Bibliography
§13.4: on decision making under complete ignorance
Download 7.23 Mb.
|
| §13.4: on decision making under complete ignorance.
§13.5: pp 304-305 present the multiple priors (maxmin EU) model and the -maxmin model, referring to Hurwicz (1951, Econometrica) for it. %} Luce, R. Duncan & Howard Raiffa (1957) “Games and Decisions.” Wiley, New York. {% P. 380 top writes, nicely, about recent developments in psychology that do not use techniques of measurement theory: “A general comment: we are very aware that the measurement approach we take here is not currently fashionable, having been “replaced” by various process models. Unlike the measurement models for which the behavioral assumptions are directly testable, the process models are composed of unobservable, hypothetical mechanisms. We feel that the added flexibility of process models comes at the (usually unacknowledged) very high cost of unobservable mechanisms which, to this day, has not really been resolved by such imaging techniques as fMRI. And we feel that the very successful approach of four centuries of classical physics has not been given anything like a comparable effort in psychology. The first author has devoted the last 12 years of his career attempting to apply our knowledge of measurement to developing both psychophysical and utility measurement models, and collaborating with the second author and others he has focused on experimental studies suggested by these models.” Section 2 first points out that preference conditions such as double cancellation, in the presence of separability/monotonicity, are somewhat redundant relative to their indifference versions such as the Thomsen condition. Then it argues that the Thomsen condition is not statistically symmetric in a way that I did not really try to understand. I guess that the hexagon condition and the Reidemeister condition are symmetric. The hexagon condition is, in the presence of separability (= independence = monotonicity) and the other conditions, where unrestricted solvability can readily be weakened to restricted solvability, necessary and sufficient for additive representation. All alternative conditions discussed here are (necessary) and stronger than hexagon and, hence, trivially are also necessary and sufficient. P. 380 discusses a nice alternative reinforcement of the hexagon condition, being the less known commutativity axiom defined by Falmagne (1976) and discussed by Gigerenzer & Strube (1983). I formulate it directly in terms of indifferences: If (a,r) ~ (m,s) & (m,p) ~ (c,q) (a,p) ~ (n,q) then (n,r) ~ (c,s) . In words, both the upper two and the lower two indifferences show that the distance from a to c is matched by that from p to q plus that from r to s. The hexagon condition is the special case where we impose the implication only if s = p and m = n. This observation provides a proof alternative to that in the Appendix of this paper, using the well-known result that the hexagon condition characterizes additive representation in the presence of the other conditions (Karni & Safra 1998). %} Luce, R. Duncan & Ragnar Steingrimsson (2011) “Theory and Tests of the Conjoint Commutativity Axiom for Additive Conjoint Measurement,” Journal of Mathematical Psychology 55, 379–385. {% error theory for risky choice: Chs. 19.5-19.8, pp. 331-402, are on probabilistic choice theories. §19.5.3 is on random utility, and Ch. 19.7 on probabilistic choice for decision under uncertainty. P. 334 footnote 6 provides the counterargument against Fechnerian (strong) utility model of p(x,y) and p(y,z) being close to 0.5, but y dominating z by very small differences but clearly, so that p(y,z) = 1. They cite Leonard J. Savage (personal communication) for it. Definition 22 (p. 340) defines weak stochastic transitivity. inverse-S: §4.3 reviews the literature up to that point on probability transformation, finding inverse-S as the prevailing pattern. %} Luce, R. Duncan & Patrick Suppes (1965) “Preference, Utility, and Subjective Probability.” In R. Duncan Luce, Robert R. Bush, & Eugene Galanter (eds.) Handbook of Mathematical Psychology, Vol. III, 249–410, Wiley, New York. {% Derives additively decomposable representation for two components, by means of weak ordering, unrestricted solvability, the Archimedean axiom, and a cancellation axiom which is the Thomsen condition with preference iso equivalence. Introductory text is nice. It first demonstrates the conjoint measurement technique in physical examples when a direct concatenation operation is also available. Next it extends that to cases (prevailing in social sciences) where no concatenation operation is available but still the conjoint measurement techniques can be adopted. P. 5 gives a useful sentence for people who inefficiently apply “ordinal” conjoint measurement techniques in situations where cardinal information is easily available: “That we can devise alternative ways to measure familiar physical quantities is philosophically interesting, but is of little practical significance to physics as long as conventional measurement based on concatenation is possible. In the behavioral and biological sciences, however, these new methods may be of considerable importance. Many of the quantities that one would like to measure, and that many scientists have felt it should be possible to measure, do not come within the scope of the classical axiomatization because no one has been able to devise a natural concatenation operation.” (P. 12/13: they don’t give correct description of Debreu (1960) by writing joint independence condition but not the hexagon condition. P. 14 shows that Pfanzagl’s bisymmetry implies the preference-version of Thomsen condition. §9, p. 14, presents standard sequences. %} Luce, R. Duncan & John W. Tukey (1964) “Simultaneous Conjoint Meassurement: A New Type of Fundamental Measurement,” Journal of Mathematical Psychology 1, 1–27. {% Suggest that of the violations of SEU commonly found, reference dependence may have more rationality status than the other violations. Receipt of two sums of money need not be the same as receiving their sum. %} Luce, R. Duncan & Detlof von Winterfeldt (1994) “What Common Ground Exists for Descriptive, Prescriptive and Normative Utility Theories,” Management Science 40, 263–279. {% P. 189 gives references to people who treat gaines and losses separately. %} Luce, R. Duncan & Elke U. Weber (1986) “An Axiomatic Theory of Conjoint, Expected Risk,” Journal of Mathematical Psychology 30, 188–205. {% Examine preference reversals, asking subjects how certain they are about their preferences. More certain subjects have fewer preference reversals. %} Luchini, Stéphane & Verity Watson (2013) “Uncertainty and Framing in a Valuation Task,” Journal of Economic Psychology 39, 204–214. {% Mostly a general book on statistical research. Some case studies of marketing are discussed. %} Luck, David J., Hugh G. Wales, & Ronald S. Rubin (1952) “Marketing Research.” Prentice-Hall, New Jersey. (5th edn. 1978.) {% The authors report a preference reversal: if, in isolation, a risky payoff and a delayed payoff are equivalent (I assume that the certainty equivalent and the present value are the same) then in direct choice they prefer the delayed payoff. %} Luckman, Ashley, Chris Donkin, & Ben R. Newell (2017) “People Wait Longer when the Alternative is Risky: The Relation between Preferences in Risky and Inter-temporal Choice” Journal of Behavioral Decision Making 30, 1078–1092. {% risky utility u = strength of preference v (or other riskless cardinal utility, often called value): Seems that the authors do the following: they study choices with time and risk. Reckoning with parsimony (avoiding overfitting) they find that assuming one common utility function is best. %} Luckman, Ashley, Chris Donkin, & Ben R. Newell (2017) “Can a Single Model Account for Both Risky Choices and Inter-Temporal Choices? Testing the Assumptions Underlying Models of Risky Inter-Temporal Choice,” Psychonomic Bulletin & Review, forthcoming. {% Does what the title says, and finds that debiasing is effective. The end of the abstract mentions absence of conceptual rigor as a challenge for future research. Many references. %} Ludolph, Ramona & Peter J. Schulz (2017) “Debiasing Health-Related Judgments and Decision Making: A Systematic Review,” Medical Decision Making 38, 3–13. {% Find extremity-orientedness in DFE. The authors say that this gives more risk seeking for gains and more risk aversion for losses, and is opposite to prospect theory. However, as crucial point here is whether the extreme outcomes have low or high probability because, if low, then the finding agrees with prospect theory. I did not see this point discussed, although I may not have searched long enough. The authors do discuss 50-50 probabilities, e.g. p. 153 penultimate para, but I did not see this solve my problem. %} Ludvig, Elliot A., Christopher R. Madan, & Marcia L. Spetch (2014) “Extreme Outcomes Sway Risky Decisions from Experience,” Journal of Behavioral Decision Making 27, 146–156. {% Study DFD-DFE gap for events with probability ½. Find usual reflection with risk aversion for gains and risk seeking for losses for DFD, but find the entire opposite for DFE. The authors suggest that their finding for DFE may be due to utility being convex for gains and concave for losses, but it may equally well be the w(½) > ½ for DFE and, in fact, the latter explanation is more plausible because the uncertainty about outcomes is different under DFE than under DFD and not the outcomes themselves. My biggest problem is that it is not at all clear what the subjects are maximizing in this experiment. My main problem is not that the choices are hypothetical per se, but that even when allowing for that it still is not clear what the (hypothetical) motivation should be. They do repeated choices, receiving points after each choice, but it is unclear what these points serve for. In the first experiment, during the experiment, some high total scores up to then were displayed and subjects were encouraged to try to beat these scores. Whatever findings this paper has, can be driven by whatever motivation came from such encouragements, and thus does not speak to general risk attitudes. %} Ludvig, Elliot A. & Marcia L. Spetch (2011) “Of Black Swans and Tossed Coins: Is the Description-Experience Gap in Risky Choice Limited to Rare Events?,” PLoS ONE 6, e20262. {% Use dynamic inconsistency of CEU (Choquet expected utility) to derive implications in (il)liquid assets. %} Ludwig, Alexander & Alexander Zimper (2006) “Investment Behavior under Ambiguity: The Case of Pessimistic Decision Makers,” Mathematical Social Sciences 52, 111–130. {% Use Neo-Additive Capacities and do updating there. %} Ludwig, Alexander & Alexander Zimper (2008) “A Parsimonious Model of Subjective Life Expectancy,” {% DC = stationarity. Para on pp. 1274-1275 and especially p. 1275 last sentence of 2nd para: “This property of exponential discounting is referred to as the stationarity axiom (Koopmans, 1960) and guarantees that an exponential discounter will never exhibit dynamic inconsistency.” N = 51 subjects, with hypothetical choice. The author implicitly assumes linear utility. Tests hyperbolic discounting t Considers a number of choices, then adds three front-end delays (10, 20, 30 days). Finds decreasing impatience, but not as strong as hyperbolic discounting would predict. Strangely enough, the whole paper focuses entirely on hyperbolic suggesting that no-one has tested it yet, to cite more advanced literature only on the last page 1278, including the extensive parametric tests by Takahashi et al. (2008). %} Luhmann, Christian C. (2013) “Discounting of Delayed Rewards is not Hyperbolic,” Journal of Experimental Psychology: Learning, Memory, and Cognition 39, 1274–1279. {% %} Lukas, Josef (1987) “Additiv Verbundene Messung der Wahrgenommenen Flächengrösse: Ein Experimentelles Verfahren zur Lösung des Testbarkeitsproblems,” Zeitschrift für Experimentelle und Angewandte Psychologie 34, 416–430. {% %} Lundberg, Erik (1972) “Invar Svennilson: A Note on his Scientific Achievements and a Bibliography of his Contributions to Economics,” Swedish Journal of Economics 74, 313–328. {% Surveys role of (cognitive) financial literacy on financial decisions. %} Lusardi, Annamaria & Olivia S. Mitchell (2014) “The Economic Importance of Financial Literacy: Theory and Evidence,” Journal of Economic Literature 52, 5–44. {% Tradeoff method: discuss it. Show that risk attitudes measured experimentally in the lab, are related to actual decisions about eating “risky” (genetically modified) food. %} Lusk, Jayson L. & Keith H. Coble (2005) “Risk Perceptions, Risk Preference, and Acceptance of Risky Food,” American Journal of Agricultural Economics 87, 393–405. {% loss aversion: erroneously thinking it is reflection: happening here. They consider bargaining with either only gains or only losses, and never mixed prospects, implying that loss aversion plays no role, unlike what they claim. They use the term loss aversion for utility being different for losses than for gains. (Which, given different domains, is by definition.) %} Lusk, Jayson L. & Darren Hudson (2010) “Bargaining over Losses,” International Game Theory Review 12, 83–91. {% %} Luttmer, Erzo G.J., & Thomas Mariotti (2003) “Subjective Discounting in an Exchange Economy,” Journal of Political Economy 111, 1–30. {% A short proof is provided by Lindenstrauss (1966) %} Lyapunov, Alexey A. (1940) “Sur les Fonctions-Vecteurs Complètement Additives,” Bulletin de l’Académie des Sciences de l’URSS, Série Mathématique 4, 465–478. {% %} Lybbert, Travis J. & David R. Just (2007) “Is Risk Aversion Really Correlated with Wealth? How Estimated Probabilities Introduce Spurious Correlation,” American Journal of Agricultural Economics 89, 964–979. {% P. 44 says some on the abandoning of behaviorism, but not much in detail. %} Lyons, William (1986) “The Disappearance of Introspection.” MIT Press, Cambridge, MA. {% dynamic consistency Discussed in Paris on March 8, 1999. Uses a “piece-wise monotonicity condition”: if, given every element of a partition, I prefer replacing f by g only given that one element of the partition, then I prefer replacing f by g in total. Given dynamic consistency (which is defined in this paper to imply reduction of events), the condition is weaker than forgone-event independence but is “in that spirit.” The definition of “interim Pareto optimal” is in the same spirit. %} Ma, Chenghu (1998) “A No-Trade Theorem under Knightian Uncertainty with General Preferences,” {% Real incentives with RIS. Paper considers classical preference reversals under risk, and under ambiguity (generated by uniform 2nd-stage probability distributions over probability intervals, discussed in §8). The author finds stronger, very strong, preference reversals under ambiguity. Data fitting shows that utility is the same under risk and ambiguity, both for choice and for WTA (p. 2060). It is all perfectly well explained by a(mbiguity-generated) insensitivity, with inverse-S being more pronounced for ambiguity than for risk (inverse-S+ uncertainty amplifies risk). §7 reports parametric fitting where for ambiguity the midpoints of the probability intervals are taken as argument. The weighting function is similar to the source functions of Abdellaoui et al. (2011 AER). %} Maafi, Hela (2011) “Preference Reversals under Ambiguity,” Management Science 57, 2054–2066. {% %} Maas, Arne (1991) “A Model for Quality of Life after Laryngectomy,” Social Science and Medicin 33, 1373–1377. {% %} Maas, Arne (1992) “The Use of Conjoint Measurement in Medical Decision Making,” Ph.D. dissertation, Dept. of Psychology, University of Nijmegen, the Netherlands. {% %} Maas, Arne (1993) “A Relativized Measure of Circularity,” Mathematical Social Sciences 26, 79–91. {% %} Maas, Arne (1994) “Time-Intensity Measurement: A Feasibility Study,” LPVD 94 3025, Unilever Research, Vlaardingen, the Netherlands. {% %} Maas, Arne (1996) “A Method for Solving Intransitivities.” In Wing Hong Loke (ed.) Perspectives on Judgment and Decision-Making, Scarecrow, Lanham, MD. {% %} Maas, Arne (2003) “McDonald’s Springt in Culturele Valkuil,” Adformatie (Nov. 16), 31. {% %} Maas, Arne (2004) “De Mondiale Consument als Universele Vergissing,” Tijdschrift voor Marketing 38 (January 2004) 40-41. {% ISBN: 9789051798265. %} Maas, Arne (2013) “De Redenloze Consument. Over Framing in Marketing.” Rotterdam University Press, Rotterdam, the Netherlands. {% risky utility u = strength of preference v (or other riskless cardinal utility, often called value) %} Maas, Arne, Thom G.G. Bezembinder, & Peter P. Wakker (1995) “On Solving Intransitivities in Repeated Pairwise Choices,” Mathematical Social Sciences 29, 83–101. Link to paper
Maas, Arne & Lucas J.A. Stalpers (1992) “Assessing Utilities by Means of Additive Conjoint Measurement: An Application in Medical Decision Analysis,” Medical Decision Making 12, 288–297. {% %} Maas, Arne & Peter P. Wakker (1994) “Additive Conjoint Measurement for Multiattribute Utility,” Journal of Mathematical Psychology 38, 86–101. Link to paper
Maccheroni, Fabio & Massimo Marinacci (2006) “A Strong Law of Large Numbers for Capacities,” Annals of Probability 33, 1171–1178. {% DOI: http://dx.doi.org/10.3982/ECTA9678 Consider smooth model, and calculate ambiguity premiums, i.e., Pratt-Arrow type risk premiums, in the second stage, and implications for investments. %} Maccheroni, Fabio, Massimo Marinacci, & Doriana Ruffino (2013) “Alpha as Ambiguity: Robust Mean-Variance Portfolio Analysis,” Econometrica 81, 1075–1113. {% biseparable utility violated; This paper was previously entitled: “Ambiguity Aversion, Malevolent Nature, and the Variational Representation of Preferences.” It generalizes the existing axioms of maxmin EU in a natural manner, coming with an easy-to-write new model unifying many existing things, so the paper is important and pretty. They consider the following generalization of multiple priors, with S a Savagean state space and infimum INF below over all probability measures over S INF [∫S(U(f(s))dP(S) + c(P)] with c a convex function of probability measures. The multiple priors model, with set D of probability measures, results by letting c be 0 on D and infinite outside of D. In general, the bigger c(P), the less likely it is that P will deliver the inf and be relevant. Hence, P’s judged implausible by the decision maker have higher c values. One way to go is to take some “most plausible” probability measure Q as starting point, and then to use the above model where c is a distance measure of P from Q. One such distance measure could be the relative entropy or that multiplied by some positive factor, and this is what Hansen & Sargent did in macro-economics. Thus, the authors have obtained a joint generalization of multiple priors and Hansen & Sargent. Another distance measure could be a generalized Gini index and then, if I understood right, the mean-variance model comes out, that is, the mean-variance model only where it is interesting; i.e., where it is monotonic. (Because of their monotonicity imposed on c their functional simply truncates mean-variance where it starts violating monotonicity). It worries me that if utilities are increased (not by a meaningless rescaling but by improving outcomes) by a factor 100 or so, then the role of c becomes less and less important, it it goes more and more to just maximizing minimal outcome. So very extreme pessimism/uncertainty aversion. The authors use the Anscombe-Aumann model which, in my interpretation and also put central by them, means just linear utility. They use the axioms of Gilboa & Schmeidler (1989) with certainty independence weakened. Not, for all prospects f,g and constants (certain acts) c, c´ f + (1)c g + (1)c ==> f + (1)c´ g + (1)c´ (which is one way to state certainty independence) but this axiom only for = . It amounts to considering translation invariance (adding the constant (cc´) to everything but not scale invariance. Relative to EU they seem to add only one “parameter” being c. But c is a formidable parameter. First we go from S to the set of all probability measures on S which is of higher cardinality, and then c maps this set to the reals, being again a higher level of cardinality. So c is not just one parameter/dimension added like U, but it is an infinity more. Thus, that they can accommodate so many existing models may be no surprise, and measurability and testability is the problem. Maxxmin EU is already of an untractably high dimensionality because of the set of priors to be chosen, and this model goes way beyond it. It may however be a convenient starting point for specifying special cases, showing unity. Axiom A8 (weak monotone continuity) ensures that only countably additive probability measures are involved. %} Maccheroni, Fabio, Massimo Marinacci, & Aldo Rustichini (2006) “Ambiguity Aversion, Robustness, and the Variational Representation of Preferences,” Econometrica 74, 1447–1498. {% Dynamic version of their variational model. %} Maccheroni, Fabio, Massimo Marinacci, & Aldo Rustichini (2006) “Dynamic Variational Preference,” Journal of Economic Theory 128, 4–44. {% Use a variation of mean-variance analysis that avoids violation of monotonicity. For mean-variance, such a violation of monotonicity can result if an outcome is increased that is much higher than the expectation, so much that its increase worsens the variance more than that it improves the expectation. The basic idea of this paper is to simply truncate at the level of outcomes where the worsening of the variance becomes worse than the improvement of the expectation (and, I guess, condition on the non-truncated event). This is a special case of their variational preference model. They use their model to get a variation of CAPM. I disagree with their claim that they avoid arbitrage. They base this claim on not violating monotonicity, but arbitrage involves more, being linear combinations of prospects. No-arbitrage implies as-if risk neutral, so subjective expected value, and then there is no place for ambiguity aversion for instance, a phenomenon central to their functional. Even if they fix the monotonicity violation of mean-variance, I find it crude to simply ignore the best outcomes. %} Maccheroni, Fabio, Massimo Marinacci, Aldo Rustichini, & Marco Taboga (2009) “Portfolio Selection with Monotone Mean-Variance Preferences,” Mathematical Finance 19, 487–521. {% Find evidence for superadditivity, rather than the commonly found subadditivity, in probability judgment. Suggest it occurs when there is little evidence for the events. %} Macchi, Laura, Daniel Osherson, & David H. Krantz (1999) “A Note on Superadditive Probability Judgment,” Psychological Review 106, 210–214. {% %} Mach, Ernest (1883) “Die Mechanik in Ihrer Entwicklung Historisch-Kritisch Dargestellt.” Translated into English by Thomas J. McCormack (1893) “The Science of Mechanics: A Critical and Historical Account of Its Development,” Open Court, La Salle, Illinois. (6th edn. 1960.) {% %} Mach, Ernst (1896) “Prinzipien der Wärmelehre,” Leipzig. {% %} Machauer, Archim & Martin Weber (1998) “Bank Behavior based on Internal Credit Ratings of Borrowers,” Journal of Banking and Finance 22, 1355–1383. {% %} Machielse, Irma A. (1995) “Wat Wil de Verzekerde,” Zorg en Zekerheid, Sector Zorg, Afdeling Beleidsinformatie & Onderzoek, Leiden, the Netherlands. {% %} Machina, Mark J. (1981) “ ‘Rational’ Decision Making versus ‘Rational’ Decision Modeling,” A Review of Maurice Allais & Ole Hagen (eds.) “Expected Utility Hypotheses and the Allais Paradox,” Journal of Mathematical Psychology 24, 163–175. {% %} Machina, Mark J. (1981) “On Path Independent Randomized Choice,” Econometrica 49, 1345–1347. {% uncertainty amplifies risk: somewhat on p. 292: “It is useful to keep in mind the distinction between an oversensitivity to changes in the probabilities of small probability events and any tendency, under conditions of uncertainty rather than ris, to overestimate the probabilities of rare events.” [Italics from original.] Download 7.23 Mb. Share with your friends:
|