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§IV describes much of assumption of additively decomposable utility function among economists in the preceding section
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§V, ascribes to p. 11 ff of Fisher (1982) a reasoning that is not present in Fisher’s work in this form. Stigler’s reasoning reflects the idea of Tradeoff method measurement in the additively decomposable MAU context, and of a standard sequence, but Fisher’s original text does not: “Select arbitrarily a quantity of any commodity, say, 100 loaves of bread. Let the marginal utility of this quantity of commodity be the unit of utility (or util). Grant the ability of the individual to order the utilities of specified amounts of two goods, i.e. to indicate a preference (if one exists) or indifference between the two quantities. Then it is possible to construct the utility schedule of (say) milk. Start with no milk and find the increment of milk (m1) equivalent to the hundredth loaf of bread, i.e. the minimum amount of milk the individual would accept in exchange for the hundredth loaf of bread. Find a second increment (m2), given the possession of m1, equivalent to the hundreth loaf, etc. We obtain thus a schedule (or function) such as that given” The procedure described gives a sequence 0, m1, m2, m3, m4, ... of amounts of milk that are equally-spaced in utility units, a “standard sequence,” based on indifferences (100,0) ~ (99,m1), ..., (100,mi) ~ (99,mi+1), ... etc. Fisher (1892) only shows that marginal utilities can be compared under additive representation (even, more restrictively, independence of marginal utility of a commodity from the levels of other commodities) by assuming that in optimum chosen the marginal utility of money for each commodity is the same (so, Gossen’s 2nd law), but he does not construct a standard sequence. And Fisher never considers direct tradeoffs between bread and milk. Blaug (1962), §9.2 ascribes to Fisher (1927) what Stigler ascribes to Fisher (1892). I spent many hours checking out the two Fisher works, and the idea is not there. Blaug (Feb. 12, 2002, personal communication) explained that he had taken the reference from Stigler (1950) without checking the original. §VII, on Marshall, discusses assumptions of linear utility for money. P. 381 seems to ascribe to Pareto, incorrectly, that strengths of preferences cannot be measured (Ellingsen 1994 footnote 18). %} Stigler, George J. (1950) “The Development of Utility Theory: I; II,” Journal of Political Economy 58, 307–327; 373–396. Reprinted in Alfred N. Page (1968) Utility Theory: A Book of Readings, Wiley, New York, 55–119. {% Seems to point out that it makes little sense to cite separate texts from works that are ambiguous or self-contradictory. %} Stigler, George J. (1965) “Textual Exegesis as a Scientific Problem,” Economica 32, 447–450. {% %} Stigler, George J. (1965) “The History of Economics.” University of Chicago Press, Chicago. {% P. xiv, about the risk/uncertainty distinction assigned to Knight: “Fortunately this is an extreme caricature of his work, because modern analysis no longer views the two classes [risk and uncertainty] as different in kind.” It is not clear whether Stigler means here that risk is a special, extreme, case of uncertainty (the interpretation that I like) or that he means that people should satisfy the Savage axioms and then wants to interpret subjective probabilities as objective probabilities (SEU = risk). The latter is a new, and I think unfortunate, interpretation of the term risk that deviates from the traditional and still most common terminology. People who use the deviating terminology may write things such as “Savage showed that we need not distinguish between risk and uncertainty.” In the common terminology, risk refers to objective probability, and Savage’s SEU model with additive subjective probabilities is uncertainty and not risk. I prefer the traditional common terminology because I prefer that whether something is decision under risk or under uncertainty does not depend on the decision attitude of the decision maker. %} Stigler, George J. (1971) “Introduction.” In Frank H. Knight, Risk, Uncertainty, and Profit. Chicago University Press, Chicago. {% Can be cited for strict ordinalist view of economics. U(x) depends on past consumption y and, hence, that should be added in the formula. Many people add past consumption as an index to U and then have the utility function Uy(x) depending on past consumption. This paper adds past consumption as an index to x, U(x,y) and then has nonchanging U: voilà! “Market good” is the tangible object you consume, “commodity bundle” is the consequentialist thing that simply comprises “everything relevant” such as your secret admiration of your wife etc. P. 76: “tastes (do) neither change capriciously nor differ importantly between people ... one does not argue over tastes for the same reason that one does not argue over the Rocky mountains - both are there, will be there next year, too, and are the same to all men.” P. 89: “Indeed, given additional space, we would argue that the assumption of time preference impedes the explanation of life cycle variations in the allocation of resources, the secular growth in real incomes, and other phenomena.” P. 78, discounting normative: uses formula with discounting, but footnote 4 says that “A consistent application of the assumption of stable preferences implies that the discount rate is zero; that is, the absence of time preference” It seems that they do not distinguish between ageing effect and discounting: DC = stationarity. When they say somewhere that discounting means that your taste for 1984 consumption changes as you move closer, they are confusing a number of things. (For example, tradeoff between 1984 and 1980 remains constant, also between 1984 and 1981, but ‘present’ is not well defined if you assume it moving.) %} Stigler, George J. & Gary S. Becker (1977) “De Gustibus non Est Disputandum,” American Economic Review 67, 76–90. {% foundations of probability %} Stigler, Stephen M. (1988) “The Dark Ages of Probability in England: The Seventeenth Century Work of Richard Cumberland and Thomas Strode,” International Statistical Review 56, 75–88. {% foundations of probability; foundations of statistics %} Stigler, Stephen M. (1986) “The History of Statistics, The Measurement of Uncertainty before 1900.” Harvard University Press, Cambridge, MA. {% In 1693 the 1st application of probability theory was in medicine and took place in Leiden. %} Stigler, Stephen M. (March 26, 1999) lecture honoring Willem van Zwet’s 65th birthday, Leiden. {% foundations of statistics %} Stigler, Stephen M. (2012) “Stigler Studies in the History of Probability and Statistics, L: Karl Pearson and the Rule of Three,” Biometrika 99, 1–14. {% Z&Z: shows that adverse selection can be detrimental for competitive markets. %} Stiglitz, Joseph E. & Andrew Weiss (1981) “Credit Rationing in Markets with Imperfect Information,” American Economic Review 71, 393–410. {% Uses differentiability assumptions along the diagonal. %} Stigum, Bernt P. (1972) “Finite State Space and Expected Utility Maximization,” Econometrica 40, 253–259. {% %} Stigum, Bernt P. (1990) “Toward a Formal Science of Economics.” MIT Press, London. {% %} Stigum, Bernt P. & Fred Wenstop (1983) “Foundations of Utility and Risk Theory with Applications.” Reidel, Dordrecht. {% Gives references to Savage’s probability measure not being countably additive in lotteries with one nonzero outcome %} Stinchcombe, Maxwell B. (1997) “Countably Additive Subjective Probabilities for Expected and Non-Expected Utility,” Review of Economic Studies 64, 125–146. {% First version 2010 %} Stinchcombe, Maxwell B. (2018) “Learning Finitely Additive Probabilities: An Impossibility Theorem,” {% The author repeatedly emphasizes that we should not reduce uncertainty to risk, i.e. to single additive probabilities, citing Knght. I as Bayesian think that in the end uncertainties should be expressed in terms of probabilities. But this happens only in the last five seconds before the final decision is taken by the ultimate decision maker. I agree that in the preceding years of analyzing the situation, subjective probabilities do not play much of a role. I do not agree that in the last five seconds of the final decision one should go violating the sure-thing principle, and I see no role for ambiguity decision theories for rational decisions. %} Stirling, Andy (2010) “Keep it Complex,” Nature 468, December 2010, 1029–1031. {% Deals with convex sets of probability measures, refers to Shafer, Levi etc. Gives heuristics on how to use it. %} Stirling, Wynn C. & Darryl R. Morrell (1991) “Convex Bayes Decision Theory,” IEEE Transactions on Systems, Man, and Cybernetics 21, 173–183. {% Nice display of probabilities; references to studies in belief in luck %} Stockman, Carol K. & Mark S. Roberts (2005) “Risk Preferences over Health and Monetary Domains in a Patient Population,” {% %} Stomper, Alex & Marie-Louise Vierø (2014) “Iterated Expectations under Cumulative Prospect Theory: an Impossibility Result,” working paper. {% %} Stone, Bob & Ron Jacobs (1988) “Successful Direct Marketing Methods;” 4th edn. Lincolnwood, Illinois: NTC Business Books. {% probability communication: showing only “foreground risk” (bad outcome) and not “background risk” (the good outcome) makes the former more salient. The authors investigate further details and combinations of numerical/graphical, where graphical is by pie charts in experiment 1, and pie charts and bar graphs in study 2. %} Stone, Eric R., Winston R. Sieck, Benita E. Bull, J. Frank Yates, Stephanie C. Parks, & Carolyn J. Rusha (2003) “Foreground: Background Salience: Explaining the Effects of Graphical Displays on Risk Avoidance,” Organizational Behavior and Human Decision Processes 90, 19–36. {% probability communication: %} Stone, Eric R., J. Frank Yates, & Andrew M. Parker (1997) “Effects of Numerical and Graphical Displays on Professed Risk-Taking Behavior,” Journal of Experimental Psychology: Applied 3, 243–256. {% Showed that every algebra is isomorphic to an algebra of subsets. The same isomorphism cannot be obtained for -algebras. %} Stone, Marshall H. (1936) “The Theory of Representation for Boolean algebras,” Transactions of the American Mathematical Society 37–111. {% Dutch book %} Stone, Marshall H. (1949) “Postulates for the Barycentric Calculus,” Annali di Matematica Pura ed Applicata 29, 25–30. {% Dutch book %} Stone, Mervyn (1976) “Strong Inconsistency from Uniform Priors,” Journal of the American Statistical Association 71, 114–116. {% real incentives: random incentive system. Average outcome in experiment was £2130, but when paying subjects it was divided by 1000 (brrrr!) (p. 113 top). error theory for risky choice: central; inverse-S: almost not found, Prelec’s one-parameter family fits best with parameter 0.94, which is very close to linear and has almost no inverse-S. (Utility x0.19 is very concave.) Data are nonrepresentative because it is always a choice between two two-outcome prospects where one of the two has one outcome equal to 0 (p. 112 3rd para). Birnbaum, Slovic, and others have shown that the 0 outcome generates many special biases. Is impressive data fitting using PT. The data-fitting uses Akaike’s method to discount for the number of parameters used. P. 104 bottom: error theories always have choice probability depend only on preference value, and not on other aspects such as monotonic configurations. 90 prospect choices were elicited from N=96 subjects, combining several parametric families for utility, probability weighting, and error theory. P. 112 middle has discussion of interactions between parameters in parametric fitting (“multicollinearity”), and P. 121 ff. (Subsection 5.3) has results on it. BEST FIT: power utility U(x) = xr for r = 0.19, Prelec’s one-parameter family w(p) = exp( (ln(p))r) for r = 0.94 (very close to linear), and a logit error function using Luce’s (1959) probabilistic choice theory. (V(f)/(V(f)+V(g)) for = ? (I did not find it). P. 102, and p. 123 top: the mean-variance model behaves very poorly in fitting data. P. 101 last para claims that to fit one parameter, the others must be assumed. This need not be so for specially constructed data sets. For instance when using data from the Tradeoff method for parametric fitting, the parameter of utility can be fit irrespective of what weighting-function parameter is taken. Arguments in favor of nonparametric fitting will be given on p. 125. The author uses the term “nonparametric” to refer solely to the approach where the utility of each outcome considered and the probability weight of each probability considered is taken as a separate parameter, without the stimuli targeted much to optimally give the parameters (p. 107 6th para). Then it will not perform well because it has too many parameters (each charged by Akaike’s formula) that, accordingly, mostly pick up noise. The author is a psychologist and theoretical parts sometimes deviate from economic conventions. The author uses the term normative to indicate that a preference foundation (“axiomatization”) has been given, irrespective of whether this foundation is supposed to have a normative status. equate risk aversion with concave utility under nonEU: |As do most economists, in absence of EU as working hypothesis he confuses risk attitude with utility curvature, writing for instance on p. 106 that linear utility reflect risk neutrality. P. 106: the HARA family in Table 2 is not correct. The formula for Luce’s theory in Table 4b (V(f)/(V(f)+V(g)) is the probability of prospect f being preferred to g), the one found to perform best, is unacceptable for zero or negative values of V, and will already misbehave for positive V values close to 0. P. 108, top: the author incorrectly suggests that power probability transformation could not satisfy quasi-concavity and quasi-convexity. Wakker (1994) proves that quasi-concavity holds if and only if w is convex, and quasi-convex if and only if w is concave, which shows that these things go together well with power utility. The 2nd displayed formula on p. 108 has probabilities not summing to 1. P. 111 middle has a strange claim that indifference data cannot be used to investigate choice functions (i.e., error theories). Glenn Harrison also has sometimes written so (e.g., Harrison & Rutström 2009 p. 139 end of §2). Indifference data is way more informative than choice data. It is only that these authors use statistical techniques that only work for binary choice. P. 114: e64.2 = 0.49??? %} Stott, Henry P. (2006) “Cumulative Prospect Theory’s Functional Menagerie,” Journal of Risk and Uncertainty 32, 101–130. {% Ambiguity aversion is related to the degree of violation of independence of irrelevant alternatives, using an Anscombe-Aumann setup. %} Stoye, Jörg (2011) “Axioms for Minimax Regret Choice Correspondences,” Journal of Economic Theory 146, 2226–2251. {% foundations of statistics: points out analogy between maxmin EU and models in statistics. %} Stoye, Jörg (2012) “New Perspectives on Statistical Decisions under Ambiguity,” Annual Review of Economics 4, 257–282. {% Proposes weighted average between upper and lower expectations. %} Strat, Thomas M. (1990) “Decision Analysis Using Belief Functions,” International Journal of Approximate Reasoning 4, 391–418. {% dynamic consistency (?); biconvergence and tail insensitivity resemble truncation-continuity of Wakker (1993, MOR) but are more restrictive because they require that after some time point the tail is cut down to either 0 or some other value, à la de Finetti. Unfortunately, some notation such as 1c is not defined; is as in Koopmans (1960, 1972). Takes production function F, programs start from c1 and then at each time t, the capital available, say xt, is divided into ct, consumption at t, and F(xtct), the capital left for t+1. The whole paper is conditional on this process, with some fixed F assumed. Theorem G shows that for time-additivity, discounted utility is bounded in the domain considered if and only if bi-convergence holds. The result depends on the production function F assumed, which determines the domain. %} Streufert, Peter A. (1990) “Stationary Recursive Utility and Dynamic Programming under the Assumption of Biconvergence,” Review of Economic Studies 57, 79–97. {% %} Streufert, Peter A. (1991) “Nonnegative Stochastic Dynamic Preferences,” Stanford Institute for Theoretical Economics. {% %} Streufert, Peter A. (1992) “An Abstract Topological Approach to Dynamic Programming,” Journal of Mathematical Economics 21, 59–88. {% %} Streufert, Peter A. (1993) “Abstract Recursive Utility,” Journal of Mathematical Analysis and Applications 175, 169–185. {% Extends the results of Gorman (1968) to countable product sets. A node is a separable set which is not overlapped by any other separable set. There are simple, complex, and envelope nodes. Assumes, like Gorman, arcconnected topologically-separable components. The main condition driving the extension from finite to infinite separability is continuity with respect to the product topology, which given the weakness of this topology is a very restrictive assumption. Basically, continuity w.r.t. the product topology entails that for every open set R in the range we need to specify open domains for only finitely many coordinates, and can leave all other coordinates completely free, to already be in the inverse of R. So, it lets tails be unimportant. %} Streufert, Peter A. (1995) “A General Theory of Separability for Preferences Defined on a Countably Infinite Product Space,” Journal of Mathematical Economics 24, 407–434. {% %} Strickland, Lloyd H., Roy J. Lewicki, & Arnold M. Katz (1966) “Temporal Orientation and Perceived Control as Determinants of Risk-Taking,” Journal of Experimental Social Psychology 2, 143–151. {% risky utility u = strength of preference v (or other riskless cardinal utility, often called value): p. 84: utility is “as a psychological entity measurable in its own right” %} Strotz, Robert H. (1953) “Cardinal Utility,” American Economic Review 43, 384–397. {% dynamic consistency: favors abandoning time consistency, so, favors sophisticated choice, because he considered precommitment only viable if an extraneous device is available to implement it. First to note the problem of time inconsistency (called the “intertemporal tussle”). P. 165 bottom & p. 167 bottom distinguish between time distance and calendar time. Mistake in derivation of optimal path was pointed out by Pollak (1968): According to Epstein & Le Breton (1993) beginning of changing tastes literature, which provides a number of ways to describe dynamic inconsistent approaches. P. 165 describes two solutions to myopic (called “spendthrifty”), firstly, precommit future behavior (“resoluteness,” in the terminology of McClennen), secondly, take account of future disobedience (in modern terminology, “sophisticated choice”) Sentence on p. 170-171 clearly favors sophisticated choice as the rational thing. P. 173 penultimate para expresses amazement that precommitment devices are not more wide-spread than they are. Time-inconsistency is accepted without further ado by Strotz. P. 177 writes: “Special attention should be given, I feel, to a discount function ... which differs from a logarithmically linear one in that it “overvalues” the more proximate satisfactions relative to the more distant ones.” Takes commitment for the future in sense of committing to debts discounting normative: argues that only constant discounting is DC (dynamic consistency): p. 178, footnote 1 gives tongue-in-cheek text argument against zero discounting. P. 177: “There is a rationale for discounting at a constant rate of interest.” Olson & Bailey (1981, p. 20) claim that Strotz calls positive time preference “myopia” and that he argues for zero discounting, and that “consumer sovereignty has no meaning in the context of the dynamic decision making problems” (p. 179). %} Strotz, Robert H. (1955) “Myopia and Inconsistency in Dynamic Utility Maximization,” Review of Economic Studies 23 (Issue 3, June 1956) 165–180. {% %} Strotz, Robert H. (1957) “The Empirical Implications of a Utility Tree,” Econometrica 25, 269–280. {% %} Strotz, Robert H. (1958) “How Income Ought to be Distributed: A Paradox in Distributive Ethics,” Journal of Political Economy 66, 189–205. {% %} Strotz, Robert H. (1961) “How Income Ought to be Distributed: Paradox Regained,” Journal of Political Economy 69, 271–278. {% Nice introduction to nonstandard analysis, recommended to me on April 6, 1989 by Jan Jansen. %} Stroyan, Keith D. & Wilhelm A.J. Luxemburg (1976) “Introduction to the Theory of Infinitesimals.” Academic Press, New York. {% This paper takes the variational model of Maccheroni, Marinacci, & Rustichini (2005) as point of departure. It thus uses the Anscombe-Aumann model. It adds Savage’s sure-thing principle to the pure horse-race acts. This gives exactly enough extra separability to reduce the variational model to a version of the robust Hansen & Sargent model, where the relation is if and only if. A pretty result! §3.3 relates the model to recursive expected utility (called SOEU), for which I think that Kreps & Porteus (1978) is the primary reference. I guess that in general Savage’s s.th.pr. in itself only gives a state-dependent generalization of recursive expected utility, but that the additional axioms, primarily certainty independence which is similar to constant absolute risk aversion, then reduce it to really recursive EU. This is similar to the one-stage models where constant absolute risk aversion, if added to state-dependent expected utility, not only implies linear-exponential utility but also, as an extra bonus so to say, implies state independence (Wakker 1989 book, Theorem VII.7.6). On several occasions (e.g. Section 4) the paper uses Tversky’s source idea. It mostly cites Chew & Sagi (2008), Ergin & Gul (2009), and Nau, but not Tversky, for this idea, although it is Tversky’s idea. P. 62 top points out that KMM’s axiomatization of smooth ambiguity aversion is not behavioral and gives an alternative condition (quasi-concavity type) that is. biseparable utility: satisfied if we focus on purely subjective acts, in which case we even have SEU (p. 57 footnote 10). %} Strzalecki, Tomasz (2011) “Axiomatic Foundations of Multiplier Preferences,” Econometrica 79, 47–73. {% For variational preferences, probabilistic sophistication <==> EU if there exists an event for which independence holds. Extends Marinacci (2002). %} Strzalecki, Tomasz (2011) “Probabilistic Sophistication and Variational Preferences,” Journal of Economic Theory 146, 2117–2125. {% DOI: http://dx.doi.org/10.3982/ECTA9619
Strzalecki, Tomasz (2013) “Temporal Resolution of Uncertainty and Recursive Models of Ambiguity Aversion,” Econometrica 81, 1039–1074. {% %} Stucki, Gerold, Magnus Johannesson, & Matthew H. Liang (1996) “Use of Misoprostol in the Elderly: Is the Expense Justified?,” Drugs and Aging 8, 84–88. {% a famous poet from Song dynasty. Wrote the romantic sentence: “Although I am thousands of miles away from you, I will watch the same moon as you do.” In Chinese it seems to be: 但愿人长久，千里共婵娟 来自我的华为手机 The title of the poem is below. The author is also known as Su Dongpo. %} Su, Shi (1037–1101) “When Will the Bright Moon Come?” {% %} Suárez Garcìa F. & P. Gil Àlvarez (1986) “Two Families of Fuzzy Integrals,” Fuzzy Sets and Systems 18, 67–81. {% foundations of quantum mechanics: causation for Einstein–Podolsky–Rosen %} Suárez, Mauricio (2014) “Interventions and Causality in Quantum Mechanics,” Erkenntnis 78, 199–213. {% Seems to review effects of cognitive biases on investor’s behavior, so part of behavioral finance. %} Subrahmanyam, Avanidhar (2008) “Behavioral Finance: A Review and Synthesis,” European Financial Management 14, 12–29. {% Under Obama, Sunstein led the Office of Information and Regulatory Affairs. %} Subramanian, Courtney (2013) “ ‘Nudge’ Back in Fashion at White House,” TIME.com (August 9, 2013), {% When can set with ordering be considered a Cartesian product. %} Suck, Reinhard (1990) “Conjointness as a Derived Property,” Journal of Mathematical Psychology 34, 57–80. {% %} Suck, Reinhard (1994) “A Theorem on Order Extensions: Embeddability of a System of Weak Orders to Meet Solvability Constraints,” Journal of Mathematical Psychology 38, 128–134. {% Assumes relations R and R1, ..., Rn given on a set X and then considers conditions such that the set X can be considered an n-fold product set with the Rjs coordinate orderings and independence (so monotonicity) satisfied. Continues on Suck (1990). %} Suck, Reinhard (1998) “Ordering Orderings,” Mathematical Social Sciences 36, 91–104. {% confirmatory bias People prefer like-minded advisors with coarse info. If info is costly, bias can become perpetual. A theoretical model and simulations illustrate the point. %} Suen, Wing (2004) “The Self-Perpetuation of Biased Beliefs,” Economic Journal 114, 377–396. {% Gives examples of context-dependence leading to violations of revealed preference conditions. For example, regret theory. Uses term contraction consistency. Context-dependence is nicely explained through sports that are interactive or noninteractive. Uses term basic utility for utility without regret incorporated. %} Sugden, Robert (1985) “Why Be Consistent? A Critical Analysis of Consistency Requirements in Choice Theory,” Economica 52, 167–183. {% %} Sugden, Robert (1986) “New Developments in the Theory of Choice under Uncertainty,” Bulletin of Economic Reserves 38, 1–24. Reprinted in John D. Hey & Peter J. Lambert (1987, eds.) Surveys in the Economics of Uncertainty, Basil Blackwell, Oxford. {% %} Sugden, Robert (1989) Book Review of: Peter C. Fishburn (1988) “Nonlinear Preference and Utility Theory,” Johns Hopkins University Press, Baltimore, MD; Economic Journal 99, 1191–1192. {% Nash equilibrium discussion; P. 752: “within economics ... received theory of rational choice: expected utility theory.” game theory can/cannot be seen as decision under uncertainty: Sugden’s paper says that it has been generally accepted that Savage’s SEU, with strategies as states, is appropriate for game theory. I think that this may be so in Aumann’s papers but doubt if it is elsewhere. Sugden himself points out difficulties in that assumption, e.g. at the end of §V and also end of §VII. Seems to point out that opponent strategies cannot be modeled as extraneous states of nature because a player, when thinking about his own strategy, thus also affects his probabilities over opponents’ strategies. §XI, p. 782 bottom, states the point in a crystal-clear manner. P. 754, footnote 4: how indifference is a problem of revealed preference P. 755 free-will/determinism: on Kant who says humans are part of physical world and have physical explanations. But when we reason we cannot do other than conceive ourselves as autonomous ... Kant wants categorical imperatives, which are normative (more in ethical sense) principles to agree upon by reason with no concern of desires or Hume’s passions. paternalism/Humean-view-of-preference: p. 757: I regret that Sugden puts Savage forward as representative of the consistency view of rationality (also called coherentism). The consistency view says that rationality should require no more than consistency, i.e., consistency is sufficient for rationality. Savage, unlike his more narrow-minded colleague de Finetti, never committed to that, but only has consistency as necessary for rationality. P. 758: that the interpretation of preference as binary choice, and nothing else, is in Sugden’s opinion standard in economics. P. 760: I disagree with the reasoning. It takes reason as fixed, and then says that it is an empirical question whether our passions, desires/beliefs, are such that reason can always maximize them. I take reason not as fixed. Whatever the passions, reasons/desires, are, reason must be such as to optimize them. P. 760/761 says he finds it hard to formulate rationality of Savage’s theory; I wonder if it is in the sense that Savage’s conditions can at most be necessary for rrationality, never sufficient. This is well understood! completeness-criticisms: §IV pp. 760-761 gives criticism of completeness axiom as sort of indecisiveness, the argument I find unconvincing. Then discusses regret and transitivity. Assigns normative status to intransitivities resulting from regret. “Savage’s theory, of course, tells us nothing about how we should form probability judgements about states of nature; that is not its function.” P. 763 top claims that regret is just yet another passion in Hume’s sense, but I disagree. Regret can be a silly, “nonfundamental,” emotion. The discussion on rationality in game theory centers around the paradoxes if infinite hierarchies of beliefs and common knowledge, but also brings in the view I like, that there is a meta-dependence generated by rationality (if a rational players decides on something it automatically implies that his rational opponent decides the same, bringing a meta-dependency). See also conclusion p. 783 top. conservation of influence: §§I-IV give many nice refs etc. %} Sugden, Robert (1991) “Rational Choice: A Survey of Contributions from Economics and Philosophy,” Economic Journal 101, 751–785. {% Preference axioms invoke complicated utility elicitation procedures %} Sugden, Robert (1993) “An Axiomatic Foundation for Regret Theory,” Journal of Economic Theory 60, 159–180. {% paternalism/Humean-view-of-preference: seems to cite Hume for anti-paternalism. %} Sugden, Robert (1998) “Measuring Opportunity: Toward a Contractarian Measure of Individual Interest,” Social Philosophy & Policy 15, 34–60. {% Presented in Amsterdam on March 12, 1998. Takes descriptions of outcomes in game theory as referring to physical objects, takes utility as self-interest-valuation of those elicited through vNM utility or otherwise, at any rate referring to things outside the game. A similar explicit reference to utility measurement to get the utility in game theory is in Luce & Adams (1956). Then allows players to do other things than just maximize utility, e.g., consider moral considerations and, thus, cooperate in prisoner’s dilemma. He, thereby, explicitly disagrees with Binmore (1993). %} Sugden, Robert (1998) “Convention and Courtesy: A Theory of Normative Expectations,” School of Economics and Social Studies, University of East Anglia, Norwich, UK. Published as: Sugden, Robert (2000) “The Motivating Power of Expectations.” In Julian Nida-Rümelin & Wolfgang Spohn (eds.) Rationality, Rules and Structure, 103–129, Kluwer, Dordrecht. {% Reference-dependent subjective expected utility evaluates, at reference point h, an act f by the expectation of v(f(s),h(s)). Imposing Savage’s axioms for each separate h gives expectation of v(f(s),h) as representation with probability P depending on h. Having more-likely-than independent of h gives P independent of h. Separability of (f(s),h(s)) implies that v(f(s),h) depends only on h through h(s), so that the above representation results. It constitutes a very desirable and appealing extension of classical models. Theorem 2 considers the case v(f(s),h(s) = (u(f(s) u(g(s)). This is obtained by ordering the separable pairs ((f(s),g(s)) and imposing preference-difference axioms on this ordering. Sugden’s axioms S1-S4 amount to the axioms of Debreu (1960, Theorem 2), Köbberling (2003, “Preference Foundations for Difference Representations”), and Shapley (1975). In particular, Sugden’s S4 is the crossover axiom. u is called a satisfaction function and is interpreted as a riskless component, and is a gain/loss evaluation function. Risk attitude is composed of these two. It seems to me that affects more of risk attitude than only gains versus losses. For example, if we restrict attention to the subdomain of one fixed reference point and only gains, then the model (u(x)-u(0)) coincides with the value-utility model that was popular in decision analysis in the 1980s and 1990s (Dyer & Sarin 1982, etc.), where u is taken as riskless value function and adds risk attitude (and loss aversion plays no role). More concave generates more risk aversion in this domain where loss aversion plays no role. If we consider variable reference points and reference-independence, then must be linear (so “absent”) and u governs all of risk attitude. Pp. 178 and 180 write that u(x) may reflect satisfaction from x. The interpretation can, for reference independence, be maintained only if vNM utility is taken as a riskless u, an interpretation that I am sympathetic to (risky utility u = strength of preference v (or other riskless cardinal utility, often called value)) although the common terminology in the field today deviates and it is too late now to change. Schmidt (2003) also considers reference-dependence, but only for constant (riskless) acts. P. 173, para 2, incorrectly claims that prospect theory would have utility independent from the reference point. Footnote 2 weakens the mistake, but does not correct it. Kahneman & Tversky (1979, pp. 277-278) gives the right nuances. P. 173, para 3, incorrectly claims that prospect theory has no states of nature. The ’92 version of prospect theory does have states of nature. P. 175 1st para, f > g|h is interpreted as: if the agent is in h and can choose between f,g, and h, then he rather takes f than g. This interpretation is unrealistic if h is most preferred. Would be better not to leave the option of staying at h, or not to have his completeness axiom R1 and instead restrict the analysis to the acts preferred to h (requiring considerably more difficult proofs). Savage (1954) used the term sure-thing principle in an informal sense, comprising his P2, P3, and P7. In its modern use, it refers only to Savage’s P2. Sugden’s verbal text on p. 177 relates it, however, to Savage’s P1 and P2. Presenting so many valuable and sophisticated results in such a short space is an impressive achievement. Obviously, the proofs then have to be concise, and many details must be skipped. Indeed, the latter happens in this paper, and many of the more complex technical steps in the proofs are claimed without justification. This makes it hard for the readers to verify correctness of the results. At some places, there are inaccuracies. Theorem 1 claims necessity of the preference axioms, but the richness axiom of state-space continuity, R.8, can never be implied by the representation. (Counterexample: SEU with two states of nature, equally likely, real outcomes, and expected value, so that also Sugden’s uniqueness requirements are fulfilled.) The last sentence of the proof of Theorem 1, p. 188, suggests an assumption of atomlessness that is, however, neither claimed nor defined in the main text. Atomlessness is complex under finite (contrary to countable) additivity as here. I conjecture that a convex-rangedness condition as in Gilboa (1987) and Savage (1954) (that I prefer to call solvability) can work, but this remains to be proved. P. 178: in Def. 10, the domain of varies as u varies (discussed at the bottom of p. 188). P. 179, Consequence-space continuity, S2, is hard to read because most of the “for all” quantifiers are in the wrong place. In Definition 13, it is not clear what “distinct” means for acts. I guess that acts that differ only on a null event are not distinct. No proof of Theorem 3 is given so that the confusion cannot be clarified. %} Sugden, Robert (2003) “Reference-Dependent Subjective Expected Utility,” Journal of Economic Theory 111, 172–191. {% %} Sugden, Robert (2004) “Alternatives to Expected Utility.” In Salvador Barberà, Peter J. Hammond, & Christian Seidl (eds.) Handbook of Utility Theory, Vol. II, 685–755, Kluwer Academic Publishers, Dordrecht. {% conservation of influence: opportunity = potential influence; paternalism/Humean-view-of-preference: assigns an intrinsic value to opportunity sets; i.e., the very fact that one can choose from available options. So will be against paternalism. Reminds me of intrinsic value of information in papers by Grant, Kajii, & Polak (1992). Sugden’s work is in the spirit of liberty-of-choice literature. He says that, rather than getting optimal option, having opportunity set is central. Develops a model where arbitrageurs present choice sets and the economy benefits from competition between arbitrageurs. %} Sugden, Robert (2004) “The Opportunity Criterion: Consumer Sovereignty without the Assumption of Coherent Preferences,” American Economic Review 94, 1014–1033. {% conservation of influence: agent identifies herself with past, present, and future own decisions, as “locus of responsibility,” also called “responsible agent.” Sugden writes “she identifies with her own actions, past, present and future” Sugden’s set of opportunities is like my potential influence. Section 9.1 discusses Aristotle’s telos (goal). Hasppiness (eudaimonia) comes from serving the goals. %} Sugden, Robert (2017) “The Community of Advantage: A Behavioural Defence of the Liberal Tradition of Economics.” In preparation. {% %} Sugeno, Michio (1974) “Theory of Fuzzy Integrals and their Applications,” Ph.D. Thesis, Tokyo Institute of Technology. {% %} Sugeno, Michio & Toshiaki Murofushi (1987) “Pseudo-Additive Measures and Integrals,” Journal of Mathematical Analysis and Applications 122, 197–222. {% %} Sugeno, Michio & Toshiaki Murofushi (1988) “Choquet’s Integrals as an Integral Form for the General Class of Fuzzy Measures,” Preprints of 2nd IFSA Congress, 408–411. {% Points out that people can be in better physical shape than regular perfect health, involving utility exceeding 1. It means that regression techniques need not reckon with truncating at 1. %} Sullivan, Patrick W. (2011) “Are Utilities Bounded at 1.0? Implications for Statistical Analysis and Scale Development,” Medical Decision Making 31, 787–789. {% %} Sumalee, Agachai, Richard D. Connors, Paramet Luathep, William H. K. Lam, Sze C. Wong, & Hong K. Lo (2009) “Network Equilibrium under Cumulative Prospect Theory and Endogenous Stochastic Demand and Supply.” In William H.K. Lam, Sze C. Wong, & Hong K. Lo, eds.) Transportation and Traffic Theory 2009, 19–38, Springer, Berlin. {% Use hypothetical choice, with delays of several years. Consider intertemporal choice with SS (small soon) versus LL (large late). But add additional common payments at other times, before, between, or after. The extra payments always reduce discounting. The authors ascribe this to the SS and LL payments becoming less salient. Although the authors do not seem to discuss it, it means that intertemporal separability is violated (intertemporal separability criticized). %} Sun, Hong-Yue & Cheng-Ming Jiang (2015) “Introducing Money at Any Time Can Reduce Discounting in Intertemporal Choices with Rewards: An Extension of the Upfront Money Effect,” Judgment and Decision Making 10, 564–570. {% Simpler proof for Jaffray’s and Fagin & Halpern’s result. %} Sundberg, Carl & Carl G. Wagner (1992) “Generalized Finite Differences and Bayesian Conditioning of Choquet Capacities,” Advances in Applied Mathematics 13, 262–272. {% %} Sunstein, Cass R. (1991) “Preferences and Politics,” Philosophy and Public Affairs 20, 3–38. {% %} Sunstein, Cass R. (1993) “Endogenous Preferences, Environmental Law,” Journal of Legal Studies 22, 217–254. {% Decribed utilitarianism as “Bentham not Kant.” %} Sunstein, Cass R. (2016) Lecture at SABE/IAREP. {% %} Sunstein, Cass R. & Richard H. Thaler (2003) “Libertarian Paternalism is not an Oxymoron,” University of Chicago Law Review 70: 1159–1202. {% %} Suppes, Patrick (1956) “The Role of Subjective Probability and Utility in Decision Making.” Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, 1954–1955, 5, 61–73. {% %} Suppes, Patrick (1957) “Introduction to Logic.” Van Nostrand, New York. (12th print 1969.) {% %} Suppes, Patrick (1970) “A Probabilistic Theory of Causation.” North Holland, Amsterdam. {% Text of plenary lecture for statistical society. Hence, it briefly discusses preference axioms in general, which is very interesting. It considers upper and lower probabilities and, probably to have something novel to offer, adds a new preference axiomatization. Download 7.23 Mb. Share with your friends:
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