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§3, p. 913 1st para is on randomization: “goes against our intuition. We are reluctant to believe that our decisions are made at random.”
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| §3, p. 913 1st para is on randomization: “goes against our intuition. We are reluctant to believe that our decisions are made at random.”
P. 922 1st para seems to assume that future repetitions of a game just exist, which is Rubinstein’s favorite assumption %} Rubinstein, Ariel (1991) “Comments on the Interpretation of Game Theory,” Econometrica 59, 909–924. {% real incentives/hypothetical choice: p. 626 argues against the necessity of real incentives, mentioning many informal game experiments where it did not matter. %} Rubinstein, Ariel (2001) “A Theorist’s View of Experiments,” European Economic Review 45, 615–628. {% Argues that the phenomena described by Rabin (2000, Econometrica) can be explained by a “minor” modification of expected utility, i.e., one where consequences are changes with respect to a reference point, referring also to Kahneman & Tversky (1979). Does not seem to be aware that this is the same as the idea of reference dependence of Kahneman & Tversky (1979) about consequences, and that Rabin refers to this same idea by writing that loss aversion is a plausible explanation. %} Rubinstein, Ariel (2002) “Comments on the Risk and Time Preference in Economics,” text of lecture on Dec. 5th, 2001; working paper 867. {% Probability matching %} Rubinstein, Ariel (2002) “Irrational Diversification in Multiple Decision Problems,” European Economic Review 46, 1369–1378. {% decreasing/increasing impatience: find counter-evidence against the commonly assumed decreasing impatience and/or present effect. Kirsten&I: intro has countably many outcomes and time points. The alternative model, starting in §2, however, takes uncountably many time points. This is used in his similarity model. Theoretically, it could also be a countable but dense subset of the time axis, such as the rational time points. There can be several consumptions, as in the second experiment. Really the hybrid model, with outcomes evaluated separately discretely and not as flow per time unit. Presents three intertemporal choice problems data (no real incentives) that violate constant discounting for future and not present consumptions, so that the quasi-hyperbolic discounting that only overweights current consumption is violated also. Tries to explain the data through Rubinstein’s (1988) similarity model, although it was not clear to me why some dimensions were more similar than others. An alternative explanation for experiments I and III at least can be that for choices with small differences subjects choose the least complex option. The auther argues that greater brakeaways from traditional economic models may be desirable and concludes: “We need to open the black box of decision making, and come up with some completely new and fresh modeling devices.” %} Rubinstein, Ariel (2003) “Economics and Psychology?” The Case of Hyperbolic Discounting”,” International Economic Review 44, 1207–1216. {% Criticizes the famous kindergarten experiment by Gneezy & Rustichini, questioning the data. %} Rubinstein, Ariel (2006) “Comments on Behavioral Economics.” In Richard Blundell, Whitney K. Newey & Torsten Persson (eds.) Advances in Economics and Econometrics Theory and Applications, vol. II, 246–254, Cambridge University Press, Cambridge. {% Personal view about theoretical economics, complaining many times that it is not useful. Starts with a story about Adam in paradise, having time-consistent invariant preferences over apples, but preferring one apple today to two apples tomorrow and 2 today to 1 today and 1 tomorrow. Then he prefers 1 apple today to one apple each day from day 17 till age of 100. This is not desirable and is Adam’s “first traumatic experience.” The following traumatic experiences nicely illustrate the gradual development away from classical economics. Many claims, such as that against new models as much counterevidence will be found as against classical ones (e.g. p. 871 1st para), should be taken as subjective personal opinions backed up with little evidence. P. 869 is very negative about Rabin’s calibration theorem. Rubinstein’s “solution” is that outcomes should be interpreted as changes with respect to a reference point and not as final wealth. He cites Kahneman & Tversky (1979) for it, and also Cox & Sadiraj in an affirmative manner. What Rubinstein does not realize here is that this “solution” is not a minor modification of expected utility, but a major breakaway, half of the breakaway comprised by prospect theory. What he does not realizes either is that Rabin himself also agrees with this solution and puts it forward as a primary explanation (Rabin 2000, Econometrica, when putting forward loss aversion which entails reference dependence; see last para of the main text, pp. 1288-1289). Rubinstein’s time paradox attempts to suggest that Rabin’s paradox is a routine exercise and, thus, to downplay it. %} Rubinstein, Ariel (2006) “Dilemmas of an Economic Theorist,” Econometrica 74, 865–883. {% No real incentives were used. Decisions to be taken after thinking take more time than decisions to be taken instinctively. Demonstrated through internet experiment with many different things such as game situations. Last experiment is Allais paradox. Risky choice always takes more time. %} Rubinstein, Ariel (2007) “Instinctive and Cognitive Reasoning: A Study of Response Times,” Economic Journal 117, 1243–1259. {% %} Rubinstein, Ariel & Peter C. Fishburn (1986) “Algebraic Aggregation Theory,” Journal of Economic Theory 38, 63–77. {% game theory for nonexpected utility; Nash bargaining solution; nice explanation of role of alternatives underlying utility space and restrictive nature of affine-utility-transformation-invariance. A local optimality condition characterizes Nash B.S without resort to EU. %} Rubinstein, Ariel, Zvi Safra, & William Thomson (1992) “On the Interpretation of the Nash Bargaining Solution and Its Extension to Non-Expected Utility Preferences,” Econometrica 60, 1171–1186. {% %} Rubinstein, Ariel & Yuval Salant (2016) “ “Isn't Everyone Like Me?”: On the Presence of Self-Similarity in Strategic Interactions,” Judgment and Decision Making 11, 168–173. {% common knowledge %} Rubinstein, Ariel & Asher Wolinsky (1990) “On the Logic of “Agreeing to Disagree” Type Results,” Journal of Economic Theory 51, 184–193. {% %} Rubinstein, Ariel & Lin Zhou (1999) “Choice Problems with a ‘Reference’ Point,” Mathematical Social Sciences 37, 205–209. {% %} Rubinstein, Mark (1994) “Implied Binomial Trees,” Journal of Finance 49, 771–818. {% %} Rudin, Walter (1964) “Principles of Mathematical Analysis; 2nd edn.” McGraw-Hill, New York. {% Cooperative game theory. For a cooperative game, find the allocation (probability measure after normalization v(N) = 1) that most closely fitst the game by quadratic distance. Given that they normalize, this is equivalent to minimizing the variance of the excess vS) x(S), which would be a kind of egalitarian principle. Unfortunately, the authors put the latter central, whereas I find the former more appealing. The authors give many properties of their solution. %} Ruiz Luis M., Frederico Valenciano, & Jose M. Zarzuelo (1996) “The Least Square Prenucleolus and the Least Square Nucleolus. Two Values for TU Games Based on the Excess Vector,” International Journal of Game Theory 25, 113–134. {% Relaxes completeness axiom for SEU with linear utility. There exists some events E1,…,En such that f g iff there exists a subjective probability such that the conditional expectation of f given Ej exceeds that of g, for each j. %} Rumbos, Beatriz (2001) “Representing Subjective Orderings of Random Variables: An Extension,” Journal of Mathematical Economics 36, 31–43. {% This and more is on http://www.slate.com/id/2081042/ THE UNKNOWN As we know, There are known knowns. There are things we know we know. We also know There are known unknowns. That is to say We know there are some things We do not know. But there are also unknown unknowns, The ones we don't know We don't know. Rumsfelt, Donal (2002) “The Unkown.” Department of Defense News Briefing, February 12, 2002. {% risky utility u = strength of preference v (or other riskless cardinal utility, often called value) & questionnaire versus choice utility: Pigou cites Russell, referring to p. 182-183, on the point that, if we cannot measure quantities, then we may still be able to judge them, and even to judge on difference comparisons. This is, however, not really what Russell writes there. Anyway, this is a moot point for strength of preference, for instance. %} Russell, Bertrand A.W. (1903) “The Principles of Mathematics.” (Later edn. 1972, Allen & Unwin, London). {% preferring streams of increasing income: P. 462, on Spibnoza’s ideas: “if the universe is gradually improving, we think better of it than if it is gradually deteriorating, even if the sum of good and evil be the same in the two cases. … Accoring to Spinoza this is irrational. … as God sees it; to Him, the date is irrelevant” (the latter is on discounting normative) %} Russell, Bertrand A.W. (1945) “A History of Western Philosophy.” Simon & Schuster, New york. {% On bipolar scales. %} Russell, James A. & James M. Carroll (1999) “On the Bipolarity of Positive and Negative Affect,” Psychological Bulletin 125, 3–30. {% P. 557 3rd para: value of life in the us now is 6.5 million dollar. %} Russell, Louise B. (2014) “Do We Really Value Identified Lives More Highly than Statistical Lives?,” Medical Decision Making 34, 556–559. {% The panel, 13 people, was convened by the US public Health Service (PHS), met 11 times during 2.5 years (first in 1993), in order to improve standardization in Cost-Effectiveness studies. They take societal perspective. P. 1175, top: health states worse than death have negative utility. P. 1175: they take QALY, which has advantage of combining length of time and health quality P. 1175: “Second, since the purpose of investing in health is to make people better-off, it seems appropriate to let them be the judge of what constitutes better or worse outcomes and of the relative magnitudes of health effects.” I disagree with the opinion suggested here and stated also elsewhere, that the utility of the general public having to be maximized, would automatically imply that the general public is best to decide on what that utility function is. P. 1175 discusses question of whether people in a health state judge it more favorable than others, and gives several references. Some find the effect but others don’t find it and find equal judgments. The issue is not clear. %} Russell, Louise B., Marthe R. Gold, Joanna E. Siegel, Norman Daniels, & Milton C. Weinstein (1996, for the Panel on Cost-Effectiveness in Health and Medicine) “The Role of Cost-Effectiveness Analysis in Health and Medicine,” JAMA 276, 1172–1177. {% Book seems to be most popular textbook on AI. P. 532 of 2nd edn., Ch. 14, has nice discussion of fuzzy measures, belief functions, and the like, and their relations with probability. %} Russell, Stuart & Peter Norvig (1993) “Artificial Intelligence A Modern Approach.” (3rd edn. 2009.) Prentice-Hall, Englewood Cliffs, NJ. {% Seems to have recursive EU. %} Rustichini, Aldo (1992) “Decision Theory with Higher Order Beliefs.” In Proceedings of TARK IV. {% One page on Ellsberg and multiple priors, nicely written, with deck of cards rather than urns. %} Rustichini, Aldo (2005) “Neuroscience: Emotion and Reason in Making Decisions,” Science 310 (5754) 1624–1625. {% P. 672 2nd para takes choosing university degree as choice. There, however, is no situation in which we can simply choose a university degree. P. 673 point f (independence) claims that according to classical economics time and risk attitude are uncorrelated, and that these are also uncorrelated with intelligence and other personality traits: ???? No-one ever claimed such a thing, to my knowledge. P. 673 2nd para claims that in classical economics, man is two-dimensional, completely characterized by risk attitude and intertemporal attitude: ??? What about marginal rates of substitution between commodities, to mention just one of million other thing? DC = stationarity: p. 673 2nd column 2nd para middle + p. 674 2nd column 1st para near end. The latter also claims that the management of deviations from past plans (time inconsistencies) has never been discussed in classical economics: ??? Didn’t Strotz himself already discuss it? P. 674 near end claims that according to neuro-economics, the classical two-dimensional man (see above) should be replaced by a five-dimensional man, but it is not explained what the (3 I guess) extra dimensions are. %} Rustichini, Aldo (2009) “Neuroeconomics: What Have We Found, and What Should We Search for,” Current Opinion in Neurobiology 19, 672–677. {% Choices between riskless, risky, very ambiguous, and somewhat ambiguous prospects. The usual ambiguity aversion is found. Neuro-effects are analyzed. %} Rustichini, Aldo, John Dickhaut, Paolo Ghirardato, Kip Smith & José V. Pardo (2005) “A Brain Imaging Study of Procedural Choice,” Games and Economic Behavior 52, 257–282. {% %} Ruszczyński, Andrzej & Alexander Shapiro (2006) “Optimization of Convex risk Functions,” Mathematics of Operations Research 31, 433–452. {% probability elicitation: applied to experimental economics; Experimentally show that eliciting subjective beliefs using scoring rules in a game situation can impact the play in the game after. questionnaire versus choice utility: pp. 617-618 argue that stated beliefs may better predict game behavior than elicited beliefs, and they find it confirmed in the experiment. No real incentives for stated beliefs!? %} Rutström, Elisabet E. & Nathaniel T. Wilcox (2009) “Stated Beliefs versus Inferred Beliefs: A Methodological Inquiry and Experimental Test,” Games and Economic Behavior 67, 616–632. {% SG gold standard: seem to write that; Seem to argue that the rating scale has drawback of making participants “spread” answers over whole scale. %} Rutten-van Molken, Maureen P.M.H., Carla H. Bakker, Eddy K.A. van Doorslaer, & Sjef van der Linden (1995) “Methodological Issues of Patient Utility Measurement,” Medical Care 33, 922–937. {% %} Rutten, Frans F.H., Han Bleichrodt, Werner B.F. Brouwer, Marc A. Koopmanschap, & Frederik T. Schut (2001) “Handbook of Health Economics,” Journal of Health Economics 20, 855–879. {% %} Rutten, Frans F.H., & Gouke J. Bonsel (1992) “High Cost Technology in Health Care: A Benefit or a Burden?,” Social Science and Medicine 4, 567–577. {% %} Rutten, Frans H., Han Bleichrodt, Werner B.F. Brouwer, Marc A. Koopmanschap, & Frederik T. Schut (2001), Book Review of Antony J. Culyer & Joseph P. Newhouse (2001) “Handbook of Health Economics,” Elsevier, Amsterdam; Journal of Health Economics 20, 855–879. {% What they call completeness is consistency (repeating same choice some time later so that independent and not remembered), and what they call discontinuous is lexicographic (no tradeoffs). They test and discuss these conditions. %} Ryan, Mandy, Verity Watson, & Vikki Entwistle (2009) “Rationalising the Irrational: A Think Aloud Study of Discrete Choice Experiment Responses,” Health Economics 18, 321–336. {% Definition of support in nonadditive measure theory %} Ryan, Matthew J. (1996) “CEU Preferences and Game-Theoretic Equilibria,” Yale University. {% dynamic consistency: updating capacities %} Ryan, Matthew J. (2001) “Capacity Updating Rules and Rational Belief Changes,” Theory and Decision 51, 73–87. {% Generalizes/simplifies result of Chew, Karni, & Safra, and many related results. %} Ryan, Matthew J. (2006) “Risk Aversion in RDEU,” Journal of Mathematical Economics 42, 675–697. {% Didactical survey of nonEU representation theorems using the Anscombe-Aumann approach. %} Ryan, Matthew J. (2009) “Generalizations of SEU: A Geometric Tour of Some Non-Standard Models,” Oxford Economic Papers 61, 327–354. {% Gives examples of finite sets that are mixture sets. Then usually all nontrivial mixtures of x and y are either x or y. Relates it to a mathematical theory of antimatroids. This paper is useful for alternative axiomatizations of vNM EU. Refers to Hausner (1954), for one. %} Ryan, Matthew J. (2010) “Mixture Sets on Finite Domains,” Decisions in Economics and Finance 33, 139–147. {% revealed preference: a variation on Plott’s path independence. %} Ryan, Matthew (2014) “Path Independent Choice and the Ranking of Opportunity Sets,” Social Choice and Welfare 42, 193–213. {% Z&Z; inverse-S: is used to explain some empirical findings on moral hazard. %} Ryan, Matthew J. & Rhema Vaithianathan (2000) “Medical Insurance with Rank-Dependent Expected Utility,” Working paper, Dept. of Economics, Australian National University, Canberra, Australia. {% Z&Z; inverse-S: is used to explain some empirical findings on adverse selection %} Ryan, Matthew J. & Rhema Vaithianathan (2000) “Adverse Selection and Insurance Contracting: A Non-Expected Utility Analysis,” Working paper, Dept. of Economics, Australian National University, Canberra, Australia. {% %} Ryan, Terence M. (1974) “The Use of Unbounded Utility Functions in Expected-Utility Maximization: Comment,” Quarterly Journal of Economics 88, 133–135. {% Reconsider Gneezy & Rustichini (2000). Support the Camerer & Hogarth (1999) view that cognitive effort is important. %} Rydval, Ondrej & Andreas Ortmann (2004) “How Financial Incentives and Cognitive Abilities Affect Task Performance in Laboratory Settings: An Illustration,” Economics Letters 85, 315–320. {% Re-examine and doubt about Gneezy, List, & Wu (2006). %} Rydval, Ondřej, Andreas Ortmann, Sasha Prokosheva & Ralph Hertwig (2009) “How Certain is the Uncertainty Effect?,” Experimental Economics 12, 473–487. {% Introduced logical behaviorism: one can talk of mental states, which ultimately can be re-expressed in behavioral language. %} Ryle, Gilbert (1949) “The Concept of Mind.” Penguin, Harmondsworth, UK. {% %} Saaty, Thomas L. (1980) “The Analytic Hierarchy Process.” McGraw-Hill, New York. {% %} Saaty, Thomas L. (1986) “Axiomatic Foundation of the Analytic Hierarchy Process,” Management Science 32, 841–855. {% questionnaire for measuring risk aversion: p. 39 table 1 has nice way to measure risk attitude: people choose one from 10 prospects, and the more to the right they choose the more risk seeking they are. Bit like Binswanger (1981). %} Sabater-Grande, Gerardo & Nikolaos Georgantzis (2002) “Accounting for Risk Aversion in Repeated Prisoners’ Dilemma Games: An Experimental Test,” Journal of Economic Behavior and Organization 48, 37–50. {% utility elicitation; They list five questions on utility measurement as their central topics; I am puzzled about the answers to Questions 3 and 5 below, which seem to be contradictory. Question 3 asks if the utility of a health state depends on the time spent in that health state. They find that the utility of a health state falls “dramatically” (p. 703; i.e., a violation of Stalmeier’s proportionality heuristic) as the duration is longer. Question 5 addresses the question of whether being in a health state affects its utility. They find that people in a health state (e.g., kidney dialysis patients) value their state higher than the general public does (which runs contrary to strategic answering). %} Sackett, David L. & George W. Torrance (1978) “The Utility of Different Health States as Perceived by the General Public,” Journal of Chronic Disease 31, 697–704. {% This paper introduces a nice paradox for RDU that is a sort of analog of Rabin’s (2000) calibration paradox for EU. It is tested empirically in the follow-up paper by Cox, Sadiraj, Vogt, & Dasgupta (2013). It is discussed in Exercise 7.4.2 of Wakker (2010), who cites Cox et al. (2013 EE; well, their 2007 working paper version) for it. But this paper by Sadiraj has the priority. Assume RDU. For each i = 0,…,98, we write ri = i/100. Assume that a subject exhibits risk averse preferences as follows: (ri:6, 0.01:6, 0.01:0, (1 ri 0.02):0) (ri:6, 0.01:2, 0.01:2, (1 ri 0.02):0) and that, with U(0) = 0, U(6)/U(2) > 2.1. Then it follows that w(0.5) < 0.01. %} Sadiraj, Vjollca (2014) “Probabilistic Risk Attitudes and Local Risk Aversion: A Paradox,” Theory and Decision 77, 443–454. {% information aversion: cites literature, including Savage (1954), that some versions of maxmin EU are vulnerable to aversion to info. Wakker 1988 JBDM, showed that this happens for all nonEU that are not dynamically consistent, with p. 173 first objection in §4 putting forward that forgone-event independence is assumed. This paper shows there are even situations in which all info is rejected. %} Sadler, Evan (2015) “Minimax and the Value of Information,” Theory and Decision 78, 575–586. {% preference for flexibility: %} Sadowski, Philipp (2013) “Contingent Preference for Flexibility: Eliciting Beliefs from Behavior,” Theoretical Economics 8, 503–534. {% %} Sadrieh, Abdolkarim, Werner Güth, Peter Hammerstein, Stevan Harnard, Ullrich Hoffrage, Bettina Kuon, Bertrand R. Munier, Peter M. Todd, Massimo Warglien, & Martin Weber (1999) “Is there Evidence for an Adaptive Toolbox?,” Arbeitsbericht 99-51, Universität Mannheim. {% A 2002 paper was called Discounting and Future Selves, and Weibull and I discussed it in Amsterdam General discounted utility says that U = SUMt=0n f(t)u(xt) is to be maximized, with u some instant utility, maybe hedonic. The case f(t) = t is constant discounting. The authors rewrite it as a linear combination u(x0) + SUMt=1n a(t)Ut(x) where each Ut(x) is a linear combination of u(xt) and the Uj(x)’s for j > t. Ut is the total happiness experienced at time t. The authors impose conditions on the Ut’s and analyze when then all a(t)’s can be nonnegative. It feels some like double counting where xn affects the happiness at time n, then also that at time n1 through altruism of self at time n1 with time n, then at time n2, and thus affects happiness at time 0 indirectly through all intermediate utilities. Constant discounting can be obtained as the special case where Ut depends only on xt and Ut+1 (reminiscent of recursive formulas) and is a boundary case (p. 260 end of §3). %} Sáez-Martí, María & Jörgen Weibull (2005) “Discounting and Altruism to Future Decision-Makers,” Journal of Economic Theory 122, 254–266. {% Nice introduction to, frequent, use of multi-attribute utility, or conjoint measurement, in marketing research literature. %} Safizadeh, M. Hossein (1989) “The Internal Validity of the Trade-Off Method of Conjoint Analysis,” Decision Sciences 20, 451–461. {% %} Safra, Zvi & Uzi Segal (1993) “Dominance Axioms and Multivariate Nonexpected Utility Preferences,” International Economic Review 34, 321–334. {% %} Safra, Zvi & Uzi Segal (1995) “How Complicated Are Betweenness Preferences?,” Journal of Mathematical Economics 24, 371–381. {% What they call “constant risk aversion” is constant absolute !and! constant RRA. Theorem 1: Fréchet differentiable functional V over lotteries that satisfies constant absolute and RRA is an expected value functional. P. 29 argues against the use of rank-dependence in axioms (similarly to Luce, 1996): “Since rank dependent functionals evaluate outcomes not only by their value but also by their relative rank as compared to other possible outcomes, axioms that presuppose attitudes that are based on outcomes’ relative rank are arguably less convincing than axioms that do not make an explicit appeal to such ranks.” Theorem 3 characterizes the Yaari functional, so RDU with linear utility, for a quadratic probability weighting function of the form w(p) = p + cp cp2. %} Safra, Zvi & Uzi Segal (1998) “Constant Risk Aversion,” Journal of Economic Theory 83, 19–42. {% The authors argue, as do Safra & Segal (1998) and Luce, that axiomtizations of rank-dependent utility explicitly using rank-ordering of outcomes are unsatisfactory. I agree that it is interesting to have an axiomatization that does not explicitly use rank-dependence. I disagree, however, with the claim that an explicit use of rank-ordering be unsatisfactory: the rank-ordering of outcomes is directly observable (and there is an intuition to using it) and, hence, there is no reason not to use it explicitly. %} Safra, Zvi & Uzi Segal (2001) “Rank-Dependent Preferences without Ranking Axioms,” Journal of Mathematical Economics 35, 547–562. {% %} Safra, Zvi & Uzi Segal (2008) “Calibration Results for Non-Expected Utility Theories,” Econometrica 76, 1143–1166. {% BDM (Becker-DeGroot-Marschak) %} Safra, Zvi, Uzi Segal, & Avia Spivak (1990) “Preference Reversals and Non-Expected Utility Behavior,” American Economic Review 80, 922–930. {% %} Safra, Zvi, Uzi Segal, & Avia Spivak (1990) “The Becker-DeGroot-Marschak Mechanism and Anticipated Utility,” Journal of Risk and Uncertainty 3, 177–190. {% favors sophisticated choice %} Safra, Zvi & Eyal Sulganik (1995) “On the Nonexistence of Blackwell’s Theorem-Type Results with General Preference Relations,” Journal of Risk and Uncertainty 10, 187–201. {% information aversion %} Safra, Zvi & Eyal Sulganik (1995) “Schur Convexity, Quasi-Convexity and Preference for Early Resolution of Uncertainty,” Theory and Decision 39, 213–218. {% %} Safra, Zvi, Lin Zhou, & Itzhak Zilcha (1990) “Risk Aversion in the Nash Bargaining Problem with Risky Outcomes and Risky Disagreement Points,” Econometrica 58, 961–965. {% Preference condition considered concerns choice with reference points. It is a no-regret condition of the following kind: assume that, with some arbitrary reference point, you can choose between x and y, and you choose x. Then, so it is assumed, x becomes your new reference point (an essential modification and clarification of this point comes later). The paper then assumes that, with x as new reference point, y should never be preferred to x. So a point should always become more preferred if it becomes a reference point, suggesting a status-quo preference. The paper shows that most theories violate this condition unless reference independence. The essential modification and clarification announced above is that for a prospect x not x itself (a random reference point as in Sugden 2003; this paper is referenced in footnote 13, but as a betweenness paper, and not for his modeling of reference dependence; data of Roca, Hogarth, & Maule 2006 support that x itself, and not its certainty equivalent, is taken as reference point) is taken as reference point, but instead a constant outcome, being the certainty equivalent of the prospect. The reference point above is defined in an implicit manner because the preference relation w.r.t. which the certainty equivalent is determined, depends on the reference point and hence on the certainty equivalent. The following example on prospect theory clarifies what is going on. Assume that PT holds with linear probability weighting and linear utility for gains and for losses, and loss aversion factor 2. This means that prospects are judged relatively unfavorable, with certainty equivalent below expectation, if the reference point is somewhere between the outcomes of the prospect so that the prospect is mixed, and they are judged relatively favorable, with certainty equivalent being expectation as under risk neutrality if the reference point is below or above all outcomes of the prospect. Now for each prospect the reference point is the sure outcome such that the absolute value of the expectation of the prospect below the outcome is half of its expectation above; this reference point is smaller than the expectation of the prospect. Imagine that a current reference point is below a prospect’s lowest outcome. The decision maker must choose between that prospect and its expectation minus a very small positive epsilon. All outcomes being above the reference point and, hence, expected value governing preference, the decision maker prefers the prospect and takes it. Then, so it is assumed, the decision maker adjusts the reference point to the present situation, taking the reference point as explained above. In this new situation the reference point is between the outcomes of the prospect, loss aversion with overweighting of the lowest outcomes is effective and generates risk aversion, and the decision maker now prefers the expectation minus epsilon to the prospect, and regrets the previous choice. The phenomenon is generated by the reference point being the sure outcome and not the prospect. %} Sagi, Jacob S. (2006) “Anchored Preference Relations,” Journal of Economic Theory 130, 283–295. {% %} Sagi, Jacob (2006) “What is an `Endogenous State Space´?,” Economic Theory 27, 305–320. {% %} Sagi, Jacob, David Laughton, & Michael Samis (2000) “Modern Asset Pricing and Project Evaluation in the Energy Industry?,” Journal of Energy Literature. {% %} Sagi, Jacob & Mark S. Seasholes (2007) “Firm Specific Attributes and the Cross-Section of Momentum?,” Journal of Financial Economics 84, 389–434. {% utility families parametric: expo-power utility function, u(x) = 1exp(x), for > 0; (I think that =0 and =0 can be included also, for = 0 it is x, for = 0 it seems to be logarithmic I’m not sure). Arrow-Pratt measure: U''/U' = r + (1r)x1r. Discusses some properties of the family; for 1 the functions are concave and exhibit decreasing absolute risk aversion; for > 0 (i.e., > 0) they exhibits increasing RRA. In short, for 0 < < 1 they are really nice. P. 906: refs to some studies on risk attitude in agriculture using negatively exponential utility. %} Saha, Atanu (1993) “Expo-power Utility: A Flexible Form for Absolute and Relative Aversion,” American Journal of Agricultural Economics 75, 905–913. {% %} Saha, Atanu, C.Richard Shumway, & Hovav Talpaz (1994) “Joint Estimation of Risk Preference Structure and Technology Using Expo-Power Utility,” American Journal of Agricultural Economics 76, 173–184. {% second-order probabilities to model ambiguity %} Sahlin, Nils-Eric (1983) “On Second-Order Probabilities and the Notion of Epistemic Risk.” In Bernt P. Stigum & Fred Wendstøp (eds.) Foundations of Utility and Risk Theory with Applications, 95–104, Reidel, Dordrecht. {% %} Sahlin, Nils-Eric (1985) “Three Decision Rules for Generalized Probability Representations,” The Behavioral and Brain Sciences 84, 751–753. {% Ch. 1 discusses Ramsey’s work. %} Sahlin, Nils-Eric (1990) “The Philosophy of F.P. Ramsey.” Cambridge University Press, Cambridge. {% %} Sahlin, Nils-Eric (1991) “Bacon Inductivism in Research on Human Decision-Making,” Theory & Psychology 1, 431–450. {% second-order probabilities to model ambiguity: p. 13 bottom cites many discussions, with Keynes (1921) the earliest. Nice citation of Hume on uncertainty about uncertainty about ... ad infinitum. Nice citation of Ramsey who writes, a.o., on the probability of Fermat’s last theorem being true. He says, having accepted some objective physical notion of probability, that its probability is 1 or 0. “but we cannot see it.” Then he goes on to explain that “our attitude towards it ... we may attach considerable probability in virtue of our knowledge of Fermat, and this probability must determine our conduct with regard to this theorem, whose own probability we cannot determine.” In next paragraph, Ramsey explains in fact Bayesian priors: “We have to make some hypothesis as to the initial likelihood of different values of its probability.” Let me repeat that the term probability here seems to by objective physical probability. I disagree with Sahlin’s discussion of Savage’s writing on p. 24/25 and in his closing sentence, because one should understand Savage’s writing within Savage’s model, and not within Sahlin’s model as Sahlin does on p. 25. %} Sahlin, Nils-Eric (1994) “On Higher Order Beliefs.” In Jacques-Paul Dubucs (ed.) Philosophy of Probability, 13–34. Kluwer, Dordrecht. {% %} Sahlin, Nils-Eric & Johannes Persson (1994) “Epistemic Risk: The Significance of Knowing What One Does Not Know.” In Berndt Brehmer & Sahlin, Nils-Eric (eds.) Future Risks and Risk Management, 37–62, Kluwer, Dordrecht. {% %} Sainfort, François & Jean M. Deichtmann (1993) “Decomposition of Utility Functions on Subsets of Product Sets.” {% Shows a mistake in Halevy (2008, AER) and corrects it. See my comments at Halevy (2008). %} Saito, Kota (2011) “Strotz Meets Allais: Diminishing Impatience and the Certainty Effect: Comment,” American Economic Review 101, 2271–2275. {% DOI: http://dx.doi.org/10.1257/aer.103.7.3084 Analyzes ex post versus ex ante equity in a lottery setup. It is a probabilized extension of Fehr-Schmidt. P. 3087 gives axiomatization of Fehr-Schmidt (formal result in Lemma 1 in Appendix) very similar to Rohde (2010). P. 3093 3rd para claims simultaneous independent discovery. I recommend dropping such novelty claims three years after. %} Saito, Kota (2013) “Social Preferences under Risk: Equality of Opportunity versus Equality of Outcome,” American Economic Review 103, 3084–3101. {% quasi-concave so deliberate randomization: has it. criticism of monotonicity in Anscombe-Aumann (1963) for ambiguity. Discusses Raiffa’s randomization argument against Ellsberg. That Raiffa implicitly assumes dynamic decision principles that amount to (most of) EU anyhow. Raiffa assumes that prior commitment can be. Further, Raiffa assumes conditioning on the ambiguous events, but one can as well condition on the risky events and then his randomization does not remove ambiguity. I want to add here a point in my 2008 paper for which I credit Jaffray there: it is more natural to condition on the unambiguous event, say the roulette wheel, than on the ambiguous event. This paper proposes and axiomatizes a model that with weight has the ambiguous events precede the objective probabilities, and with 1 takes the ordering the other way around, doing backward induction in both cases. %} Saito, Kota (2015) “Preferences for Flexibility and Randomization under Uncertainty,” American Economic Review 105, 1246–1271. {% measure of similarity %} Saito, Takayuki (1994) “Psychological Scaling of the Asymmetry Observed in Comparative Judgement,” British Journal of Mathematical and Statistical Psychology 47, 41–62. {% %} Salanié, Bruno (2003) “The Economics of Taxation.” The MIT Press, Cambridge, MA. {% revealed preference They formalize framing simply as a new empirical primitive. (C,f) with C a subset of the conceivable choice prospects designates choosing from C under framing f. Derive some theorems. Is similar to Bernheim & Rangel (2009). Reminds me some of Wang & Fischbeck (2004) who took as extra parameter whether subjects used a gain or loss frame. %} Salant, Yuval & Ariel Rubinstein (2008) “Choice with Frames,” Review of Economic Studies 75, 1287–1296. {% %} Sales, Célia M.D. (2005) “Terapia Familiar en Contexto Psiquiátrico: Aportaciones para la Comprensión del Cambio Psicoterapéutico.” Seville: Faculty of Medicine, Department of Psychiatry. Ph.D. Thesis. {% measure of similarity %} Sales, Célia M.D. & Peter P. Wakker (2009) “The Metric-Frequency Measure of Similarity for Ill-Structured Data Sets, with an Application to Family Therapy,” British Journal of Mathematical and Statistical Psychology 62, 663–682. Link to paper
Sales, Célia M. D., Peter P. Wakker, Paula C. G. Alves, & Luís Faísca (2015) “MF Calculator: A Web-based Application for Analyzing Similarity,” Journal of Statistical Software 65, May 2015, code snippet 2. Link to paper
Salminen, Pekka & Jyrki Wallenius (1993) “Testing Prospect Theory in a Deterministic Multiple Criteria Decision-Making Environment,” Decision Sciences 24, 279–294. {% %} Salo, Ahti A. (1995) “Interactive Decision Aiding for Group Decision Support,” European Journal of Operational Research 84, 134–149. {% MAUT with imprecise, interval, statements %} Salo, Ahti A. & Raimo P. Hämäläinen (1992) “Preference Assessment by Imprecise Ratio Statements,” Operations Research 40, 1053–1061. {% PT, applications: nonadditive measures, overbidding. Use convex capacities to obtain alternative explanation for phenomenon that submitted bids exceed EU-Nash-Equilibrium predictions in first-price sealed-bid auctions. %} Salo, Ahti A. & Martin Weber (1995) “Ambiguity Aversion in First-Price Sealed-Bid Auctions,” Journal of Risk and Uncertainty 11, 123–137. {% conditional probability %} Salop, Steven C. (1987) “Evaluating Uncertain Evidence with Sir Thomas Bayes: A Note for Teachers,” Economic Prespectives 1, 155–160. {% foundations of statistics: a book on the history of statistics aiming at a general public. %} Salsburg, David (2001) “Who Said Statistics is a Dull Subject? The Lady Tasting Tea: How Statistics Revolutionized Science in the 20th Century.” W.H. Freeman and Company, New York. {% common knowledge %} Samet, Dov (1990) “Ignoring Ignorance and Agreeing to Disagree,” Journal of Economic Theory 52, 190–207. {% Value of independent sources is not additive %} Samson, Danny, Andrew Wirth, & John Rickard (1989) “The Value of Information from Multiple Sources of Uncertainty in Decision Analysis,” European Journal of Operational Research 39, 254–260. {% real incentives/hypothetical choice : whether and how much real incentives improve performance is not at all clear, and depends on many details. This paper investigates it in the context of the use of decision aids. %} Samuels Janet A. & Stacey M. Whitecotton (2011) “An Effort Based Analysis of the Paradoxical Effects of Incentives on Decision-Aided Performance,” Journal of Behavioral Decision Making 24, 345–360. {% %} Samuels, Warren J. (1988) “An Essay on the Nature and Significance of the Normative Nature of Economics,” Journal of Post Keynesian Economics 10, 347–354. {% General observations regarding theories and experiments. Pp. 88-91 discuss Rabin’s (2000) paradox, suggesting utility of income as solution, and I guess he missed the last para of Rabin’s paper where Rabin suggests the same solution through the term loss aversion. %} Samuelson, Larry (2005) “Economic Theory and Experimental Economics,” Journal of Economic Literature 63, 65–107. {% Seems to be his first publication. marginal utility is diminishing: p. 158: “In general, economists assume on a priori grounds that marginal utility decreases with income in a monotonic manner.” time preference; derives cardinal utility from additive (or integrated) utility of money over time, assuming discounting that is known a priori; (by the way, it could be done without knowing the discount factor by means of the Tradeoff method of Wakker & Deneffe, 1996). P. 161: “ordering differences in utility by the individual. The advantage of our experiment is that it compels indidividuals to make just such judgments.” [italics from original]. P. 160, last full paragraph, already describes, I think, Becker’s idea, “theory of history,” that one might incorporate all of history in utility, and calls theory of history a contradiction in terms, maybe for being too general. risky utility u = transform of strength of preference v: this paper is not at all on risk, but on time preference. There it explicitly distinguishes (last paragraph of paper, on p. 161), the cardinal utility function of constant discounting from cardinal utility for welfare theory. DC = stationarity? P. 160 third paragraph beginning describes, I think, forgone-act independence (often called consequentialism) (the 1940 sentence), and then after that DC (e.g., mentioning precommitment). So he never explicitly mentions stationarity but it’s nicely implied à la Han & I. P. 155 l.-2 describes DC vaguely: “whose tastes maintain a certain invariance throughout the time” Top of p. 160 says that functions that allow unlimited interrelationships become so general as to be almost vacuous. risky utility u = transform of strength of preference v: well, he says that time-pref. utility is not welfare utility, but that’s the same kind of thinking. risky utility u = transform of strength of preference v (?latter doesn’t exist?): p. 161 discusses that additive time preference leads to cardinal utility and, hence, meaningful comparison of utility difference and writes: “…we must invoke Pareto’s Postulate Two, which relates to the possibility of ordering differences in utility by the individual. … The advantage of our experiment is that it compels the individual to make just such judgments. …any connection between utility as discussed here and any welfare concept is disavowed.” [italics from original.] %} Samuelson, Paul A. (1937) “A Note on Measurement of Utility,” Review of Economic Studies 4 (Issue 2, February 1937) 155–161. {% utility = representational? revealed preference; p. 71 (Sen’s citation) wants the analysis to be “freed from any vestigial traces of the utility concept.” Introduced WARP. %} Samuelson, Paul A. (1938) “A Note on the Pure Theory of Consumer’s Behaviour,” Economica, N.S. 5, 61–71, 353–354. {% risky utility u = transform of strength of preference v, latter doesn’t exist; P. 344: “Secondly, there has been a progressive movement toward the rejection of hedonistic, introspective, psychological elements.” Derives, I think, some results of prices, equilibria, for consumer theory, showing that nothing more than ordinal utility is needed. %} Samuelson, Paul A. (1938) “The Empirical Implications of Utility Analysis,” Econometrica 6, 344–356. {% risky utility u = transform of strength of preference v, latter doesn’t exist: argues that cardinal utility in welfare economics is useless, p. 65: “Only those who consider general welfare as the algebraic sum of individual utilities require that utility be measurable in a cardinal sense. It is not only that we can get along without this cardinal concept, but literally nothing is added by its assumption.” P. 66 shows that, under smoothness, same ordering of utility differences implies cardinal equivalence. P. 70 shows, on strength of preferences, that [X1;X2] ~* [X1';X2'] and [X2;X3] ~* [X2';X3'] should imply [X1;X3] ~* [X1';X3'] is the main condition required to have a utility difference representation. Claims that it is not a plausible condition. A theoretical study of Samuelson’s axiom, generalizing all existing characterizations of strength-of-preference through utility difference, is in Köbberling (2004, Economic Theory). %} Samuelson, Paul A. (1938) “The Numerical Representation of Ordered Classifications and the Concept of Utility,” Review of Economic Studies 6 (Issue 1, October 1938) 65–70. {% %} Samuelson, Paul A. (1940) “Foundations of Analytical Economics, The Observational Significance of Economic Theory,” (Ph.D. dissertation), Harvard University, Dept. of Economics, Cambridge, MA. {% %} Samuelson, Paul A. (1942) “Constancy of the Marginal Utility of Income.” In Oskar Lange, Francis McIntyre, & Theodore O. Yntema (eds.) Studies in Mathematical Economics and Econometrics: In Memory of Henry Schultz, 75–91, The University of Chicago Press, Chicago. {% P. 206: “To a man like Edgeworth, steeped as he was in the Utilitarian tradition, individual utility—nay social utility—was as real as his morning jam.” Seems to write: “The method of comparative statics consists of the study of the response of our equilibrium unknowns to designated changes in the parameters.” %} Samuelson, Paul A. (1947) “Foundations of Economic Analysis.” Harvard University Press, Cambridge, MA. Enlarged edn. 1983. {% revealed preference %} Samuelson, Paul A. (1948) “Consumption Theory in Terms of Revealed Preference,” Economica, N.S. 15, 243–253. {% End of footnote 2 already predicts that different methods for utility elicitation, that should lead to identical results under expected utility, in reality can be expected to give different empirical results. P. 120 gives the famous Samuelson saying that the axioms should satisfy themselves, ascribing it to a friend. Samuelson presents the most rational man that he knows, Ysidro (most probably Edgeworth), presents a nonEU functional for him, and then writes about him: “When told that he did not satisfy all of the v. Neumann-Morgenstern axioms, he replied that he thought it more rational to satisfy his preferences and let the axioms satisfy themselves.” Footnote on p. 119 nicely credits Marschak for working on preference conditions for risk. On later occasions Samuelson, in personal correspondence to Fishburn and me, wrote that he learned the independence condition from Marschak. In a 1965 postscript, Samuelson says that Marschak, in this work, enjoyed many discussions on the topic with Herman Rubin. Footnote on p. 121: risky utility u = transform of strength of preference v, latter doesn’t exist %} Samuelson, Paul A. (1950) “Probability and the Attempts to Measure Utility,” Economic Review 1, 117–126. Reprinted in Joseph E. Stiglitz (1966, ed.) The Collected Scientific Papers of Paul A. Samuelson, Ch. 12, MIT-Press, London. {% revealed preference %} Samuelson, Paul A. (1950) “The Problem of Integrability in Utility Theory,” Economica, N.S. 17, 355–385. {% Seems to compare utility with potential energy. 29Jun2015: I think that this is not in this paper. Para on pp. 672-673: It is this independence axiom that is crucial for the Bernoulli-Savage theory of maximization of expected cardinal utility, and which is the concern of the present symposium. Within the stochastic realm, independence has a legitimacy that it does not have in the nonstochastic realm. Why? Because either heads or tails must come up: if one comes up, the other cannot; so there is no reason why the choice between A1 and B1 should be "contaminated" by the choice between A2 and B2.3 How different this is as compared to the two blends of gasoline, where we must reckon with physical and chemical interactions. The footnote 3, on p. 673, starts with: “Around 1950, Marschak, Dalkey, Nash, and others independently recognized the crucial importance of the independence axiom.” %} Samuelson, Paul A. (1952) “Probability, Utility, and the Independence Axiom,” Econometrica 20, 670–679. {% %} Samuelson, Paul A. (1953) “Utilité, Préférence et Probabilité” (including discussion; paper given before the conference on “Les Fondements et Applications de la Théorie du Risque en Économetrie,” May, 1952) Colloques Internationaux du Centre National de la Recherche Scientifique (Econométrie) 40, 141–164. Translated into English in Joseph E. Stiglitz (1966, ed.) The Collected Scientific Papers of Paul A. Samuelson, Ch. 13, MIT-Press, London. {% %} Samuelson, Paul A. (1953) “Consumption Theorems in Terms of Over-Compensation Rather than Indifference Comparisons,” Economica, N.S. 20, 1–9. {% %} Samuelson, Paul A. (1958) “An Exact Consumption-Loan Model of Interest with or without the Social Contrivance of Money,” Journal of Political Economy 46, 467–482. {% P. 146 suggests that utility functions are bounded. linear utility for small stakes: bottom of p. 147 says that utility tends to linearity if outcomes tend to zero (which I agree, though it does not hold for log-power utility; but that is a problem of that parametric family). Point 7 on p. 35 repeats the point, with the premise of smoothness made explicit though. Point 7 on p. 35 points out, à la de Finetti, that we can elicit subjective probabilities by taking small stakes to that utility is approximately linear. Footnote 5 points out the problem that there is no incentive for small stakes. This is a nice footnote anyhow, because it also points out a similarity to the Heisenburg uncertainty principle, though the similarity refers only to utility being nonlinear for methods requiring linear utility, and not to the constructive view of preference in full force. %} Samuelson, Paul A. (1959) “The St. Petersburg Paradox as a Divergent Double Limit,” International Economic Review 1, 31–37. Reprinted as Ch. 15 in Joseph E. Stiglitz (1966, ed.) “The Collected Scientific Papers of Paul A. Samuelson.” MIT-Press, London. {% Colleague did not accept 50/50 gamble for $200 and -$100, but would accept multiple gambles of that sort. Note that the point had already been mentioned by Edwards (1954). P. 2 l. 3 writes: “I won’t bet because I would feel the $100 loss more than the $200 gain.” Footnote 2 on p. 50 also states loss aversion as a “corner” in utility at the “initial point.” %} Samuelson, Paul A. (1963) “Risk and Uncertainty: A Fallacy of Large Numbers,” Scienta 98, 108–113. {% Discussions about the vNM independence axiom: Vol. I Ch. 12 (1950), Ch. 13 (1952), Ch. 14 (1952), Ch. 14 (1952), %} Samuelson, Paul A. (1966-1986) “The Collected Scientific Papers of Paul A. Samuelson,” Vol. I-V. Vols I and II, Joseph E. Stiglitz (ed. 1966) MIT-Press, Cambridge, MA. Vol. III, Robert C. Merton (ed. 1970), MIT-Press, Cambridge, MA. Vol. IV, Hiroaki Nagatani & Kate Crowley (ed. 1977) MIT-Press, Cambridge, MA. Vol. V, Kate Crowley (ed. 1986) MIT-Press, Cambridge, MA. {% %} Samuelson, Paul A. (1969) “Lifetime Portfolio Selection by Dynamic Stochastic Programming,” Review of Economics and Statistics 51, 239–246. {% Pp. 34, 49, 29 note that unbounded EU iff infinite certainty equivalent.. P. 34 2nd para points out that bounded utility implies that Ces of truncations of the St. Petersburg paradox converge to a real-valued limit, citing Menger. This is a special case of my truncation-continuity (Wakker 1993 MOR). %} Samuelson, Paul A. (1977) “St.-Petersburg Paradoxes: Defanged, Dissected and Historically Described,” Journal of Economic Literature 15, 24–55. {% Below p. 509-518: Samuelson’s development w.r.t. independence. %} Samuelson, Paul A. (1983) “Foundations of Economic Analysis; enlarged edn.” Harvard University Press, Cambridge, MA. {% I have this paper in my folder on history of independence. %} Samuelson, Paul A. (1992) “A Long-Open Question on Utility and Conserved-Energy Functions.” In Mukul Majumdar (ed.) Essays in Honor of David Gale, 287–306, St. Martin’s Press, New York. {% p. 8 seems to write: “economists cannot perform the controlled experiments of chemists or biologists because they cannot easily control other important factors” %} Samuelson, Paul A. & William Nordhaus (1985) “Economics,” 12 edn. McGraw-Hill, New York. {% §2.2 considers retirement plans of 850,000 teachers in the TIAA association. They can divide their money over a safe TIAA fund consisting of bonds and other safe investments, and a more risky CREF stock funds. Tables 12 and 13 shows that the mode division is 50-50, chosen by some 47% of participants. The second most-chosen is all in the safe fund (22% of participants). Although they can every year redivide at no cost, almost no-one ever changes. %} Samuelson, William F. & Richard J. Zeckhauser (1988) “Status Quo Bias in Decision Making,” Journal of Risk and Uncertainty 1, 7–59. {% %} Sánchez, M. Carmen (1999) “Rationality of Bargaining Solutions,” Journal of Mathematical Economics 33, 389–399. {% revealed preference %} Sánchez, M. Carmen (1998) “Rational Choice on Non-Finite Sets by Means of Expansion-Contraction Axioms,” Theory and Decision 45, 1–17. {% %} Sanders, Marianne, Andrée Tingloo, & Hans Verhulst (1992) “Advanced Writing in English; A Guide for Dutch Authors.” Garant-Uitgevers, Apeldoorn. (4th edn. 1998.) {% %} Sandmo, Agnar (1970) “The Effect of Uncertainty on Savings Decisions,” Review of Economic Studies 37, 353–360. {% Generalize Foster & Vohra (1997) and Lehrer (2001). %} Sandroni, Alvaro, Rann Smorodinsky, & Rakesh V. Vohra (2003) “Calibration with Many Checking Rules,” Mathematics of Operations Research 28, 141–153. {% measure of similarity; Use fuzzy measures and Choquet integral (p. 877). %} Santini, Simone & Ramesh Jain (1999) “Similarity Measures,” IEEE Transactions on Pattern Analysis and Machine Intelligence 21, 871–883. {% losses from prior endowment mechanism: explained top of p. 579 Experiment with all mixed two-outcome lotteries. 50% of subjects satisfy EU and 50% violate it. The authors use the term reference dependence for what I would call sign dependence. The reference point is always fixed at 0 so reference dependence plays no role. But losses can be treated differently than gains, which is sign dependence. For non-EU, sign-dependence of probability weighting works well, and there is no loss aversion. They use choice-lists to get mixed lotteries equivalent to 0. %} Santos-Pinto, Luis, Adrian Bruhin, José Mata, & Thomas Astebro (2015) “Detecting Heterogeneous Risk Attitudes with Mixed Gambles,” Theory and Decision 79, 573–600. {% %} Sapienza, Paola, Anna Toldra‐Simats, & Luigi Zingales (2013) “Understanding Trust,” The Economic Journal 123, 1313–1332. {% gender differences in risk attitudes: women more risk averse than men. %} Sapienza, Paolo, Luigi Zingales, & Dario Maestripieri (2009) “Gender Differences in Financial Risk Aversion and Career Choices are Affected by Testosterone,” Proceedings of the National Academy of Sciences 106, 15268–15273. {% %} Saponara, Nick (2017), “Revealed Understanding,” working paper. {% %} Sarin, Rakesh K. (1982) “Strength of Preference and Risky Choice,” Operations Research 30, 982–997. {% dynamic consistency; didactical description of nonEU models %} Sarin, Rakesh K. (1990) “Analytical Issues in Decision Methodology.” In Ira Horowitz (ed.) Organization and Decision Theory, 13–62, Kluwer, Dordrecht. {% dynamic consistency %} Sarin, Rakesh K. (1992) “What Now for Generalized Utility Theory.” In Ward Edwards (ed.) Utility Theories: Measurement and Applications, 137–163, Kluwer Academic Publishers, Dordrecht. {% %} Sarin, Rakesh K. & Peter P. Wakker (1992) “A Simple Axiomatization of Nonadditive Expected Utility,” Econometrica 60, 1255–1272. Link to paper
Sarin, Rakesh K. & Peter P. Wakker (1994) “Folding Back in Decision Tree Analysis,” Management Science 40, 625–628. Link to paper
Sarin, Rakesh K. & Peter P. Wakker (1994) “A General Result for Quantifying Beliefs,” Econometrica 62, 683–685. Link to paper Extended version {% %} Sarin, Rakesh K. & Peter P. Wakker (1994) “Gains and Losses in Nonadditive Expected Utility.” In Mark J. Machina & Bertrand R. Munier (eds.) Models and Experiments on Risk and Rationality, 157–172, Kluwer Academic Publishers, Dordrecht. Link to paper
Sarin, Rakesh K. & Peter P. Wakker (1997) “A Single-Stage Approach to Anscombe and Aumann’s Expected Utility,” Review of Economic Studies 64, 399–409. Link to paper
Sarin, Rakesh K. & Peter P. Wakker (1998) “Revealed Likelihood and Knightian Uncertainty,” Journal of Risk and Uncertainty 16, 223–250. Link to paper
Sarin, Rakesh K. & Peter P. Wakker (1998) “Dynamic Choice and Nonexpected Utility,” Journal of Risk and Uncertainty 17, 87–119. Link to paper
Sarin, Rakesh K. & Peter P. Wakker (2000) “Cumulative Dominance and Probabilistic Sophistication,” Mathematical Social Sciences 40, 191–196. Link to paper
Sarin, Rakesh K. & Martin Weber (1992) “Risk-value Models,” European Journal of Operational Research 70, 135–149. {% Two different market organizations, sealed bid auctions and double oral auctions, were used to let graduate business students and bank executive choose between ambiguous and unambiguous lotteries. The ambiguous ones were valued lower. ambiguity seeking for unlikely: no ambiguity aversion around p = .05. %} Sarin, Rakesh K. & Martin Weber (1993) “Effects of Ambiguity in Market Experiments,” Management Science 39, 602–615. {% Seem to argue that ambiguity can be modeled through utilities of outcomes, rather than through beliefs. %} Sarin, Rakesh K. & Robert L. Winkler (1992) “Ambiguity and Decision Modeling: A Preference-Based Approach,” Journal of Risk and Uncertainty 4, 389–407. {% %} Sarver, Todd (2008) “Anticipating Regret: Why Fewer Options May Be Better,” Econometrica 76, 263–305. {% measure of similarity %} Sattath, Shmuel & Amos Tversky (1977) “Additive Similarity Trees,” Psychometrika 42, 319–345. {% Use big real incentives. Find that temporal distance increases insensitivity to probability. %} Savadori, Lucia & Luigi Mittone (2015) “Temporal Distance Reduces the Attractiveness of P-Bets Compared to $-Bets,” Journal of Economic Psychology 46, 26–38. {% P. 6 writes that not only the vNM book, but also repeated conversations with vN, confirm that vN is no frequentist. %} Savage, Leonard J. (1950, 19 May) Letter to Paul Samuelson. {% %} Savage, Leonard J. (1950) “The Role of Personal Probability in Statistics” (abstract), Econometrica 18, 183–184. {% P. 56 writes: “Acts have consequences for the actor, and these consequences depend on facts, not all of which are generally known to him. The unknown facts will often be referred to as states of the world, or simply states,” and thus can be taken as an early appearance of the “acts map states to outcomes” model. P. 57, footnote 3: acknowledges Samuelson for putting him right on a mistake in the Friedman & Savage (1948) paper. P. 61 last para credits de Finetti, but, unfortunately, for Savage’s uninteresting ideas on minimax. Pp. 63-64 seem to argue that a statistical loss function is different than a negative economic utility function, partly because the latter may not be known, but it remains mysterious to me. %} Savage, Leonard J. (1951) “The Theory of Statistical Decision,” Journal of the American Statistical Association 46, 55–67. {% I copied this reference from Allais (1953, 1979). %} Savage, Leonard J. (1952) “An Axiomatisation of Reasonable Behavior in the Face of Uncertainty.” {% Paper is at http://personal.eur.nl/wakker/refs/pdf/savage52.pdf Also in “The Writings of Leonard Jimmie Savage—A memorial Selection,” The Amer. Statis. Assn. and the Institute of Math. Statist., 1981. %} Savage, Leonard J. (1953) “Une Axiomatisation du Comportement Raisonnable Face à l’Incertitude.” Colloques Internationaux du Centre National de la Recherche Scientifique (Econométrie) 40, 29–40. {% As explained for instance by Fienberg (2008), when Savage wrote this book he did not know that his sure-thing principle amounted to the likelihood principle for statistics (later Barnard seems to have explained the likelihood principle to Savage), nor that it implies a breakaway from classical statistics. The whole second part of the book tries to do classical-like statistics and decisions, such as through minimax, and is not interesting. On Savage’s use of the term sure-thing principle, which has raised many misunderstandings: p. 22 2nd para: “It will be preferable to regard the principle as a loose one that suggests certain formal postulates well articulated …”. In his analysis, the principle is related to three formal postulates, P2 and P3 (page 21 and the rest of §2.7), and P7 (p. 77, the para preceding P7). Since, the terminology in the field has shifted. Nowadays, it is commonly accepted to let the term sure-thing principle refer only to Savage’s P2 and not, as he did, to P2, P3, and P7. P. 17 seems to briefly mention the problem of indifference for observability of revealed preference. utility = representational?: p. 17: “I think it of great importance that preference, and indifference, between f and g be determined, at least in principle, by decisions between acts and not by response to introspective questions.” P. 20 seems to say about the use of his axioms: “to make complicated decisions depend on simpler ones.” Section 3.1, pp. 27-30, on general meaning of preference is nice. utility = representational?: pp. 27-28 argue that one should observe choice rather than do direct questioning. P. 27 writes: “direct interrogation has justifiably met with antipathy from most statistical theorists.” Pp. 27-28: if the state of mind in question is not capable of manifesting itself in some sort of extraverbal behavior, it is extraneous to our main interest. If, on the other hand, it does manifest itself through more material behavior, that should, at least in principle, imply the possibility of testing whether …” At the end of p. 28 it says that questioning “what would you do if” seems fine. P. 28 penultimate para says that for normative it is right. P. 29, by way of digression, discusses empirical observations for descriptive purposes. Top says that real incentives is problematic for high stakes and losses. Middle nicely discusses observability problem that choice f from {f,g,h} does not reveal preference between g and h, and the paradox that for transitivity testing you need to observe three choices but take each one as only choice. Income effect if observing more than one. Then it proposes, last para, the random incentive system (RIS), ascribing the idea to his teacher the statistician W. Allen Wallis but also writing that Allais used it. Lines -3/-2 point out that one needs a conditioning assumption (the point of Holt AER 1986) to justify the RIS. Pp. 40-43, §3.4: for Savage countable additivity was not central and it was only a pragmatic matter of convenience. He used all subsets of the state space (which excludes countable additivity) and not a sigma-algebra only for expositional purposes, actually preferring sigma-algebra other than for exposition. Savage did express a slight preference for not committing to countable additivity but, again, not out of principle but only pragmatically, and not committing clearly. (Probably to quite some extent so as not to get in conflict with de Finetti who was in a less refined league than Savage.) Download 7.23 Mb. Share with your friends:
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