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| §7 propagates constructive proofs of preference foundations, that show how the subjective concepts can be measured. If self-references can be allowed, I always week for such constructive proofs, as explained for instance in Step 4 of the five steps in Wakker (2010 p. 8), in Abdellaoui & Wakker (2018) “Savage for Dummies,” and so on.
p. 304: “If one assumes that the axioms are satisfied, then the definitions in terms of preferences (Def-pref) seem to satisfy the strictest empiricist and operationalist criteria. Indeed, they correspond to what Carnap (1936/1937) refers to as ‘explicit definitions. These theorems, and more specifically the [constructive] proofs discussed above, contain explicit definitions of decision-theoretic concepts that, in the eyes of an anti-holist … , are preferable to the Lewis definitions.” The authors suggest repeatedly, e.g. p. 306 l. 15, that behavioral economics attaches less importance to behavioral foundations than was done before. I don’t see this. Of course, behavioral models can be explicitly nonnormative, and then there obviously is less interest in normative preference foundations. But there then is more interest in descriptive preference foundations. %} Cozic, Mikael & Brian Hill (2015) “Representation Theorems and the Semantics of Decision-Theoretic Concepts,” Journal of Economic Methodology 22, 292–311. {% Multiple priors, with definition of independence, Kyburg’s argument against convexity of that set, and several mathematical tools developed. This paper is a nice reference to the large literature on sets of priors outside of decision theory. %} Cozman, Fabio G. (2012) “Sets of Probability Distributions, Independence, and Convexity,” Synthese 186, 577–600. {% Extend results on prudence and so on to risk seekers. %} Crainich, David, Louis Eeckhoudt, & Alain Trannoy (2013) “Even (Mixed) Risk Lovers are Prudent,” American Economic Review 103, 1529–1535. {% utility families parametric: first proposes bounded utility in order to resolve St. Petersburg paradox, described by Nicolas Bernoulli in 1713; then proposes, alternatively, square-root utility for money. Nicolas is a cousin of Daniel, the one who wrote the famous EU paper in 1738. So Cramer’s letter proposed EU 10 years before Daniel! Daniel correctly cites and credits Cramer. His text can be interpreted as saying that in a truncated version of the St. Petersburg paradox risk neutrality is not unreasonable. 24 tosses have expected value of 13 ducates which Cramer judges as reasonable. %} Cramer, Gabriel (1728) Letter from Cramer to Nicholas Bernoulli. Translated into English by Louise Sommer in Bernoulli, Daniel (1954) “Exposition of a New Theory on the Measurement of Risk,” Econometrica 22, 23–36. {% foundations of statistics %} Cramer, Harald (1981) “Mathematical Probability and Statistical Inference.” In Omar F. Hamouda & J.C. Robin Rowley (1997, eds.) “Statistical Foundations for Econometrics.” Edward Elgar, Cheltenham. {% %} Crawford, Ian (2010) “Habits Revealed,” Review of Economic Studies 77, 1382–1402. {% %} Crawford, Vincent P. (1990) “Equilibrium without Independence,” Journal of Economic Theory 50, 127–154. {% %} Crawford, Vincent P., Miguel Costa-Gomes, & Nagore Iriberri (2013) “Structural Models of Nonequilibrium Strategic Thinking: Theory, Evidence, and Applications,” Journal of Economic Literature 51, 5–62. {% Restores the reference-dependent explanation of the Cab drivers finding of Camerer et al. (1997) by using the Köszegi & Rabin (2006) reference dependence. %} Crawford, Vincent P. & Juanjuan Meng (2011) “New York City Cab Drivers’ Labor Supply Revisited: Reference-Dependent Preferences with Rational-Expectations Targets for Hours and Income,” American Economic Review 101, 1912–1932. {% Two experts and a decision maker all maximize maxmin expected utility. A Pareto optimality condition is equivalent to the priors of the decision making being a convex combination of the priors of the experts. %} Crès, Hervé, Itzhak Gilboa, & Nicolas Vieille (2011) “Aggregation of Multiple Prior Opinions,” Journal of Economic Theory 146, 2563–2582. {% Propose monotonicity/continuity criteria that cannot be reconciled with symmetry. %} Crespo, Juan Alfons, Carmelo Nuñez, & Juan Pablo Rincón-Zapatero (2009) “On the Impossibility of Representing Infinite Utility Streams,” Economic Theory 40, 47–56. {% About the British NICE H/E evaluations. %} Cressey, Daniel (2009) “life in the Balance,” Nature 461/17 September 2009, 336–339. {% common knowledge: agents receive private signals that are independent over time, but not over agents. If signal space is finite, approximate common knowledge will develop, if infinite then need not. %} Cripps, Martin W., Jeffrey C. Ely, George J. Mailath, & Larry Samuelson (2008) “Common Learning,” Econometrica 76, 909–933. {% %} Crone, Eveline A. & Maurits W. van der Molen (2004) “Developmental Changes in Real Life Decision Making: Performance on a Gambling Task Previously Shown to Depend on the Ventromedial Prefrontal Cortex,” Developmental Neuropsychology 25, 251–279. {% %} Cropper, Maureen L., Sema K. Aydede, & Paul R. Portney (1994) “Preferences for Live Saving Programs: How the Public Discounts Time and Age, Journal of Risk and Uncertainty 8, 243–265. {% %} Crosby, Fave (1976) “A Model of Egoistical Relative Deprivation,” Psychological Review 83, 85–113. {% questionnaire for measuring risk aversion: the authors introduce the BRET (bomb risk elicitation task) method: subjects can choose a number of boxes from 100 boxes. One of those contains a bomb. Payment is linear in nr. of boxes if no bomb (10 €-cents times), and 0 if bomb. Risk neutrality implies choosing 50 boxes. The authors consider both a dynamic version, choosing boxes one by one until stop-decision, and all-in-once version. They analyze the data assuming EU with power (CRRA) utility. A good move: whether or not the boxes selected contain the bomb is determined only at the end of the experiment, thus avoiding truncation. Hence the bomb is called time bomb. The authors favor the dynamic version, but my hunch is to prefer the all-in-once version because the dynamic version does not inform subjects that their choices will influence future options offered. Nice, and similar to balloon task of Lejuez et al. (2002) which the authors cite. These are all variations of the Binswanger (1981) method. Even closer, and maybe nicer (for not referring to the emotional bomb) is the Columbia card task by Figner et al. (2009, Journal of Experimental Psychology 35, 709–730), which the authors are unaware of, maybe because it is in a psychological journal. decreasing ARA/increasing RRA: in one task, they double the stakes. It leads to higher relative risk aversion, confirming the common increasing RRA. In another treatment, they let subjects first make some money from another task, and then carry out the bomb task. Then they find no clear result, with risk aversion increasing for prior gains between 0 and €2.7, but decreasing after, so no clear results on increasing/decreasing ARA. I think that whatever effects the prior gains have, these are psychological effects other than wealth effects, because the prior gains are too small to generate real wealth effects. gender differences in risk attitudes: analyzed in §3.2, where a reference point of €2.5 is framed in. Here, and in several places, the authors claim to find that women are more loss averse then men, but their results in fact are not significant. Women are not more risk averse otherwise. This agrees with Booij & van de Kuilen (2009). The authors’ BRET method has some less risk aversion than other methods, which surprises me because I would expect the term bomb to generate risk aversion. %} Crosetto, Paolo & Antonio Filippin (2013) “The “Bomb” Risk Elicitation Task,” Journal of Risk and Uncertainty 47, 31–65. {% P. 615 Footnote 2: BDM is difficult. Analyze four ways to elicit risk attitudes: multiple price lists (I prefer the efficient term price list; bw., to me this is not a specific risk elicitation, but in general a way to obtain indifferences), ordered lottery selection à la Binswanger (1981), investment game, and bomb elicitation. They also do general introspection. They first analyze the different methods using simulations, to see what differences are due to the methods. Then they investigate in experiment. There they find differences more than what the methods themselves induce, showing that the underlying risk theory is violated. Unfortunately, the authors implicitly assume EU throughout (stated only on p. 631), with constant relative risk aversion (CRRA), so, logpower utility. Much is known about violations of EU which gives insights into what happens here, but, as often in experimental economics (Holt & Laury 2002), the authors ignore this literature. They find that the presence or not of a riskless, sure, option matters a lot. This is no surprise given that the certainty effect is about the main cause of EU violations. The authors do mention this point on p. 637 2nd para in the discussion. They don’t find clear superiority of any method. %} Crosetto, Paolo & Antonio Filippin (2016) “A Theoretical and Experimental Appraisal of Four Risk Elicitation Methods,” Experimental Economics 19, 613–641. {% probability elicitation: applied to experimental economics %} Croson, Rachel (2000) “Thinking like a Game Theorist: Factors Affecting the Frequency of Equilibrium Play,” Journal of Economic Behavior and Organization 41, 299–314. {% gender differences in risk attitudes &? gender differences in ambiguity attitudes (?): review, a.o., gender differences in risk attitudes. Women more risk averse than men. %} Croson, Rachel & Uri Gneezy (2009) “Gender Differences in Preferences,” Journal of Economic Literature 47, 448–474. {% %} Crouzeix, Jean-Pierre & Per Olov Lindberg (1986) “Additively Decomposed Quasiconvex Functions,” Mathematical Programming 35, 42–57. {% Do what title says, following up on %} Crupi, Vincenzo, Nick Chater, & Katya Tentori (2013) “New Axioms for Probability and Likelihood Ratio Measures,” British Journal for the Philosophy of Science 64, 189–194. {% Compare risk attitude measurements that use choice lists. In standard gamble questions (finding indifference between a sure outcome and a two-outcome prospect) matching, through choice list, on the highest outcome works best. The distinction between matching on various of the entries was also discussed by Farquhar (1984). %} Csermely, Tamás & Alexander Rabas (2016) How to “Reveal People’s Preferences: Comparing Time Consistency and Predictive Power of Multiple Price List Risk Elicitation Methods,” Journal of Risk and Uncertainty 53, 107–136. {% Coherent measures of risk are used to distribute diversification benefits over portfolios. %} Csóka, Péter, P., Jean-Jacques Herings, & László Á. Kóczy (2009) “Stable Allocations of Risk,” Games and Economic Behavior 67, 266–276. {% dynamic consistency; see Alias-literature %} Cubitt, Robin P. (1996) “Rational Dynamic Choice and Expected Utility Theory,” Oxford Economic Papers 48, 1–19. {% “We cannot observe plans, only actions.” %} Cubitt, Robin P. (1997) discussion at FUR conference in Mons 1997. {% Discuss the BDM (Becker-DeGroot-Marschak) mechanism and random incentive mechanism, referring to the independence-violation criticism of this mechanism leveled at the end of the 1980s. They do not refer to the counterarguments based on isolation published in later papers such as Cubitt, Starmer, & Sugden (1998), which are referred to only for other reasons. Instead they use an alternative design, claimed not to be subject to the same criticism. At first it was not clear to me why the alternative design would not be subject to the same independence-violation criticism. The logic seems to be as follows: even if there is no isolation, no systematic differences of directions of preference reversals can be expected. So, although they have a random lottery, they have a stronger test for preference reversals because they need not rely on the isolation demonstrated in Cubitt, Starmer, & Sugden (1998). %} Cubitt, Robin P., Alistair Munro, & Chris Starmer (2004) “Testing Explanations of Preference Reversals,” Economic Journal 114, 709–726. {% Preference elicitation where subjects indicate CEs and are rewarded by some BDM (Becker-DeGroot-Marschak) procedure. In addition, subjects are asked to indicate an interval for the CE value, where they doubt. This is not incentivized (would be hard to find incentivization). The authors investigate factors influencing the intervals. %} Cubitt, Robin P., Daniel Navarro-Martinez, & Chris Starmer (2015) “On Preference Imprecision,” Journal of Risk and Uncertainty 50, 1–34. {% time preference; The paper analyzes experimental intertemporal choice from a purely theoretical perspective, assuming that there are market opportunities outside the laboratory of borrowing or lending at the market interest rate, and assuming a perfectly rational optimizing agent. It argues that there then is no easy way to experimentally elicit the subjective interest rate, for instance. The paper in particular discusses Coller & Williams (1999), which also addressed this question. This C&R paper is the best to cite on this problem. I think that an argument against perfect-market driven is the individual variation in measured discount rates. %} Cubitt, Robin P. & Daniel Read (2007) “Can Intertemporal Choice Experiments Elicit Time Preferences for Consumption?,” Experimental Economics 10, 369–389. {% dynamic consistency: use the term separability for what is often called consequentialism in dynamic decision making under risk, and which here entails both indendence of forgone acts and of forgone events. Test the condition and do not find it violated, even though the subjects do violate independence/EU. %} Cubitt, Robin, Maria Ruiz-Martos, & Chris Starmer (2012) “Are Bygones Bygones?,” Theory and Decision 73, 185–202. {% Compare, for choices between simple lotteries, the random incentive system to single-choices (with real payment), and find they are not different, confirming their 91-AER finding. This paper adds to it a check of cross-task contamination, which is something between complete isolation and complete no-isolation I understand. Seems that they also test (paying only some subjects) (between-random incentive system). P. 116 takes single choices as gold standard: “We define true preferences with respect to a given task as those that would be elicited by single choice experimental design in which each subject faces onlym that task, and knows it to be for real.” [italics from original] Birnbaum (1992 Contemporary Psychology) gives counterarguments. They conclude that isolation may hold for simple stimuli as studied in their paper, but can still be violated for complex stimuli, citing Beattie & Loomes (1997) for it. %} Cubitt, Robin P., Chris Starmer, & Robert Sugden (1998) “On the Validity of the Random Lottery Incentive System,” Experimental Economics 1, 115–131. {% dynamic consistency. Nicely split the static vNM independence condition for risk (that axiomatizes EU) into four dynamic decision principles: separability (I’d prefer the term forgone-event independence), timing independence (I’d prefer the term time consistency), frame independence (I’d prefer the term decision-tree independence), and reduction. I disagree with them suggesting that frame independence would be the one that Kahneman & Tversky in their prospect theory would want to give up so as to explain violations of independence. K&T consider its violations of frame independence, but never commit to other conditions not being violated. They find that timing independence is mostly violated (e.g. p. 1378). %} Cubitt, Robin P., Chris Starmer, & Robert Sugden (1998) “Dynamic Choice and the Common Ratio Effect: An Experimental Investigation,” Economic Journal 108, 1362–1380. {% Discuss Plott’s discovered preference hypothesis versus the constructive view of preference. Then discuss their experimental methods where each participant will only make one choice in one situation, which should not mean that the participant is not well-instructed or -trained. Para on pp. 401/ 402 says that people commonly find power utility with power 0.3 (so RRA = 1 0.3 = 0.7). Says that utility in terms of final wealth can, in fact, not explain this, and outcomes must be reference dependent. P. 401 second half suggests that if subjects by learning and repetition get closer to EU, it may be not because their true preferences are EU and are better revealed, but because subjects better learn to use heuristics independently of true. preference and these heuristics, rather than true preference, may get closer to EU. P. 402 writes: “…are entirely explained by the relative sizes and relative probabilities of the payoffs in each task. This striking regularity….We cannot eliminate the possibility that the regularity is induced by context-dependent heuristics which are learned in the course of these experiments.” This is very reminiscent of Stalmeier’s proportional heuristic for time-tradeoff questions in the health domain. It is like their shaping hypothesis as they call it in later papers (e.g. Loomes, Starmer, & Sugden 2003 EJ), but the term is not yet used here. %} Cubitt, Robin P., Chris Starmer, & Robert Sugden (2001) “Discovered Preferences and the Experimental Evidence of Violations of Expected Utility Theory,” Journal of Economic Methodology 8, 385–414. {% Nash bargaining solution: p. 761 extensively discusses the (weakness of) assuming vNM utility in game theory. P. 770 4th para explains that transitivity is a kind of separability requiring separate preferability of each individual prospect. So that it is kind of unitary evaluation, in Burks’ (1977) terminology. %} Cubitt, Robin P. & Robert Sugden (1998) “The Selection of Preferences through Imitation,” Review of Economic Studies 65, 761–771. {% dynamic consistency; Dutch book, etc.; gives formal definition of money pump, relating it to the sure-thing principle; argues, citing Fishburn (1988 pp. 43-44), that an agent would not take all trades knowing several trades are to come. They formalize “surprise choices,” being choices not announced beforehand. %} Cubitt, Robin P. & Robert Sugden (2001) “On Money Pumps,” Games and Economic Behavior 37, 121–160. {% dynamic consistency; Assume some independent boxes, each with probability p a win box and with probability 1p a loss box (p may depend on box). A participant is endowed with an initial endowment b > 0, and m > 0 is a constant. At each round, if the participant draws a win box, then his endowment of that moment is multiplied by m, if a loss box then by 0 (so the game is over with no gain). Participants can choose to take 0, 1, or 2 (extra) rounds. Some do only this (de novo). Others, prior to this choice, had to take 4 compulsory rounds, and only if they win all these they get the choice. Of these others, some do prior commitment, others do posterior choice. This framework is the usual test of consequentialism and dynamic consistency. Given the dynamic framing, no common ratio effect is to be predicted a priori, as shown by Kahneman & Tversky (1979). What emotions the prior-commitment rounds arouse, I could not predict. It turned out that they make the participants less risk seeking, so lead to a reversed common ratio. In the beginning of the paper, the authors present a formal model way more complex than used in the experiment, and they discuss several general issues of decision theory before turning to their particular experiment. %} Cubitt, Robin P. & Robert Sugden (2001) “Dynamic Decision-Making under Uncertainty: An Experimental Investigation of Choices between Accumulator Gambles,” Journal of Risk and Uncertainty 22, 103–128. {% %} Cubitt, Robin, Gijs van de Kuilen, & Sujoy Mukerji (2013) “Sensitivity towards Ambiguity: A Qualitative Test and a Measurement,” working paper. {% one-dimensional utility: %} Cui, Zhenyu (2014) “Comment on “Modeling Non-Monotone Risk Aversion Using SAHARA Utility Functions” [J.Econ.Theory 146 (2011) 2075–2092],” Journal of Economic Theory 153, 703–705. {% utility elicitation %} Culyer, Anthony J. & Adam Wagstaff (1993) “QALYs versus HYEs,” Journal of Health Economics 11, 311–323. {% real incentives/hypothetical choice; hypothetical WTP is higher than real WTP; participants could borrow cash if not with them, would then have to sign loan agreement; such practical complications may have deterred them in the real WTP! %} Cummins, Robert G., Glenn W. Harrison, & E. Elisabet Rutström (1995) “Homegrown Values and Hypothetical Surveys: Is the Dichotomous Choice Approach Incentive-Compatible?” American Economic Review 85, 260–266. {% ambiguity seeking for unlikely: well, only null hypothesis there. Curley & Yates (1989, JMP) do find it and suggest that this paper lacks power. They assume that p is unknown in an interval [R2, R1] with midpoint C. Thus, boundary effect precludes high ambiguity for extreme values C. P. 282: for C .45, they find ambiguity aversion, for C .40 they find null hypothesis. Fig. 6 might suggest an ambiguity-seeking trend below C = .2, with weird counterevidence when both choices have ambiguity but one has larger ambiguity-interval than the other (the most ambiguous of the two has probability zero as option, the other hasn’t, which might enhance ambiguity aversion). ambiguity avoidance increases with probability of winning whenever second-order probabilities assign positive probability to 0 probability (second-order probabilities to model ambiguity) %} Curley, Shawn P. & J. Frank Yates (1985) “The Center and Range of the Probability Interval as Factors Affecting Ambiguity Preferences,” Organizational Behavior and Human Decision Processes 36, 273–287. {% ambiguity seeking for unlikely: finds clear ambiguity seeking for “central unknown probability” p= .25, and ambiguity aversion for p = .50 and p = .75. %} Curley, Shawn P. & J. Frank Yates (1989) “An Empirical Evaluation of Descriptive Models of Ambiguity Reactions in Choice Situations,” Journal of Mathematical Psychology 33, 397–427. {% Always real incentives with RIS. Find that “other-evaluation” hypothesis, (choice should be justifiable to others) explains ambiguity aversion. Do usual two-color Ellsberg in five ways. 1 (hostile nature). Ask subjects if they think that the unknown urn will be biased to their disfavor. 2 (other-evaluation). Subjects must stand in front of the whole group when their choice is revealed and the content of the unknown urn is also revealed. 3 (self-evaluation). Content of unknown urn is revealed to subject but in private, others don’t know. 4 (forced choice). People are actually indifferent and ambiguity avoidance is second-order lexicographic. 5 (general uncertainty avoidance). Ambiguity avoidance is related to risk aversion, general aversion to lacking info. (If true, would imply correlation risk & ambiguity attitude.) Only 3 (self-evaluation) is found to have an effect. P. 253 contains a strange argument suggesting that accepting the null hypothesis does give strong evidence. Which it, however, does not! They gave subjects normative arguments for and against ambiguity aversion, as did Slovic & Tversky (1974). 80% preferred to be ambiguity averse. correlation risk & ambiguity attitude: find none. P. 239: Experiment 1 finds no correlation between risk- and ambiguity aversion, but N = 26 is small. Experiment 2 (N = 39) confirms this (p. 241), also if the data of the two experiments are pooled. %} Curley, Shawn P., J. Frank Yates, & Richard A. Abrams (1986) “Psychological Sources of Ambiguity Avoidance,” Organizational Behavior and Human Decision Processes 38, 230–256. {% Multiattribute preferences can be approximated well by additive representations. %} Currim, Imran S. & Rakesh K. Sarin (1984) “A Comparative Evaluation of Multiattribute Consumer Preference Models,” Management Science 30, 543–561. {% The analysis of for example value function etc. essentially uses OPT which I consider to be less interesting. Unlike the authors, I here use the OPT abbreviation of the 1979 version of prospect theory End of abstract: - for the paradoxical choices, OPT outperforms EU - on other choices it does not do better utility elicitation; Download 7.23 Mb. Share with your friends:
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