {% Bayes’ formula intuitively; confirmatory bias: many many refs %} Rabin, Matthew & Joel L. Schrag (1999) “First Impressions Matter: A Model of Confirmatory Bias,” Quarterly Journal of Economics 114, 37–82. {% %} Rabin, Matthew & Joel Sobel (1996) “Deviations, Dynamics, and Equilibrium Refinements,” Journal of Economic Theory 68, 1–25. {% Comments see the above reference Rabin (2000, Econometrica). The result is also discussed in The Economist of August 11, 2001. P. 222 explicitly brings up that the preferences are assumed for all wealth levels. P. 223, erroneously, writes for Samuelson’s colleague that, under EU, rejecting the 2000.5(100) once should imply rejecting independent repetions, but it is very well known that this is not true (Liu & Colman 2009 p. 278). It is only true if [2000.5(100) once] is rejected at every wealth level that can occur during the process, something that is implied for instance by constant absolute risk aversion. Pp. 227-228 discusses money pumps. You can get people into small books when there are small transaction costs, e.g. people who, when subscribing to the phone company, in one blow take wiring insurance. P. 228: “All said, myopic loss averters are subject to many short Dutch chapters in their lives, but not to Dutch books.” %} Rabin, Matthew & Richard H. Thaler (2001) “Anomalies: Risk Aversion,” Journal of Economic Perspectives 15, 219–232. {% Develop a theory for the hot-hand fallacy, and derive implications. %} Rabin, Matthew & Dimitri Vayanos (2010) “The Gambler's and Hot-Hand Fallacies: Theory and Applications,” Review of Economic Studies 77, 730–778. {% real incentives/hypothetical choice: find no differences. Dutch book: do it only for statistically independent prospects. Prove that under EU no-book/arbitrage then implies exponential utility. %} Rabin, Matthew & Georg Weizsäcker (2009) “Narrow Bracketing and Dominated Choices,” American Economic Review 99, 1508–1543. {% %} Rabinowicz, Wlodzimierz (1987) “Ratifiability and Stability.” In Peter Gärdenfors & Nils-Eric Sahlin (eds.) Decision, Probability, and Utility, 406–427, Cambridge University Press, Cambridge. {% conditional probability %} Rabinowicz, Wlodzimierz (1989) “On Probabilistic Representation of Nonprobabilistic Belief Revision,” Journal of Philosophical Logic 18, 69–101. {% %} Rabinowicz, Wlodzimierz (1995) “To Have One’s Cake and Eat It: How to Make Sequential Choices when One’s Preferences Violate Expected Utility Axioms,” Journal of Philosophy 112, 586–620. {% dynamic consistency: argues that Seidenfeld’s criticism of McClennen is incorrect. %} Rabinowicz, Wlodzimierz (1997) “On Seidenfeld’s Criticism of Sophisticated Violations of the Independence Axiom,” Theory and Decision 43, 279–292. {% dynamic consistency %} Rabinowicz, Wlodzimierz (2000) “Preference Stability and Substitution of Indifferents: A Rejoinder to Seidenfeld,” Theory and Decision 4, 311–318. {% concave utility for gains, convex utility for losses: finds evidence for that, convex for low incomes and concave for high. Develops a somewhat complex but pragmatic model where utility depends on reference points. Those are related to both intertemporal and social comparisons. The author makes pragmatic heuristic assumptions about these dependencies, and fits parameters for UK gross income data in 2002. %} Rablen, Matthew D. (2008) “Relativity, Rank and the Utility of Income,” Economic Journal 118, 801–821. {% Tested, according to Larrick (1993) prospect theory for animals. %} Rachlin, Howard (1989) “Judgment, Decision, and Choice: A Cognitive/Behavioral Synthesis.” Freeman, San Francisco. {% Not downloadable, strangely enough. %} Rachlin, Howard (2006) “Notes on Discounting,” Journal of the Experimental Analysis of Behavior 85, 425–435. {% dynamic consistency: p. 16 has the basic decomposition of stationarity à la consequentialism, dynamic consistency, prior commitment. They assume stopwatch time. Use a very simple model of discounting through 1/t. P. 17 credits Ainslie, unpublished, for a similar setup, described in a Rachlin (1970) book. P. 21 has nice argument that t=0 is impossible (to defend against 1/t being undefined there. Pigeon experiment was not clear to me. How about the time pigeons are waiting before making the next pick? It is hard to imagine how pigeons conceive of pre-commitment. P. 22 has strange discussion of experiment with children who, having to wait, sometimes fell asleep, and the authors explaining that as a very deliberate devise to help self-control, rather than pure boredom which I find more plausible. %} Rachlin, Howard & Leonard Green (1972) “Commitment, Choice and Self-Control,” Journal of the Experimental Analysis of Behavior 17, 15–22. {% Take social distance between people as primitive, measured through kind of introspection and test how it affects others-regarding, to find that it gets kind of discounted but stronger than intertemporal discounting. Eq. 2, referenced Rachlin (2006), is the same family as used by Goldstein & Einhorn (1987, Eqs. 22-24), also ascribed to Lattimore et al. (1992). DC = stationarity: p. 31 2nd para %} Rachlin, Howard & Bryan A. Jones (2008) “Social Discounting and Delay Discounting,” Journal of Behavioral Decision Making 21, 29–43. {% %} Rachlin, Howard, David I. Laibson, & Joeri Gorter (1998) “The Matching Law: Papers in Psychology and Economics,” Economic Journal 449, 1192–1193. {% Tested, according to Larrick (1993) prospect theory for animals; seem to point out relation between high discounting and certainty effect. %} Rachlin, Howard, Alexandra W. Logue, John Gibbon, & Marvin Frankel (1986) “Cognition and Behavior in Studies of Choice,” Psychological Review 93, 33–45. {% Seem to use Mazur (1987) discounting function, to use hypothetical questions, to assume linear utility, and fitted data at an individual level, but gives no info about outliers like increasing impatience. %} Rachlin, Howard, Andres Raineri, & David Cross (1991) “Subjective Probability and Delay,” Journal of the Experimental Analysis of Behavior 55, 233–244. {% %} Racine, Amy, A.P. Grieve, & H. Flühler (1986) “Bayesian Methods in Practice: Experiences in the Pharmaceutical Industry,” Applied Statistics 35, 93–150. {% P. 150 seems to claim that a local brother of Thomsen condition implies the globale version. Is it 1949 iso 1959? Cluj is city in Transylvania in Rumenia. %} Rado, François (1959) “Équations Fonctionnelles Caractérisant les Nomogrammes avec Trois Échelles Rectilignes,” Mathematica Universitatae Cluj 1, 143–166. {% Seem to show that subjects’ paying more attention may exacerbate rather than attenuate biases. %} Raghubir, Priya & Aradhna Krishna (1996) “As the Crow Flies: Bias in Consumers’ Map-Based Distance Judgments,” Journal of Consumer Research 23, 26–39. {% %} Raghubir, Priya & Joydeep Srivastava (2002) “Effect of Face Value on Product Valuation in Foreign Currencies,” Journal of Consumer Research 29, 335–347. {% Replies to Ellsberg’s violation of the sure-thing principle. On p. 694, Raiffa considers a fifty-fifty mixture of two ambiguous gambles and a fifty-fifty mixture of two preferred unambiguous gambles. His “strict dominance” argument requires that the second mixture be preferred. It is similar to Luce’s consequence monotonicity or Segal’s compound independence. His “objectively identical” claim is based on reduction (for events) and leads to the conclusion that the two mixtures are identical, and therefore equivalent. Because of the contradictory preferences that have resulted, Raiffa suggests that the original preference for the unambiguous gambles be changed. Of course, his argument has used all components of the vNM independence condition. P. 690, on Savage’s theory: “It is a theory which purports to advise any one of its believers how he should behave in complicated situations, provided he can make choices in a coherent manner in relatively simple, uncomplicated situations.” P. 690/691 states that a normative theory can be useful only if it sometimes !deviates! from actual behavior: “If most people behaved in a manner roughly consistent with Savage’s thory then the theory would gain stature as a descriptive theory but would lose a good deal of its normative importance. We do not have to teach people what comes naturally.” The same point is stated, but disliked, by McCord & De Neufville (1983), p. 281. %} Raiffa, Howard (1961) “Risk, Uncertainty and the Savage Axioms: Comment,” Quarterly Journal of Economics 75, 690–694. {% Risk averse for gains, risk seeking for losses: Good elementary textbook for getting to understand construction of decision trees, backward induction, and value of information. Ch. 3 on cost of sampling may be less central. Ch. 6 is kind of AA and can be skipped. Ch. 7 is a bit much on economics of sampling, and value of info. Ch. 8 is on risk sharing for groups. These could be skipped by someone interested only in individual decision under risk. Preface p. ix-x: says book is about rational decisions as if this is all decision making, then brings only aggregation of uncertainty, and then casually mentions that uncertainty is a central topic. Risk averse for gains, risk seeking for losses: p. 75: in Fig. 4.18 Raiffa suggested that people prefer 1000.50 to 45; i.e., they are risk seeking there. Download 7.23 Mb. Share with your friends:
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