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| §4.9, pp. 81-82: “If people always behaved as this prescriptive theory says they ought to, then there would be no reason to make a fuss about a prescriptive theory. We could then just tell people, “Do what comes naturally.” “
P. 85: in Allais paradox, one 0 outcome may be different from another. decreasing ARA/increasing RRA: p. 91-94 suggests that decreasing absolute risk aversion is plausible, I didn’t see RRA being discussed. P. 110: judgmental probability of event E is p: $100p0 $100A0; i.e., it is the matching probability. §4 discusses that these need not be additive. P. 112: Raiffa’s famous ’61 argument against Ellsberg. P. 146, principle of substitutability: is in fact like Anscombe & Aumann (1963), two-stage with states of nature and objective probability mixing of acts, but with prior mixing not posterior. For two states of nature. P. 161-168 seems to discuss bisection for eliciting probability. P. 287: experimentor continuing until he has a result pleasing him, does good research. Schrift p. 639 %} Raiffa, Howard (1968) “Decision Analysis.” Addison-Wesley, London. {% Utility consists of costs (expenses time etc. it takes to use model, say “process utility”) and terminal utility (value otherwise, say “consequential utility”). %} Raiffa, Howard & Robert O. Schlaifer (1961) “Applied Statistical Decision Theory.” Harvard University, Boston, MA. (5th edn. 1970, there seems to be another of 1984). {% India’s story about young prince who liberates woman with army of monkeys other big story is Mahabharata. %} “Ramayana.” {% %} Ramsey, Frank P. (1927) “A Contribution to the Theory of Taxation,” Economic Journal 37, 47–61. Reprinted in William J. Baumol & Stephen M. Goldfeld (1968, eds.) “Precursors in Mathematical Economics: An Anthology,” Selection 33, 341–354, Clowes and Sons, London. {% time preference; It seems that, to handel divergent sums of utility, he proposed an overtaking criterion with respect to some fixed bliss level. discounting normative(?): writes, p. 543: “it is assumed that we do not discount later enjoyments in comparison with earlier ones, a practice which is ethically indefensible and arises merely from the weakness of imagination;” discounting normative(?): seems to write also on p. 543: “practice which is ethically indefensible and arises merely from the weakness of the imagination” Although he doesn’t have Samuelson’s constant discounting with time separability involved, he extensively discusses discounted utility, apparently only for one nonezero outcome, and distinguishes it from discounted money on p. 553. P. 553: “In assuming the rate of discounting constant, I [mean that] the present value of an enjoyment at any future date is to be obtained by discounting it at the rate … This is the only assumption we can make, without contradicting our fundamental hypothesis that successive generations are activated by the same system of preferences. For, if we had a varying rate of discounting—say a higher one for the first fifty years—our preference for enjoyments in 2000 A.D. over those in 2050 A.D. would be calculated at the lower rate, but that of the people alive in 2000 A.D. would be at the higher.” %} Ramsey, Frank P. (1928) “A Mathematical Theory of Saving,” Economic Journal 38, 543–559. Reprinted in William J. Baumol & Stephen M. Goldfeld (1968, eds.) “Precursors in Mathematical Economics: An Anthology,” Selection 9, 125–128, Clowes and Sons, London. {% %} Ramsey, Frank P. (1929/1978) “Theories.” In David H. Mellor (Ed.), Foundations: Essays in Philosophy, Logic, Mathematics and Economics 101–125. Humanities Press, Atlantic Highlands, New Jersey. {% This text by Ramsey is one of the best in all of decision theory, with refined and deep understanding of all relevant issues found nowhere else in the literature. Brought to the attention of Arrow, Econometrica, (1951, p. 423), by Norman C. Dalkey, RAND-corporation; Ramsey’s work was called “none too clear” by Arrow (p. 424); Pp. 158-159 on frequentist probability (strongly criticized later in the paper, to my joy), that even if existing there are always situations of partial belief. Pp. 160-166 criticize the logical interpretation of probability, advocated by his teacher Keynes, and I found nuances lacking in this discussion. P. 161 has the nice concept of psychogalvanometer to directly measure degrees of belief. Pp. 166 – 169 is a nice text on measurement in social science, with scale types and framing (that models hold only approximately). Pp. 169 last para (“We are driven therefore”) - p. 174 penultimate para (“no memory of the previous ones”): is a superb discussion of the dispositional nature of preference, as of virtually any property in natural sciences and elsewhere. It is the best discussion of this point that I ever read. All modern issues such as introspection and hypothetical choice are put right there. It is unbelievable that Ramsey immediately, even before our field was born, understood these things to an extent that most researchers will do never in their life (unless they were as fortunate as I was to have been exposed to Ramsey’s text at a young age). For understanding why we need the random incentive system in experimental economics to implement real incentives, this is the best text. Ramsey wants subjective probability to be entirely revealed-preference based. utility = representational?: p. 171 writes: “Suppose, however, I am wrong about this and that we can decide by introspection the nature of belief, and measure its degree; still, I shall argue, the kind of measurement of belief with which probability is concerned is not this kind but is a measurement of belief qua basis of action.” Used just noticeable difference for cardinal utility: P. 171 puts it forward a basis for measuring beliefs/probabilities, but then propoerly criticizes it as just a different cardinal scale. P. 172 beginning of 3rd para: “It is clear that we are concerned with dispositional rather than with actualized beliefs;” That is, subj. probability is not belief now had, but only as it would be had if we had to act on it. As Tversky would put it in support theory: it is in our mind, not on our mind. P. 172 writes that a Dutch book can be made against nonEU. Does not define it, apparently considering it to be well known. However, it is the first mention of Dutch book in the literature that I am aware of. Pp. 182 & 183 will do it again. P. 172 bottom: measuring belief may automatically affect it. P. 173 penultimate para: “we seek things which we want, which may be our own or other people’s pleasure, or anything else whatever, and our actions are such as we think most likely to realize these goods.” [italics added here] Ramsey points out here that from the representation it follows that we are maximizing something, utility (or its expectation), but does not commit to anything that that might be. Para on pp. 173-174 nicely states how utility is a different, kind of exchangeable, scale differently than the scales we commonly use such as hours of swimming. P. 174 3rd para nicely points out that normative here is something different than in ethics. The term ethically neutral event emphasizes this point. linear utility for small stakes & marginal utility is diminishing: p. 176: “Since it is universally agreed that money has a diminishing marginal utility, if money bets are to be used, it is evident that they should be for as small stakes as possible. But then again the measurement is spoiled by introducing the new factor of reluctance to bother about trifles.” P. 174: in repeated choices to measure subjective probabilities there should be no learning to make this interpretation work. When Luce worked with repeated decisions in the 1990s he overlooked this point. I, exposed to Ramsey at young age, wrote Luce an email about it. He acknowledged me for it on p. 10 (footnote) in Luce, R. Duncan (2000) “Utility of Gains and Losses: Measurement-Theoretical and Experimental Approaches.” Lawrence Erlbaum Publishers, London. P. 176 2nd para: the formal analysis of his preference foundation starts. Will be until p. 184. It starts with what is called an ethically neutral event. (Ramsey uses the term proposition iso event.) This is an event that carries no value in itself. That is an event in a Savagean sense. An event that carries a value in itself is a bit like a consequence in Savage (1954), although may be also like a Savagean event, and it is not very clear how to model this, a bit Jeffrey-type may be. At any rate, Ramsey then assumes an ethically neutral event that you just as much like to gamble on as against. Under EU it means that it has subjective probability 0.5. Then observations (0.5:x, 0.5:z) ~ y show that y is the utility midpoint between x and z. In this way, we can measure utility to any desired degree of precision. With utility available, we can measure subjective probabilities. This is how Ramsey does it. Savage’s definition of acts, states, consequences, distinguishing them, is not clearly present in Ramsey’s writing. conditional probability discussed on p. 180. Nice that actual receipt of info can alter things and requires an assumption for invoking Bayes’ formula. (P.s.: simultaneity in the penultimate para refers to the discussion of Einstein on p. 169.) P. 183 last para writes that essentially we should get by with finite models. A point also central in the Shapiro (& Richter) work. P. 184 - end is philosophical, on induction and so on. P. 188, on objective/subjective probabilities: “And in a sense we may say that the two interpretations are the objective and subjective aspects of the same inner meaning,” P. 189, on finding equally probable basic events: “it is a matter of physics rather than pure logic.” His suggestion that Keynes would think differently is hard to believe and is probably driven by his young desire to disagree with his befriended teacher. One also sees that top of p. 167. Whenever Keynes is involved Ramsey becomes unreasonably negative. utility = representational?: Ramsey doesn’t need more than one sentence to, for once and for all, refute coherentism: p. 191: “we want our beliefs to be consistent not merely with one another but also with the facts.” P. 193 and also preceding texts: “the highest ideal would be always to have a true opinion and be certain of it;” Pp. 204-205 has text on statistics. Pp. 206 ff. is on the meaning of probability, criticizing frequentism. The opening: “there are no such things as objective chances” is reminiscent of de Finetti’s “probability does not exist.” Ramsey died before completing the paper. Then a friend (It may have been by the editor of this book, Richard Braithwaite, as suggested by Fienberg 2008, p. 21) finished the paper. Probably Ramsey himself had finished the text up to p. 184, which is all of the highest possible level. Braithwave finished starting p. 184 and then there are, besides strong parts, also parts of less interest. Braithwave has given a wonderful service to us by finishing this paper. %} Ramsey, Frank P. (1931) “Truth and Probability.” In Richard B. Braithwaite (ed.), The Foundations of Mathematics and other Logical Essays, 156–198, Routledge and Kegan Paul, London. Reprinted in Henry E. Kyburg Jr. & Howard E. Smokler (1964, eds.) Studies in Subjective Probability, 61–92, Wiley, New York. (2nd edn. 1980, Krieger, New York.) {% %} Ramsey, Frank P. (1978) “Foundations: Essays in Philosophy, Logic, Mathematics and Economics.” (David H. Mellor Ed.) Humanities Press, Atlantic Highlands, New Jersey. {% information aversion: under SEU, no information aversion %} Ramsey, Frank P. (1990; Nils-Eric Sahlin, ed.) “Weight or the Value of Knowledge,” British Journal for the Philosophy of Science 41, 1–4. {% Written text of lecture Ramsey gave in 1922. %} Ramsey, Frank P. (2007) “Truth and Simplicity,” British Journal for the Philosophy of Science 58, 379–386. {% %} Ramsey, Frank P. Collection of all his writings: http://digital.library.pitt.edu/cgi-bin/f/findaid/findaid-idx?c=ascead&cc=ascead&rgn=main&view=text&didno=US-PPiU-asp198301
Rao, C. Radhakrishna (1992) “R.A. Fisher: The Founder of Modern Statistics,” Statistical Science 7, 34–48. {% If people must produce randomized sequences, they can’t. (producing random numbers) %} Rapoport, Amnon & David V. Budescu (1997) “Randomization in Individual Choice Behavior,” Psychological Review 104, 603–617. {% decreasing ARA/increasing RRA: increasing RRA but not prominent %} Rapoport, Amnon (1984) “Effects of Wealth on Portfolios under Various Investment Conditions,” Acta Psychologica 55, 31–51. {% three-prisoners problem %} Rapoport, Anatol (1996) “Effects of Information on Assessment of Probabilities, A Reply to Marinoff,” Theory and Decision 41, 149–155. {% %} Rasch, George (1980) “Probabilistic Models for Some Intelligence and Attainment Tests.” University of Chicago Press, Chicago, Ill (expanded edn.). {% %} Rasmusen, Eric (2012) “Internalities and Paternalism: Applying the Compensation Criterion to Multiple Selves across Time,” Social Choice and Welfare 38, 601–615. {% %} Raspe, Rudolph E. (1786) “Baron Münchhausens Narrative of His Marvellous Travels and Campaigns in Russia.” Translated from English into German by Gottfried A. Bürger. {% probability elicitation %} Ravinder, Handanhal V., Don N. Kleinmuntz, & James S. Dyer (1988) “The Reliability of Subjective Probabilities Obtained through Decomposition,” Management Science 34, 186–199. {% Z&Z %} Raviv, Arthur (2005) “The Design of an Optimal Insurance Policy,” American Economic Review 69, 84–96. {% %} Rawling, Piers (1994) “A Note on the Two Envelopes Problem,” Theory and Decision 36, 97–102. {% discounting normative: argues for zero discounting for intergenerational justice in social welfare. Seems to use the term Reflective equilibrium for the gradual convergence between normative decision rules and their implications. P. 137 footnote 11 credits Harsanyi for the veil of ignorance. %} Rawls, John (1971) “A Theory of Justice.” Harvard University Press, Cambridge, MA. {% nonconstant discount = nonlinear time perception; Argue, as did other papers, that deviations from constant discounting may actually be due to nonlinear perception of time. In this theoretical paper it is the central point, illustrated by simulations. %} Ray, Debajyoti & Peter Bossaerts (2011) “Positive Temporal Dependence of the Biological Clock Implies Hyperbolic Discounting,” Frontiers in Decision Neuroscience 5(2). {% Consider intertemporal choice where also past consumption affects felicity, and discuss ways of discouning the past and resulting, claimed, dynamic inconsistencies. %} Ray, Debraj & Ruqu Wang (2001) “On Some Implications of Backward Discounting,” Manuscript. New York: New York Univ., Dept. Econ. {% revealed preference ; Derives choice function from group relation. The result that it then satisfies IIA(R-M) is not surprising. P. 990 1st line, 4th para (“This is the source …” and condition of partitioned information are well observed. %} Ray, Paramesh (1973) “Independence of Irrelevant Alternatives,” Econometrica 41, 987–991. {% decreasing/increasing impatience: seems to find increasing iso the common decreasing. One typically finds: $A now ~ $B in one year, $B in one year ~ $C in two years, but $A now ~ $CX in two years for a positive X. The author calls this subadditivity. It in fact entails intransitivity. Maybe such effects are underlying studies that find hyperbolic discounting. Such studies typically look at [$A now ~ $B in one year] in combination with [$A now ~ $C X] in two years. They, thus, compare time intervals of different lengths. I discovered March 5, 2014, that p. 25 Eq. 16 proposes a variation of exponentional discounting where we take t to a power s. This is what Ebert & Prelec (2007) call constant sensitivity, Bleichrodt, Rohde, & Wakker (2009) call CRDI, and Bleichrodt, Kothiyal, Prelec, & Wakker (2013) call unit invariance. Read claims that the formula implies no declining impatience but this depends on the parameter s, and is not so for s < 1. %} Read, Daniel (2001) “Is Time-Discounting Hyperbolic or Subadditive?,” Journal of Risk and Uncertainty 23, 5–32. {% real incentives/hypothetical choice: argues mostly in favor of hypothetical choice. real incentives/hypothetical choice: for time preferences: because of special problems of implementing real incentives in intertemporal choice, sems to plead here for hypothetical choice in particular. %} Read, Daniel (2005) “Monetary Incentives, What Are They Good for?,” Journal of Economic Methodology 12, 265–276. {% %} Read, Daniel & Fergus I.M. Craik (1995) “Earwitness Identification: Some Influences on Voice Recognition,” Journal of Experimental Psychology, Applied 1, 6–18. {% decreasing/increasing impatience: find counter-evidence against the commonly assumed decreasing impatience and/or present effect. Experiments show that calendar time makes subjects behave rather differently (lower discounting, and less hyperbolic) than stopwatch time (authors don’t use latter term, but instead use term of delay etc. %} Read, Daniel & Shane Frederick, Burco Orsel, & Juwaria Rahman (2005) “Four Score and Seven Years from now: The Date/Delay Effect in Temporal Discounting,” Management Science 51, 1326–1335. {% %} Read, Daniel & George F. Loewenstein (1995) “Diversification Bias: Explaining the Discrepancy in Variety Seeking between Combined and Separated Choices,” Journal of Experimental Psychology, Applied 1, 34–49. {% time preference; Total utility theory %} Read, Daniel & Goerge F. Loewenstein (1999) “Enduring Pain for Money: Decisions Based on the Perception and Memory of Pain,” Journal of Behavioral Decision Making 12, 1–17. {% Choice bracketing means the extent to which you incorporate aspects relevant to the decision into your judgment. Narrow bracketing is like myopic, broad bracketing is like unbounded rationality. Kahneman & Lovallo (1993) put forward similar arguments against narrow bracketing. %} Read, Daniel, George F. Loewenstein, & Matthew Rabin (1999) “Choice Bracketing,” Journal of Risk and Uncertainty 19, 171–197. {% dominance violation by pref. for increasing income: violations of monotonicity because of preferences for increasing sequences, à la Loewenstein & Sicherman (1991), %} Read, Daniel & Melanie Powell (2002) “Preferences for Lifetime and One-Year Distributions of Health and Money,” Journal of Behavioral Decision Making 15, 433–460. {% %} Read, Daniel & Peter H.M.P. Roelofsma (2003) “Subadditive versus Hyperbolic Discounting: A Comparison of Choice and Matching,” Organizational Behavior and Human Decision Processes 91, 140–153. {% SG higher than others; utility elicitation; standard gamble, time tradeoff, and direct scaling, are not interchangeable, and their relationships with each other are complex %} Read, J. Leighton, Robert J. Quinn, Donald M. Berwick, Harvey V. Fineberg, & Milton C. Weinstein (1984) “Preferences for Health Outcomes: Comparisons of Assessment Methods,” Medical Decision Making 4, 315–329. {% %} Rébillé, Yann (2008) “A Yosida–Hewitt Decomposition for Totally Monotone Set Functions on Locally Compact S-Compact Topological Spaces,” International Journal of Approximate Reasoning 48, 676–685. {% For weighting funnctions that are belief functions on finite state spaces and monetary outcomes, the Choquet integral is the minimum of means, and als the mean of minimums, and Möbius transform relates it to unanimity games. This paper provides many generalizations, extending the result to more general state spaces and outcomes. %} Rébillé, Yann (2015) “Integral Representation of Belief Measures on Compact Spaces,” International Journal of Approximate Reasoning 60, 37–56. {% Preferences are over C +. The author defines a quasi-linear representation as (c,) v(c) + , so additivity and linearity in money. The main axiom reflects linearity in : ((x,0) ~(0,z) (x,y) ~(0,z+y). %} Rébillé, Yann (2017) “An Axiomatization of Continuous Quasilinear Utility,” Decisions in Economics and Finance 40, 301–315. {% %} Recktenwald, H. Claus & Wilhelm E. Krelle (1988) “Gossens Gesetze: Leitmuster Moderner Nutzentheorie.” Franz Steiner Verlag Wiesbaden, Stuttgart, 1988. {% Find that discounting is not constant but decreases over time. They consider having a health problem during 4 months. It can be gotten at different times, starting in one day, six months, one year, five years, or ten years. Then they use the standard gamble (and direct scaling) to measure the utility of these. They find 10% negative discounting and 28% positive discounting. Health impairement is negative outcome and then discounting is more variable. Positive discounting gives a convex discount function. But because it is multiplied by a negative value of health the function becomes concave, giving the usual risk aversion. Hence, although they in fact consider risky decisions over waiting time as does the appealing Onay & Öncüler (2007) paper, they do not find a paradox. %} Redelmeier, Donald A. & Daniel N. Heller (1993) “Time Preference in Medical Decision Making and Cost Effectiveness Analysis,” Medical Decision Making 13, 212–217. {% %} Redelmeier, Donald A. & Daniel Kahneman (1996) “Patients’ Memories of Painful Medical Treatments: Real-Time and Retrospective Evaluations of Two Minimally Invasive Procedures,” Pain 66, 3–8. {% %} Redelmeier, Donald A., Derek J. Koehler, Varda Liberman, & Amos Tversky (1995) “Probability Judgment in Medicine: Discounting Unspecified Posibilities,” Medical Decision Making 15, 227–230. {% %} Redelmeier, Donald A., Paul Rozin, & Daniel Kahneman (1993) “Understanding Patients’ Decisions: Cognitive and Emotional Perspectives,” Journal of the American Medical Association 270 72–76. {% context-dependence, violation of IIA; adding one alternative !increases! percentage of people who chose another alternative. %} Redelmeier, Donald A. & Eldar Shafir (1995) “Medical Decision Making in Situations that Offer Multiple Alternatives,” JAMA 273, 302–305. {% Penultimate sentence suggests that the authors consider the discrepancy nonnormative: “Physicians and policy makers may wish to examine problems from both perspectives to ensure that treatment decisions are appropriate whether applied to one or to many patients.” %} Redelmeier, Donald A. & Amos Tversky (1990) “Discrepancy between Medical Decisions for Individual Patients and for Groups,” New England Journal of Medicine 322, 1162–1164. {% Seem to point out that repeated choice and income effect can enhance EV. %} Redelmeier, Donald A. & Amos Tversky (1992) “On the Framing of Multiple Prospects,” Psychological Science 3, 191–193. {% Z&Z: p. 2895/2890: “… selective matching, the tendency to focus on salient coincidences, thereby capitalizing on chance and neglecting contrary evidence.” References are given. %} Redelmeier, Donald A. & Amos Tversky (1996) “On the Belief that Arthritis Pain Is Related to the Weather,” Proceedings of the National Academy of Sciences 93, 2895–2896. {% equity-versus-efficiency: p. “Welfare economics is in a very unhappy state ... considerations of the welfare implications of envy make it impossible even to say that welfare will be increased by everyone having more of every commodity.” Referred to by Robertson (1954 p. 677 without more bibliographic info than that it was in “Welfare Economics”). %} Reder, Melvin W. (1952) “Welfare Economics.” In Bernard F. Haley (ed.) Survey of Contemporary Economics, vol. II, Irwin, Homewood, Illinois. {% conditional probability %} Redhead, Michael L.G. (1986) “Novelty and Confirmation,” British Journal for the Philosophy of Science 37, 115–118. {% foundations of quantum mechanics. Gives all the background. Maths seem to be of not too high a level, according to review in Philosophical Review XCIX (1990), 275–277. %} Redhead, Michael L.G. (1990) “Incompleteness, Nonlocality and Realism: A Prolegomenon to the Philosophy of Quantum Mechanics.” Clarendon Press, New York. {% Suggests that there is nothing new in nudge, it just being classical corrections of of market inadequacies. (It thus misses how nudge adds a subtle nuance to debates on paternalism, by exploiting incompleteness of preference.) Then it cites some references criticizing the effects of New Zealand’s KiwiSaver program, initiated by the Labour government in New Zealand in 2007 as a response to the presumption that New Zealand households were undersaving, and presented by Thaler & Sunstein as a big success of nudge. %} Reed, W. Robert (2013) Book Review of: Thaler, Richard H. & Cass R. Sunstein (2008) “Nudge: Improving Decisions About Health, Wealth, and Happiness.” Yale University Press, New Haven,” Journal of Economic Psychology 34, 302–303. {% %} Reeves, Tim & Robert S. Lockhart (1993) “Distributional versus Singular Approaches to Probability and Errors in Probabilistic Reasoning,” Journal of Experimental Psychology: General 122, 207–226. {% Dutch book %} Regazzini, Eugenio (1987) “De Finetti’s Coherence and Statistical Inference,” Annals of Statistics 15, 845–864. {% This paper criticizes traditional tests of transitivity that assume a deterministic theory and classical statistical tests of it. It thus strongly criticizes statistical analyses based on majority choices (e.g. p. 46 1st column). It favors using probabilistic choice models with what Loomes & Sugden call the random preference model (p. 47) and what can also be called a mixture model. The paper opens with an example where a decision maker randomly has one of three preference relations, each transitive, but observed majority preferences violate transitivity. Advocates of classical deterministic theories can argue that this is a type I error, which is known to happen sometimes. The paper has done an enormous work by analyzing over 100 classical data sets, and adding an experiment. It derives a triangular inequality for the mixture model, argues that this is a strong test of transitivity (p. 44). Acceptance of the null of the triangular inequality is taken as evidence for transitivity. P. 45 1st column argues that deterministic theories are reasonable only if not very much noise. The paper also strongly argues against 2-alternative forced choice (2AFC) studies, which cannot measure indifference (e.g. p. 54 2nd para). %} Regenwetter, Michel, Jason Dana, & Clintin P. Davis-Stober (2011) “Transitivity of Preferences,” Psychological Review 118, 42–56. {% %} Regenwetter, Michel, Jean-Claude Falmagne, & Bernard Grofman (1999) “A Stochastic Model of Preference Change and Its Application to 1992 Presidential Election Panel Data,” Psychological Review 106, 362–384. {% %} Regenwetter, Michel & Moon-Ho R. Ho & Ilia Tsetlin (2007) “Sophisticated Approval Voting, Ignorance Priors, and Plurality Heuristics: A Behavioral Social Choice Analysis in a Thurstonian Framework,” Psychological Review 114, 994–1014. {% %} Regenwetter, Michel & Anthony A.J. Marley (2001) “Random Relations, Random Utilities, and Random Functions,” Journal of Mathematical Psychology 45, 864–912. {% foundations of statistics %} Reid, Nancy (1995) “The Roles of Conditioning in Inference,” Statistical Science 10, 138–199. {% %} Reilly, Robert J. (1982) “Preference Reversal: Further Evidence and Some Suggested Modifications in Experimental Design,” American Economic Review 72, 576–584. {% %} Remage Russell, Jr. & William A. Thompson, Jr. (1966) “Maximum-Likelihood Paired Comparison Rankings,” Biometrika 53, 143–149. {% Nash equilibrium discussion %} Reny, Philip J. & Arthur J. Robson (2004) “Reinterpreting Mixed Strategy Equilibria: A Unification of the Classical and Bayesian Views,” Games and Economic Behavior 48, 355–384. {% Dutch book recommended by Gerry Evers-Kieboom Download 7.23 Mb. Share with your friends:
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