Bibliography
§V argues that regret is not irrational
Download 7.23 Mb.
|
| §V argues that regret is not irrational.
P. 818: probabilistic reduction is called the “equivalence axiom.” utility = representational, p. 817: “While we do not share the methodological position that the only satisfactory theories are those formulated entirely in terms of empirical propositions, …” Some drawbacks of regret theory: (1) The psychological regret that explains much of common ratio, is fundamentally different than what regret theory does. It is that if an outcome 0 has certainty of foregoing sure $1M (M: million), then regret is strong, but if it is only a probability of foregoing $1M then regret almost entirely disappears. It is a nonlinearity in probability, a sort of certainty effect. It then is important that the regret of getting the smallest outcome 0 iso the second-smallest $1M is big. The regret theory explanation goes in the other direction: the regrets of getting the smallest outcome 0 iso the 2nd-smallest outcome 1M, and of getting the 2nd smallest outcome 1M iso the largest outcome, should be relatively small, and the regret of getting the smallest iso the highest outcome should be disproportionally large. So the regret of getting 0 iso 1M should not be big, but small. This is unrelated to what happens in reality. By implying the sure-thing principle regret theory is not well suited for explaining Allais. (2) Regret is clearly a second-order effect relative to utility difference. Probability weighting, for instance, is an independent component that may explain even more than utility, but regret is second-order and only adds nuances. %} Loomes, Graham & Robert Sugden (1982) “Regret Theory: An Alternative Theory of Rational Choice under Uncertainty,” Economic Journal 92, 805–824. {% %} Loomes, Graham & Robert Sugden (1983) “Regret Theory and Measurable Utility Theory,” Economics Letters 12, 19–22. {% %} Loomes, Graham & Robert Sugden (1983) “A Rationale for Preference Reversal,” American Economic Review 73, 428–432. {% %} Loomes, Graham & Robert Sugden (1984) “The Importance of What Might Have Been.” In Ole Hagen & Fred Wendstøp (eds.) Progress in Utility and Risk Theory, 219–235, Reidel, Dordrecht. {% information aversion; Argue that regret theory is not open to aversion to information. P. 650: “Thus we do not accept that the apparently remarkable result of the farmer rejecting costless perfect information is achieved ‘via the principles of regret theory’,” %} Loomes, Graham & Robert Sugden (1984) “Regret Theory and Information: A Reply,” Economic Journal 94, 649–650. {% dynamic consistency: what they call dynamic consistency is what Machina (1989) and others call consequentialism (and what I like to call forgone-event independence in March 2000). This paper introduces their disappointment model, similar to Bell (1985) biseparable utility: yes for the special case where their disappointment function has a kink but is linear otherwise. %} Loomes, Graham & Robert Sugden (1986) “Disappointment and Dynamic Consistency in Choice under Uncertainty,” Review of Economic Studies 53, 271–282. {% %} Loomes, Graham & Robert Sugden (1987) “Testing for Regret and Disappointment in Choice under Uncertainty,” Economic Journal 97, Supplement, 118–129. {% utility = representational, P. 272: “Here “utility” is to be interpreted in the classical Benthamite or Bernouillian [Bernoullian] sense, as a sensation or mental state.” Beginning of §4 shows that transitivity implies that (x,y) + (y,z) = (x,z) (called regret neutrality). §II.7 of Sugden (2004) “Alternatives to Expected Utility” shows that regret neutrality implies expected utility. Therefore, regret theory reduces to expected utility if and only if transitivity. The same point is stated by Kreweras (1961). %} Loomes, Graham & Robert Sugden (1987) “Some Implications of a More General Form of Regret Theory,” Journal of Economic Theory 41, 270–287. {% Best core theory depends on error theory: seems to be; error theory for risky choice; refer to BDM (Becker-DeGroot-Marschak) for random utility model, not to literature from mathematical psychology. Point out that different assumptions about stochastic choice have different predictions, such as degree of violations of stochastic dominance. %} Loomes, Graham & Robert Sugden (1995) “Incorporating a Stochastic Element into Decision Theory,” European Economic Review 39, 641–648. {% error theory for risky choice; %} Loomes, Graham & Robert Sugden (1998) “Testing Different Stochastic Specifications of Risky Choice,” Economica 65, 581–598. {% Introduction to pref. reversal; rest, however, is only on preference cycles for losses, whether as predicted by regret theory; real incentives/hypothetical choice; they find on p. 259 that actual and hypothetical choices are similar %} Loomes, Graham & Caron Taylor (1992) “Non-Transitive Preferences over Gains and Losses,” Economic Journal 102, 357–365. {% %} Loomes, Graham & Martin Weber (1996) “Endowment Effects for Risky Assets.” In Wulf Albers, Werner Güth, & Eric van Damme, Experimental Studies of Strategic Interaction: Essays in Honor of Reinhard Selten, 494–512, Springer, Berlin. {% %} Loonstra, Frans (1946) “Ordered Groups” Koninklijke Academie der Wetenschap Amsterdam, 49, 41–46. {% %} Lootsma, Freerk A. (1993) “Scale Sensitivity in the Multiplicative AHP and SMART,” Journal of Multi-Criteria Decision Analysis 2, 87–110. {% %} Lopes, Lola L. (1981) “Decision Making in the Short Run,” Journal of Experimental Psychology, Human Learning and Memory 7, 377–385. {% %} Lopes, Lola L. (1982) “Doing the Impossible: A Note on Induction and the Experience of Randomness,” Journal of Experimental Psychology, Learning, Memory, and Cognition 8, 626–636. {% Seems to write: “the simple, static lottery or gamble is as indispensable to research on risk as is the fruitfly to genetics” (p. 137). %} Lopes, Lola L. (1983) “Some Thoughts on the Psychological Concept of Risk,” Journal of Experimental Psychology: Human Perception and Performance 9, 137–144. {% This paper is one of the predecessors of rank-dependent utility; sign-dependence: says that gains and losses are often treated separately in applications. P. 482: first evaluate gain part, then loss part, then combine these two, possibly additively. Proposes that choices be determined by EV and “riskiness,” where latter is cumulative distributional thing. She proposes to not yet introduce the utility function. Gives motivation that weights should depend on rank-ordering of outcomes, but then gives examples (such as where probability of winning $50 or more decides) that do not show rank-dependence as in the modern RDU. Predicts pessimism; i.e., lower outcomes get greater weight. Does give arguments where there is the idea, implicitly, that cumulative events rather than receipt of fixed outcomes, are natural primitives. %} Lopes, Lola L. (1984) “Risk and Distributional Inequality,” Journal of Experimental Psychology: Human Perception and Performance 10, 465–485. {% Nice intro on behaviorism and switch to cognitive models in psychology. Gives arguments that participants more naturally think in terms of cumulative events than in terms of fixed outcomes. Uses this finding to argue for cumulative approaches! Wow! %} Lopes, Lola L. (1986) “What Naive Decision Makers Can Tell Us about Risk.” In Luciano Daboni, Aldo Montesano, & Marji Lines (eds.) Recent Developments in the Foundations of Utility and Risk Theory, 311–326, Reidel, Dordrecht. {% P. 258: SEU = SEU P. 283: “Risk attitude is more than the psychophysics of money” Gives arguments that participants more naturally think in terms of cumulative events than in terms of fixed outcomes. Uses this finding to argue for cumulative approaches! Seems to use the term “cautiously-hopeful” for inverse-S. %} Lopes, Lola L. (1987) “Between Hope and Fear: The Psychology of Risk,” Advances in Experimental Social Psychology 20, 255–295. {% Cardinal utility is psychophysical entity: French school P. 407: the term risk aversion has nothing to do theoretically either with risk or with aversion %} Lopes, Lola L. (1988) “Economics as Psychology: A Cognitive Assay of the French and American Schools of Risk Theory.” In Bertrand R. Munier (ed.) Risk, Decision and Rationality, 405–416, Reidel, Dordrecht. {% Multioutcome lotteries; conclude that PT does not do well; seems that “cautiously hopeful” is her term for inverse-S %} Lopes, Lola L. (1990) “Re-Modeling Risk Aversion: A Comparison of Bernoullian and Rank Dependent Value Approaches.” In George M. von Furstenberg (ed.) Acting under Uncertainty: Multidisciplinary Conceptions, 267–299, Kluwer, Dordrecht. {% %} Lopes, Lola L. (1993) “Reasons and Resources: The Human Side of Risk Taking.” In Nancy J. Bell & Robert W. Bell (eds.) Adolescent Risk Taking, 29–54, Sage, Lubbock TX. {% review %} Lopes, Lola L. (1994) “Psychology and Economics - Perspectives on Risk, Cooperation, and the Marketplace,” Annual Review of Psychology 45, 197–227. {% Links process-oriented theories to algebraic decision theories. inverse-S: p. 207 gives many citations to extent to which people pay attention to good and bad outcomes. linear utility for small stakes: p. 215 explains why utility is assumed linear. %} Lopes, Lola L. (1995) “Algebra and Process in the Modeling of Risky Choice,” Psychology of Learning and Motivation 32, 177–220. {% Writes very positive about her, I think confused, 1981 paper. %} Lopes, Lola L. (1996) “When Time is of the Essence: Averaging, Aspiration, and the Short Run,” Organizational Behavior and Human Decision Processes 65, 179–189. {% %} Lopes, Lola L. & Gregg C. Oden (1987) “Distinguishing between Random and Nonrandom Events,” Journal of Experimental Psychology: Learning, Memory, and Cognition 13, 392–400. {% There is a clear definition of SP/A theory, clearer than Lopes’ papers, in Ch. 26 of Shefrin, Hersh M. (2008) “A Behavioral Approach to Asset Pricing Theory; 2nd edn.” In SP/A theory, a prospect (lottery over money) depends on (1): SP. This is a rank-dependent utility, with linear utility, and a weighting function that is a convex combination of a power function pr and a dual power function 1 (1p)r´, where the first captures pessimism and the second optimism. For the claims about mixed weighting functions in Eqs. 9 and 10 (p. 290), it is important to know that the parameters qr and qp are supposed to be positive (I assume), so that the w-weighted curve is convex and the (1w) weighted curve is concave, and the convex mix gives an inverse-S shape. (2) A: an aspiration level, i.e. an outcome, is chosen, and A is the probability of (weakly!?) exceeding it. How these two are combined, is explicitly left unspecified. P. 291 end of penultimate para writes that, if these two components prefer a different prospect (so, if the case is not totally trivial), then SP/A predicts “conflict.” This gives a revealed-preference oriented economist little hope of being informed about what choice then results. The text then writes that such conflict cannot result from “single-criterion” models such as CPT (p.s.: CPT and all economic models can consider multi-criteria optimization in utility), which further reduces my hope of being informed about the resulting choice in any not-completely-trivial situation. P. 300 2nd para will mention an aggregation of the two components but it is not clear how, apparently through a nmerical Table 5. The first para on p. 292 confuses monotonicity with absolute risk aversion, and erroneously claims that CPT would have constant absolute risk aversion. Although in several places the paper writes that it, unlike prospect theory, has no reference point but instead an aspiration level, SP/A theory turns out to have a reference point still because it does distinguish between gains and losses, where every parameter in the model (including probability weighting, contrary to what Shefrin, 2008, p. 429 last sentence, claims) can depend on the sign (pp. 290-291 & 299). In particular, the aspiration level can be different for gains than for losses (then how about mixed prospects?), and will later (p. 300 top) be taken to be 0 for losses and, ad hoc, 1 for gains. P. 302, Eq. 16 suddenly does aggregate SP and A into a decision formula, although it is a probabilistic choice model, with no deterministic model specified. For me, the formula comes out of the blue, seeming to assign the same weight to SP as to A. (I’d expect SP to have more weight.) Does this satisfy stochastic dominance? Some form of transitivity? P. 310 penultimate para has a nice text on risk aversion being conflated with utility. Shefrin (2008 p. 431 bottom) writes that the weighting function in prospect theory captures perception, but in SP/A it captures emotions. In Table 5 it is amazing that the very crude A-criterion alone (just the probability of exceeding aspiration, which is nothing but probabilities related to 0) explains data so well. Then SP/A will do better than PT! Makes me wonder about the stimuli. PT falsified: not strongly. Mostly, Lopes’ SP/A theory fits data better than her implementation of PT (which is questionable given that she, erroneously, thinks that PT satisfies constant absolute risk aversion. 1. convex utility for losses: for losses subjects are risk-neutral more than risk-seeking 2. Subjects seem to prefer (0.5, 50; 0.5, 150) to 100 for sure. Seems to agree with Lopes SP/A theory, while violating PT. Risk averse for gains, risk seeking for losses: seem to be risk neutral for losses; multioutcome lotteries. loss aversion without mixed prospects: they claim to estimate loss aversion , but they do not consider mixed prospects and, therefore, it is impossible to estimate . linear utility for small stakes: p. 290 footnote 1 %} Lopes, Lola L. & Gregg C. Oden (1999) “The Role of Aspiration Level in Risky Choice: A Comparison of Cumulative Prospect Theory and SP/A Theory,” Journal of Mathematical Psychology 43, 286–313. {% real incentives/hypothetical choice: a sender randomly sees a blue or green circle. Then sends message to receiver if it was green or red. Gets €15 if signaling green (independent of what was really seen) and €14 if signaling blue. 1/3 of the subjects rather sends true signal than most-gaining signal: lie aversion. %} López-Pérez, Raúl & Eli Spiegelman (2013) “Why Do People Tell the Truth? Experimental Evidence for Pure Lie Aversion,” Experimental Economics 16, 233–247. {% %} Lopomo, Giuseppe & Efe A. Ok (2001) “Bargaining, Interdependence, and the Rationality of Fair Division,” RAND Journal of Economics 32, 263–283. {% real incentives/hypothetical choice: on p. 51, they justify their use of hypothetical choices rather than real incentives as follows: “The experimental approach will by necessity be limited to small gambles, whereas we were interested in lotteries with very large payoffs.” Risk averse for gains, risk seeking for losses: not found. They asked 17 shipowners for certainty equivalents of 11 gambles, with outcomes between 10 and +100 and probabilities between 1/6 and 5/6, mostly 1/2. The data are remarkable. People are risk seeking under (imaginary) good liquidity, risk neutral or risk averse under weak liquidity. Probably fun through Utility of gambling was going on. %} Lorange, Peter & Victor D. Norman (1973) “Risk Preference in Scandinavian Shipping,” Applied Economics 5, 49–59. {% confirmatory bias: participants received info about capital punishment, which led to polarization iso the, normatively to be expected, convergence to neutrality %} Lord, Charles G., Lee Ross, & Mark R. Lepper (1979) “Biased Assimilation and Attitude Polarization: The Effects of Prior Theories on Subsequently Considered Evidence,” Journal of Personality and Social Psychology 37, 2098–2109. {% Methoden & Technieken %} Lord, Frederic M. & Melvin R. Novick (1968) “Statistical Theories of Mental Test Scores,” Addison-Wesley, London. {% measure of similarity %} Lord, Philip W., Robert D. Stevens, Andy Brass, & Carole A. Goble (2003) “Investigating Semantic Similarity Measures across the Gene Ontology: the Relationship between Sequence and Annotation,” Bioinformatics 19, 1275–1283. {% This paper, in a prominent journal, with quite some citations, and coverage in the popular press, is very very weak. It illustrates how the academic system can malfunction. It is interesting because of its extremity and I, hence, provide details. Wisdom of the crowd: imagine asking many individuals to estimate something, say the weight of a particular cow (Dalton 1907). Let w denote the true weight, xi the estimate of individual i, and x the average (arithmetic or geometric) or median estimate, depending on context; I will write average in what follows. The individual estimates can be far off (|xiw|’s large), but sometimes not systematically so, and then |xw| can be small meaning that x is a good estimate of w. The latter can be surprisingly good, of course depending much on the stimuli considered. If surprisingly good, people use the term wisdom of the crowd, or wisdom of crowds. This paper studies the wisdom of the crowd. Individuals estimate, being rewarded for small distance from truth, and it is inspected whether group average is close to truth, where the latter is (to be) taken as wisdom of group-as-a-whole. In a first round, subjects just submit their estimates. Then in later rounds they receive feedback about the estimate of one or a few or all others, and then can change their estimate. Unsurprisingly, and shown by many studies, the estimations usually converge, giving same group-average but smaller within-group group variance. (Some paradoxical opposite findings, usually for emotionally loaden topics such as the desirability of capital punishment with no clear true answer and with richer information-sharing, are known as confirmatory bias.) This convergence is also the empirical finding of this paper. What the paper adds is many provocative, but all erroneous, interpretations. Although many statistic books warn against interpreting a null found, the authors do interpret their null of group average x not being affected by their ways of information sharing. And although I would interpret their ways of info sharing then as irrelevant to the goodness of group prediction, x not being affected, the authors interpret their null as “undermining” for wisdom of the crowd. They seem to have in mind that wisdom of the crowd is driven by group diversity and that hence every decrease in group diversity is bad, forgetting that the real criterion is how close x is to w and that group diversity is only an instrument to make x get close to w. If not the average w were the criterion, but something like the union of the info of the members of the group, then it could be different and diversity could be desirable. This point may underly many interpretations of the authors although it should not do so in the situation specified by the authors themselves (where only |xw| matters). With some effort, I could think of a situation in which group diversity does impove the group average: if we vary the group diversity under the condition of keeping the average individual distance, so the average of |xiw|, fixed. So, not the distance of the average, but the average of the distance, is kept fixed. This condition is very rarely satisfied, and absolutely not in the experiments of this paper. My best guess for this paper is that the authors (+ referees + editor + many citing it affirmatively) are continuously confused on this point: whereas in reality the distance of average remains constant, they think that the average of distance remains constant. The convergence of individuals can be interpreted as improvements of the individual wisdoms, implying that the crowd has less wisdmom to add to the individuals, and hence the wisdom-of-the-crowd effect became less? This interpretation is highly irrelevant because only |xw| really matters. Another problem of the authors’ accepted null just discussed is that it is not really an accepted null. As the authors call it somewhere (last footnote on p. 9022), it is “partially supported by the significance tests,” and they sometimes find that x actually has come closer to w, so has really been improved. The end of the footnote reassures us that we need not worry here: “as this effect may be different for different sets of questions.” The latter holds not only for this claimed accepted null but for everything else in this paper too. Although p. 9022 (colum 1 l. -7) properly indicates that the above effect is just a statistical effect, the authors still use the misplaced term “social influence effect” for it (p. 9022 1st column last para). The authors signal a second supposed problem, using what they call a “new indicator” on p. 9021. The perfect wisdom of the crowd according to this indicator occurs if the true value is a median (so it is between the two middle scores if even group). The indicator considers how many group members should change their opinion to achieve this perfectness. This indicator is served by increasing variance given constant average x (which surely is not always a good thing I would say). Here is an algorithm of achieving universal maximal wisdom for all questions ever to be faced by mankind, simply by maximizing variance: you form a two-person group with one other person (so, even nr). Take a big number M, exceeding any other number you will ever meet in your life. Your guess (of whatever; you don’t care what) is M, and your partner’s guess is M. Every answer to every question ever faced is between your two (middle) scores and, hence, you two have achieved universal maximal wisdom. Of course, this is nonsensical, showing that the criterion proposed by the authors is not sensible. And then the authors signal a third supposed problem. If the individuals in the crowd converge, with diversity decreasing, then their confidence in their judgments will increase. If their average x is close to the true value w, then this increase is good. If, however, x is far off, then it is bad. The authors only consider the latter case in their discussion. The writing is annoying. I think that it is obvious that info sharing usually improves group estimates. The authors claim on p. 9021, l. 2, that it “can undermine” wisdom of the crowds, and this claim can be. But p. 9021 2nd column l. -5 claims that the wisdom of the crowd “is undermined” which at best is misleading, can only be defended if they claim to only refer to their own experiments. P. 9021 2nd column end of 1st para crosses the line by writing “The reason to use two different kinds of social influence was to demonstrate the robustness of our effects with regard to the specific kind of social influence.” This erroneouly suggests universality of their finding. It seems that their statistics is problematic. Figure 2 on p. 9023, seems not to give what the text claims, with full info in fact going the other way. Close inspection of, for instance, degrees of freedom in their estimates, seems to show errors there. Farrell (2011) properly criticizes the main mistakes in this paper. %} Lorenz, Jan, Heiko Rauhut, Frank Schweitzer, & Dirk Helbing (2011) “How Social Influence Can Underdermine the Wisdom of Crowd Effect,” Proceedings of the National Academy of Sciences 108, 9020–9025. {% %} Lourens, Peter F. (1984) “The Formalization of Knowledge by Specification of Subjective Probability Distributions.” Ph.D. Dissertation, University of Groningen. {% %} Lourens, Peter F. (1981) et al.: Discussion of meaning of probability, NRC Handelsblad of Friday July 24 and days before. {% %} Louviere, Jordan J. (1988) “Analyzing Decision Making: Metric Conjoint Analysis.” Sage, Newbury Park, CA. {% Classic textbook on conjoint analysis. %} Louviere, Jordan J., David A. Hensher, & Joffre D. Swait (2000) “Stated Choice Methods, Analysis and Applications.” Cambridge University Press, New York. {% CBDT %} Lovallo, Dan, Carmina Clarke, & Colin F. Camerer (2012) “Robust Analogizing and the Outside View: Two Empirical Tests of Case-Based Decision Making,” Strategic Management Journal 33, 496–512. {% Seems that he independently invented the Choquet integral, known in combinatorial optimization as the Lovász extension. %} Lovász, Laszlo (1983) “Submodular Functions and Convexity.” In Achim Bachem, Martin Grötschel & Bernard Korte (eds.) Mathematical Programming—The State of the Art, 235–257, Springer, Berlin. {% Nice citation for ambiguity aversion. “The oldest and strongest emotion of mankind is fear, and the oldest and strongest kind of fear is fear of the unknown.” %} Lovecraft, Howard P. {% First reference on representative agent. %} Lucas, Robert E. (1978) “Asset Prices in an Exchange Economy,” Econometrica 46, 1429–1445. {% intertemporal separability criticized: p. 169 seems to write: “time-additivity is neither a desirable nor an analytically necessary property to impose on preferences” %} Lucas, Robert E. & Nancy L. Stokey (1984) “Optimal Growth with Many Consumers,” Journal of Economic Theory 32, 139–171. {% %} Luce, Bryan R. & Anne Elixhauser (1990) “Standards for Socioeconomic Evaluation of Health Care Products and Services.” Springer, Berlin. {% %} Luce, R. Duncan (1956) “Semiorders and a Theory of Utility Discrimination,” Econometrica 24, 178–191. {% Abstract: “… preferences between pure alternatives and likelihood judgments between events are asssumed to be independent probabilistic processes.” Is formalized in §5. Condition R.1 shows that Luce considers compounded gambles, with events independently repeatable. just noticeable difference: gives mathematical theorems, for probabilistic choice, relating them to cardinal utilities. P. 205, l. -7/-8: “In particular, there is a good deal of skepticism about finite additivity.” Def. 6 Condition (iii) assumes binary complementarity for two-outcome gambles. P. 206, next-to-last para, points out that str. of pr. alone cannot explain choice probabilities because there may be transparent cases of monotonicity. Sentence on p. 213/214 points out that there is no mathematically interesting nonEU theory. P. 222, l. 36, on whether or not just noticeable differences can be the basis of cardinal utility, and exactly pinning down in the first sentence the weakness of just noticeable differences as basis of cardinal utility: “First of all, to treat the jnd [just noticeable difference] as a unit in any way, one must be assured that, for a particular individual, jnd’s are equal throughout his utility scale. This means, in effect, that one must show that the utility function under consideration is a sensation scale.” Here sensation scale refers to just noticeable differences. %} Luce, R. Duncan (1958) “A Probabilistic Theory of Utility,” Econometrica 26, 193–224. {% An update with corrections is in Luce (1990, Psychological Review). %} Luce, R. Duncan (1959) “On the Possible Psychophysical Laws,” Psychological Review 66, 81–95. {% %} Luce, R. Duncan (1959) “Individual Choice Behavior.” Wiley, New York. {% %} Luce, R. Duncan (1966) “Two Extensions of Conjoint Measurement,” Journal of Mathematical Psychology 3, 348–370. {% %} Luce, R. Duncan (1967) “Sufficient Conditions for the Existence of a Finitely Additive Probability Measure,” Annals of Mathematical Statistics 38, 780–786. {% Luce’s work on uncertainty in the 1990 and his 2000 book comprised a joint receipt operation that I, frankly, do not like. It is used to get cardinal utility on outcomes which I prefer to derive from joint measurement techniques applied to events treated as attributes, as in my tradeoff technique. This 1972 paper is already using a joint receipt operation, although not using the term yet. %} Luce, R. Duncan (1972) “Conditional Expected, Extensive Utility,” Theory and Decision 3, 101–106. {% %} Luce, R. Duncan (1978) “Conjoint Measurement.” In Clifford A. Hooker, James J. Leach, & Edward F. McClennen (eds.) Foundations and Applications of Decision Theory, Vol. I, 311–336, Kluwer (= Reidel), Dordrecht. {% %} Luce, R. Duncan (1978) “Lexicographic Tradeoff Structures,” Theory and Decision 9, 187–193. {% %} Luce, R. Duncan (1980) “Several Possible Measures of Risk,” Theory and Decision 12, 217–228. {% %} Luce, R. Duncan (April 1986, revision of 1985) “Uniqueness and Homogeneity of Ordered Relational Structures,” Harvard University, Department of Psychology, Boston, MA, USA. {% Just repetition of Narens & Luce (1985) %} Luce, R. Duncan (1986) “Comments on Plott and on Kahneman, Knetsch, and Thaler,” Journal of Business 59, S337–S343. {% %} Luce, R. Duncan (1988) “Rank-Dependent, Subjective Expected-Utility Representations,” Journal of Risk and Uncertainty 1, 305–332. {% %} Luce, R. Duncan (1990) “Rational versus Plausible Accounting Equivalences in Preference Judgments,” Psychological Science 1, 225–234. Reprinted with minor changes in Ward Edwards (1992, ed.) “Utility Theories: Measurements and Applications,” 187–206. Kluwer, Boston. {% Imagine two ratio scales x and y that are related through a mapping f, through y = f(x). Such data are found for instance in cross-modality matching, where subjects say if sound y is as loud as color x is intense. If f reflects physical properties that are to be preserved after rescalings, it is plausible that for each rescaling x --> rx of x (r > 0) there is a corresponding rescaling y --> s(r)y (s(r) > 0) of y such that still s(r)y = f(rx). This implies functional equations that, in turn, imply that f is a power function. This was basically shown by Luce (1959), but there were some confusions and debates, surveyed and pdated here. The present paper considers more complex relations between x and y, focusing on x and y being ratio scales. %} Luce, R. Duncan (1990) “ “On the Possible Psychophysical Laws” Revisited: Remarks on Cross-Modal Matching,” Psychological Review 97, 66–77. {% biseparable utility: does it and it is central here. Axiomatizes it but points out that he can only do it using the joint receipt operation. He also uses some nonbehavioral uniqueness axiom. End of paper points out that extension from binary to other prospects is not very clear. event/utility driven ambiguity model: event-driven binary prospects identify U and W; P. 86: “… because choice indifference points are tedious and tricky to estimate.” P. 99, penultimate sentence: “It should be remarked that binary theories that are weaker than SEU do not automatically deal with more complex gambles.” %} Luce, R. Duncan (1991) “Rank- and Sign-Dependent Linear Utility Models for Binary Gambles,” Journal of Economic Theory 53, 75–100. {% P. 5 gives transitivity and monotonicity as a principle, replace something by something better is always good. %} Luce, R. Duncan (1992) “Where Does Subjective Expected Utility Fail Descriptively?,” Journal of Risk and Uncertainty 5, 5–27. {% %} Luce, R. Duncan (1992) “Generalized Concatenation Structures that Are Translation Homogeneous between Singular Points,” Mathematical Social Sciences 24, 79–103. {% §8 seems to mention sign-dependent SEU %} Luce, R. Duncan (1992) “A Theory of Certainty Equivalents for Uncertain Alternatives,” Journal of Behavioral Decision Making 5, 201–216. {% %} Luce, R. Duncan (1993) “Sound & Hearing.” Erlbaum, Mahwah, NJ. {% %} Luce, R. Duncan (1995) “Joint Receipt and Certainty Equivalents of Gambles,” Journal of Mathematical Psychology 39, 73–81. {% Enrico & I: p. 85 criticizes Wakker & Tversky (1993) for taking rank- and sign-dependence into the preference axioms; P. 306 aggressively criticizes Tversky & Kahneman (1992) for having used power utility whereas an axiom written by Duncan (invariance w.r.t. adding a constant) and incorrectly ascribed by him to Tversky & Kahneman (“which they clearly believe”) would imply exponential utility %} Luce, R. Duncan (1996) “The Ongoing Dialog between Empirical Science and Measurement Theory,” Journal of Mathematical Psychology 40, 78–98. {% risky utility u = strength of preference v (or other riskless cardinal utility, often called value): p. 298, §1.3: “Now, if utility really is a measurable concept—some economists and many psychologists have strong doubts—it seems unlikely that there should be more than one such measure. This issue is analogous to one that recurred in psychical measurements where often one can measure the same physical attribute in more than one way. There one usually finds that there are linking laws showing that the several, apparently distinct, ways of measuring the attribute really are basically the same measure. A familiar example is mass. …” biseparable utility: uses it. P. 304, top, criticizes use of comonotonicity by me and others in axiomatizations and calls it “contrived” inverse-S: p. 306 considers case of two participants, one with p0.5, other with p1.5, as probability transformation function. Their average then gives inverse-S shape probability transformation. Nice example! Estes (1956) seems to give general viewpoints on curves derived from group data. %} Luce, R. Duncan (1996) “When Four Distinct Ways to Measure Utility Are the Same,” Journal of Mathematical Psychology 40, 297–317. {% %} Luce, R. Duncan (1997) “Associative Joint Receipts,” Mathematical Social Sciences 34, 51–74. {% coalescing; P. 101 incorrectly writes that Fennema & Wakker (1997) had proposed Luce’s Eq. (11) for gains and losses separately. This is not true. Fennema & Wakker explicitly state on p. 54, two lines above their Eq. (1): “We only give the PT value for prospects … with both positive outcomes (gains) and negative outcomes (losses).” P. 103 gives concise description of configural weight theory. In later writings Luce pointed out, based on cummunication with Marley, that the derivation of RDU in this paper is not correct. Status-quo event commutativity is too weak because it only gives a decomposition into utility and decision weight for the best outcome, not for the worst. %} Luce, R. Duncan (1998) “Coalescing, Event Commutativity, and Theories of Utility,” Journal of Risk and Uncertainty 16, 87–114. {% criticisms of Savage’s basic model §1.1.6.1. Note: Luce uses term accounting indifferences and not term accounting equations. P. 7 explains why Luce’s gambles are not formally acts à la Savage. Pp. 22-23, §1.3: this section illustrates something that I regret. The author explains that he wants to get cardinality (my term) for consequences. For this purpose he introduces joint receipts (his 4th approach). The first approach he suggests is to assume multiattributes on the consequences and then use joint analysis techniques. What he does not realize is that one can consider different events or disjoint probabilities in lotteries to be attributes, and then use the conjoint techniques there. (I do that, using conjoint analysis techniques treating events as attributes, in many papers, using for instance a tradeoff technique.) Similarly, for intertemporal choice one can treat the different timepoints as different attributes. But he lists such use of timepoints as a third, different, approach. He clearly does not realize here that uncertainty and intertemporal can be treated as special cases of conjoint analysis, as done for instance in Ch. 6 of Krantz et al. (1971). This explains his unfortunate move of using joint receipts. Luce cites Keeney & Raiffa (1976) for deriving cardinality (my term) from multi-attributes. But Keeney & Raiffa use the probabilities of lotteries, and the EU assumed there, to get cardinality, which is more in the spirit of using events/disjoint probabilities as attributes. Pp. 22-23: “People are surprisingly flexible about doing unusual things for an experimenter even though they have had no experience in life with such judgments.” Paternalism: p. 25, on conditions that are normative but not descriptive: “It is equally important to know about these, for it is here where prescriptive training can come into play.” P. 26, Total utility theory: “The approach to utility measurement we are taking is thus a very classical one—purely behavioral. Within the psychological, but not the economic, community, such behavioral approaches are decidedly out of fashion, and have been ever since the so-called “cognitive revolution”.” linear utility for small stakes: p. 86 argues for this claim. P. 55, opening sentence of §2.4.2 is nice: “Although this line of rational argument seems fairly compelling in the abstract, it loses its force in some concrete situations.” biseparable utility: Ch. 3 gives biseparable utility; i.e., RDU representations for binary acts. Unfortunately, there are difficult technical assumptions such as gains partition in Def. 3.6.1, p. 113. Event commutativity is a kind of weakened version of bisymmetry (or autodistributivity), restricted to two outcomes x,y. Luce’s repeated-events setup would have been the perfect context for full-force multi-symmetry such as used by Nakamura (1990, JET) and others! binary prospects identify U and W concave utility for gains, convex utility for losses: p. 83, end of §3.3.1: “Taken together, these studies provide sufficiently many examples of all four patterns that any overall generalization about the convexity or concavity of utility functions seems unwarranted. The most one can say is that concavity for gains and convexity for losses appears to be the most likely of the four patterns.” inverse-S: p. 100, §3.4.2.5: “Conclusion: from all of the data in this section, I think one must conclude that the inverse-S-shaped pattern for weights describes a majority of people. I remain perplexed about why so much of the earlier data failed to detect this.” In all the discussion of data here, Luce considers only the case of known probabilities, and not unknown probabilities. P. 262: “In addition, of the several proposed weighting functions, the Prelec one is by far the most satisfactory.” %} Luce, R. Duncan (2000) “Utility of Gains and Losses: Measurement-Theoretical and Experimental Approaches.” Lawrence Erlbaum Publishers, London. {% dynamic consistency: favors abandoning RCLA. Eqs 3 & 4 show that power probability weighting holds iff the simplest probabilistic reduction holds ((x,p),q) ~ (x,pq)). Luce also gives N-reduction invariance as a simpler condition to axiomatize Prelec’s compound invariance family. Big caveat in this all is that Luce assumes backward induction, as in all his works: in the compound gamble ((x,p),q), (x,p) can be replaced by its unconditional certainty equivalent. Under nonexpected utility this condition is not a simple monotonicity condition but it is a highly questionable separability condition. Because of this extra assumption, he can simplify Prelec’s axiom otherwise. %} Luce, R. Duncan (2001) “Reduction Invariance and Prelec’s Weighting Functions,” Journal of Mathematical Psychology 45, 167–179. {% Applies the axiomatizations that he developed for decision under uncertainty, to psychological intensity measurements, such as the loudness as subjective perception of sounds in two ears, say 50 DB to left ear and 57 to right. %} Luce, R. Duncan (2002) “A Psychophysical Theory of Intensity Propertions, Joint Presentations, and Matches,” Psychological Review 109, 520–532. {% Some improvements over Luce (2002, Psychological Review). %} Luce, R. Duncan (2004) “Symmetric and Asymmetric Matching of Joint Presentations,” Psychological Review 111, 446–454. (Correction in Luce 2008, Psychological Review). {% Considers models where the zero outcome (reference point, or unitary outcome as the author calls it) plays a special role deviating from usual models such as rank-dependent models. %} Luce, R. Duncan (2004) “Increasing Increment Generalizations of Rank-Dependent Theories,” Theory and Decision 55, 87–146. {% Is critical about RDU theories not incorporating violations of framing, coalescing, and so on. See beginning of §2, and top of p. 114. %} Luce, R. Duncan (2008) “Purity, Resistance, and Innocence in Utility Theory,” Theory and Decision 64, 109–118. {% %} Luce, R. Duncan (2008) “Correction to Luce (2004)” Psychological Review 115, 601. {% Seems to argue on p.7 against using average estimates (as with representative agent) because those may display properties not present for individuals. %} Luce, R. Duncan (2010) “Interpersonal Comparisons of Utility,” Theory and Decision 68, 5–24. {% Summary of his main ideas and conditions on decision under uncertainty and joint receipt. Nice intro. %} Luce, R. Duncan (2010) “Behavioral Assumptions for a Class of Utility Theories: A Program of Experiments,” Journal of Risk and Uncertainty 40, 19–37. {% %} Luce, R. Duncan (2012) “Predictions about Bisymmetry and Cross-Modal Matches from Global Theories of Subjective Intensities,” Psychological Review 119, 373–387. {% Misperceived payoffs means nothing other than that payments are in something physical such as money which may be different from utility. The paper then analyzes how utility can be measured and then brought in into game theory. A point also central in Sugden (2000). %} Luce, R. Duncan & Ernest W. Adams (1956) “The Determination of Subjective Characteristic Functions in Games with Misperceived Payoff Functions,” Econometrica 24, 158–171. {% %} Luce, R. Duncan, Robert R. Bush, & Eugene Galanter (1963, eds.) Handbook of Mathematical Psychology, Vol. I. Wiley, New York. {% %} Luce, R. Duncan, Robert R. Bush, & Eugene Galanter (1963, eds.) Handbook of Mathematical Psychology, Vol. II. Wiley, New York. {% Ch. 10 §5, by Luce & Suppes, is on probabilistic choice theory. See my comments on that chapter with Luce & Suppes. %} Luce, R. Duncan, Robert R. Bush, & Eugene Galanter (1965, eds.) Handbook of Mathematical Psychology Vol. III. Wiley, New York. {% just noticeable difference %} Luce, R. Duncan & Ward Edwards (1958) “Derivation of Subjective Scales from Just Noticeable Differences,” Psychological Review 65, 222–237. {% biseparable utility; event/utility driven ambiguity model: event-driven %} Luce, R. Duncan & Peter C. Fishburn (1991) “Rank- and Sign-Dependent Linear Utility Models for Finite First-Order Gambles,” Journal of Risk and Uncertainty 4, 29–59. {% Extends Luce & Fishburn (1991) to utility that need not be additive in joint receipt but can incorporate a multiplicative interaction term. If joint receipt is addition, then U must be exponential. %} Luce, R. Duncan & Peter C. Fishburn (1995) “A Note on Deriving Rank-Dependent Utility Using Additive Joint Receipts,” Journal of Risk and Uncertainty 11, 5–16. {% standard-sequence invariance? %} Luce, R. Duncan & David H. Krantz (1971) “Conditional Expected Utility,” Econometrica 39, 253–271. {% P. 49, l. 10: “are blurred together in the topological formulations”. Fuhrken & Richter (1991, p. 94) have a similar statement. Ch. 21 is on empirical status of Archimedean axiom. Also on impossibility to have finite number of first-order statements to axiomatize additive conjoint measurement. Theorem 21.21 shows that Archimedean axiom has no empirical meaning in additive conjoint measurement. %} Luce, R. Duncan, David H. Krantz, Patrick Suppes, & Amos Tversky (1990) “Foundations of Measurement, Vol. III. (Representation, Axiomatization, and Invariance).” Academic Press, New York. {% Discuss, a.o., the log-law of Fechner-Weber versus the power law of Stevens. %} Luce, R. Duncan & Carol L. Krumhansi (1988) “Measurement, Scaling, and Psychophysics.” In Richard C. Atkinson, Richard J. Herrnstein, Gardner E. Lindzey, & R. Duncan Luce (eds.) Stevens Handbook of Experimental Psychology 1, 3–74, Wiley, New York. {% %} Luce, R. Duncan & Anthony A.J. Marley (2000) “On Elements of Chance,” Theory and Decision 49, 97–126. {% %} Luce, R. Duncan & Anthony A.J. Marley (2005) “Ranked Additive Utility Representations of Gambles: Old and New Axiomatizations,” Journal of Risk and Uncertainty 30, 21–62. {% decreasing ARA/increasing RRA: seem to use power utility; Consider variable reference levels; assume that reference level is smallest gain when only gains, smallest loss when only losses. %} Luce, R. Duncan, Barbara A. Mellers, & Shi-Jie Chang (1993) “Is Choice the Correct Primitive? On Using Certainty Equivalents and Reference Levels to Predict Choices among Gambles,” Journal of Risk and Uncertainty 6, 115–143. {% %} Luce, R. Duncan & Louis Narens (1978) “Qualitative Independence in Probability Theory,” Theory and Decision 9, 225–239. {% %} Luce, R. Duncan & Louis Narens (1981) “Axiomatic Measurement Theory,” SIAM-AMS Proceedings 13, 213–235. {% %} Luce, R. Duncan & Louis Narens (1983) “Symmetry, Scale Types, and Generalizations of Classical Physical Measurement,” Journal of Mathematical Psychology 27, 44–85. {% %} Luce, R. Duncan & Louis Narens (1984) “Classification of Real Measurement Representations by Scale Type,” Measurement 2, 39–44. {% I like this paper for its many ideas. §7 is on decision under uncertainty. Does not give a general version of RDU because it considers only 2-outcome gambles and, as pointed out also by Fishburn (1988, Uncertainty Aversion ..., page 15), it does not provide an axiomatization. biseparable utility: Theorem 7.1 & 7.2.2 show that most general two-dimensional model to preserve interval scaling is two-dimensional RDU. Note how they use Eq. 7.5. It is difficult to read because it uses the homogeneity- and uniqueness-terminology of the preceding sections. A brief and more accessible account is in other papers by Luce, such as Luce (1988, JRU, §1), Luce (1990, Psychological Science 1, p. 228), and Luce (1991, JET, §1.) Pfanzagl (1968, Ch. 6 such as Theorem 6.1.1 (p. 97) may be similar, without rank dependent restriction. %}. Luce, R. Duncan & Louis Narens (1985) “Classification of Concatenation Measurement Structures According to Scale Type,” Journal of Mathematical Psychology 29, 1–72. {% %} Luce, R. Duncan & Louis Narens (1987) “Measurement Scales on the Continuum,” Science 236, 1527–1532. {% %} Luce, R. Duncan & Louis Narens (1994) “Fifteen Problems Concerning the Representational Theory of Measurement.” In Patrick C. Humphreys & Patrick Suppes (eds.) Scientific Philosopher, 219–249, v. 2. Kluwer Academic Publishers, Dordrecht. {% Utility of gambling %} Luce, R. Duncan, Che-Tat Ng, & Anthony J. Marley (2009) “Utility of Gambling under P(olynomial)-Additive Joint Receipt and Segregation or Duplex Decomposition,” Journal of Mathematical Psychology 53, 273–286. {% Utility of gambling %} Luce, R. Duncan, Che-Tat Ng, Anthony J. Marley, & János Aczél (2008) “Utility of Gambling I: Entropy Modified Linear Weighted Utility,” Economic Theory 36, 1–33. {% Utility of gambling %} Luce, R. Duncan, Che-Tat Ng, Anthony J. Marley, & János Aczél (2008) “Utility of Gambling II: Risk, Paradoxes, and Data,” Economic Theory 36, 165–187. {% P. 5 seems to write: “Indeed, one hopes that the unrealistic assumptions and the resulting theory will lead to experiments designed in part to improve the descriptive characte of the theory.” P. 27/28 do EU-axiomatization by substitution axiom. (substitution-derivation of EU) P. 28 has discussion of mountain climber whose utility of outcomes essentially depends on the probabilities (“gestalt” of prospect as they nicely write), something Deneffe and I once discussed. Fallacy 2: an agent might care about variance of utility. P. 32, Fallacy 3: people who equate risky utility with cardinal utility (without further ado) P. 280-282 points out that regret leads to intransitivities, citing Chernoff’s observation entailing a violation of independence of irrelevant alternatives. revealed preference; p. 288, §13.3, Example: A gentleman wandering in a strange city at dinner time chances upon a modest restaurant which he enters uncertainly. The waiter informs him that there is no menu, but that he may have either broiled salmon at $2.50 or steak at $4.00 this evening. In a first-rate restaurant his choice would have been steak, but considering his unknown surroundings and the different prices he elects the salmon. Soon after the waiter returns from the kitchen, apologizes profusely, blaming the uncommunicative chef for omitting to tell him that fried snails and frog’s legs are also on the bill of fare at $4.50 each. It so happens that our hero detests them both and would always select salmon in preference to either, yet his response is “Splendid, I’ll change my order to steak.” ... He, like most of us, has concluded from previous experience that only “good” restaurants are likely to serve snails and frog’s legs, and so the risk of a bad steak is reduced in his eyes. Download 7.23 Mb. Share with your friends:
|