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§4 of the appendix (“Psychology and the Utility Theory”), however, gives a balanced account of the matter
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| §4 of the appendix (“Psychology and the Utility Theory”), however, gives a balanced account of the matter:
“it is preferable to derive a given set of propositions from externally or ‘objectively’ observable facts, if it can be done, than to derive the same set of propositions from premisses established by introspection. And, as we shall presently see, this can actually be done in the case of the utility theory of value, at least as long as we do not ask it to do more for us than to furnish the assumptions or ‘restrictions’ that we need within the equilibrium theory of values and prices.” Note here the crucial antecedent “at least as long as” Schumpeter writes elsewhere in the §4: “the efforts of psychologists to measure psychical quantities is not a matter of indifference to any economist who is not entirely lacking in scientific imagination.” §5, on cardinal utility, gives a fine historical account, would have been useful if I had read it before October 18, 1997. %} Schumpeter, Joseph (1954) “History of Economic Analysis.” MacMillan, London. {% Tradeoff method: use this to measure utility of money; find that individuals who prefer to deliberate over decisions have more linear utility; N=200 students, 15 outliers were discarded, arguing that they did not choose deliberately. Use random incentive system; indifferences were elicited through pingpong choices. between-random incentive system (paying only some subjects); real incentives/hypothetical choice: one of every 17 subjects played one of their choices for real, however was paid only 1% of the real amounts, which can be taken as a distortion of the outcomes, in the first sample of 68 subjects. This was dropped in the second sample of 132 subjects, where it was only hypothetical choice. There were no differences in the results between the two samples. Half of their stimuli concerned losses and, although they don’t comment on this point, I assume that the real incentives were only for gains. The fitted power (; median 0.91) for gains and (; median 0.90) for losses. %} Schunk, Daniel & Cornelia Betsch (2006) “Explaining Heterogeneity in Utility Functions by Individual Differences in Decision Modes,” Journal of Economic Psychology 27, 386–401. {% %} Schwabish, Jonathan A. (2014) “An Economist’s Guide to Visualizing Data,” Journal of Economic Perspectives 28, 209–234. {% %} Schwartz, Alan J. (1998) “Rating Scales in Context,” Medical Decision Making 18, 236. {% doi: http://dx.doi.org/10.4135/9781412971980.n268 %} Schwartz, Alan J. (2015) “Prospect Theory.” In Michael W. Kattan (Ed.) Encyclopedia of Medical Decision Making, 922–925, SAGE Publications Inc., Thousand Oaks, CA. {% real incentives/hypothetical choice: the participants had to discover a rule according to which choices between L or R would give money. Half of the participants were paid according to correct choices each time, the other half not. The paid participants resorted to myopic strategies and did not try to discover the general rule and, therefore, did not discover the general pattern as well as the not-paid participants. %} Schwartz, Barry (1982) “Reinforcement-Induced Behavioral Stereotype: How not to Teach People to Discover Rules,” Journal of Experimental Psychology: General 111, 23–59. {% probability communication: people who score higher in numeracy better understand probabilistic information given to them. %} Schwartz, Lisa M., Steven Woloshin, William C. Black, & H. Gilbert Welch (1997) “The Role of Numeracy in Understanding the Benefit of Screening Mammography,” Annals of Internal Medicine 127, 966–972. {% paternalism/Humean-view-of-preference: argues that general public will not accept it if their preferences are not taken just as they are (p. 272: “but a value question of democratic process.” %} Schwarz, Norbert (1999) “Defensible Preferences and the Public: Commentary on “Measuring Constructed Preferences: Towards a Building Code” by Payne, Bettman and Schkade,” Journal of Risk and Uncertainty 19, 271–272. {% Bayes’ formula intuitively. P. 59-61 give references to papers showing how people make mistakes in using the formula of Bayes. %} Schwartz, Steven & Timothy Griffin (1986) “Medical Thinking, The Psychology of Medical Judgment and Decision Making.” Springer, Berlin. {% %} Schwartz, William B. (1979) “Decision Analysis: A Look at the Chief Complaints,” New England Journal of Medicine 300: 556–559. {% Argues that we should report power over alternative hypothesis rather than significance %} Schweder, Tore (1988) “A Significance Version of the Basic Neyman-Pearson Theory for Scientific Hypothesis Testing,” Scandinavian Journal of Statistics 15, 225–242. {% preferring streams of increasing income; questionnaire versus choice utility: p. 4 seems to have said that utility maximization “set back by generations all scientific inquiry into consumer behavior, for it seemed to rule out—any conflict between what man chooses to get and what will best satisfy him”. %} Scitovsky, Tibor (1965) “The Joyless Economy.” Oxford University Press, New York. {% %} Scott, Dana (1961) “Measurable Cardinals and Constructible Sets,” Bulletin de lAcadémie Polonaise des Sciences 9, 521–524. {% A beautiful paper explaining how the theorem of the alternative can be used to characterize linear representations through cancellation axioms. Scott (1964) shows how this can give additively decomposable representations of preferences. %} Scott, Dana (1964) “Measurement Structures and Linear Inequalities,” Journal of Mathematical Psychology 1, 233–247. {% strength-of-preference representation: p. 121/122. cancellation axioms: p. 126: no finite subset of cancellation axioms will suffice to imply the others; no finite statement in 1st order logic can capture all cancellation axioms. %} Scott, Dana & Patrick Suppes (1958) “Foundational Aspects of Theories of Measurement,” Journal of Symbolic Logic 23, 113–128. {% free-will/determinism: seems to suggests that neurobiology might find out about free will. So, the author overestimates the role of neurobiology. %} Searle, John R. (2004) “Freedom and Neurobiology: Reflections on Free Will, Language, and Political Power.” Cambridge University Press, New York. {% Risk-neutral agents with common priors cannot trade to mutual strict advantage; common knowledge %} Sebenius, James K. & John Geneakoplos (1983) “Don’t Bet on It: Contingent Agreements with Asymmetric Information,” Journal of the American Statistical Association 78, 424–426. {% foundations of quantum mechanics: why is probability given by the square of the amplitude? Derivations and discussions are given. It also discusses quantum sleeping beauty problems in quantum mechanics. %} Sebens, Charles T. & Sean M. Carroll (2018) “Self-Locating Uncertainty and the Origin of Probability in Everettian Quantum Mechanics,” British Journal for the Philosophy of Science 69, 25–74. {% Argues, a.o., that derivations of subjective probabilities à la de Finetti implicitly and incorrectly assume that probabilities must add up to 1. (p. 291 3rd para). %} Secchi, Luigi (2014) “The Main Two Arguments for Probabilism Are Flawed,” Synthese 191, 287–295. {% %} See, Kelly E., Craig R. Fox, & Yuval Rottenstreich (2006) “Between Ignorance and Truth: Partition Dependence and Learning in Judgment under Uncertainty,” Journal of Experimental Psychology: Learning, Memory and Cognition 32, 1385–1402. {% between-random incentive system (paying only some subjects): finds that people become more generous if only 25% of ultimatum games is paid than if all are paid. It is not very surprising that in such a situation the system works worse than in individual choice, because here clearly noneconomic psychological factors and perceptions of fairness play a role. Such perceptions can be different under different probability distributions, if they are affected by a priori fairness considerations as advanced in Trautmann (2006). %} Sefton, Martin (1992) “Incentives in Simple Bargaining Games,” Journal of Economic Psychology 13, 263–276. {% %} Segal, Uzi (1983) “A Theorem on the Additivity of the Quasi-Concave Closure of an Additive Convex Function,” Journal of Mathematical Economics 11, 261–266. {% schrift p. 403 ordering of subsets %} Segal, Uzi (1984) “Representation and Measurement of Qualitative Conditional Probability,” University of Pennsylvania, Dept. of Economics, Philadelphia, USA. {% %} Segal, Uzi (1985) “On the Separability of the Quasi Concave Closure of an Additively Separable Function,” Journal of Mathematical Economics 14, 129–134. {% §2 (Condition c in the first definition) %} Segal, Uzi (1986) “On Lexicographic Probability Relations,” Mathematical Social Sciences 11, 195–199. {% Theorem 2 has GAP condition. %} Segal, Uzi (1987) “Some Remarks on Quiggin’s Anticipated Utility,” Journal of Economic Behavior and Organization 8, 145–154. {% second-order probabilities to model ambiguity; p. 194: empirical tests of Ellsberg paradox %} Segal, Uzi (1987) “The Ellsberg Paradox and Risk Aversion: An Anticipated Utility Approach,” International Economic Review 28, 175–202. {% %} Segal, Uzi (1988) “Probabilistic Insurance and Anticipated Utility,” Journal of Risk and Insurance 55, 287–297. {% %} Segal, Uzi (1988) “Does the Preference Reversal Phenomenon Necessarily Contradict the Independence Axiom,” American Economic Review 78, 233–236. {% ordering of subsets. Comonotonic independence characterizes the measure approach, which is like Green & Jullien (1988), kind of RDU with state-dependent utility function. The special case where the measure is a product measure, so that RDU results, is characterized through projection independence, a geometric condition for the measures. In the proof of the latter result, the definition of utility and probability transformation are given, but it is claimed without proof that these indeed give the RDU representation. A proof of this claim will essentially need the continuum richness of the probability dimension, because projection independence operates in this dimension. %} Segal, Uzi (1989) “Anticipated Utility: A Measure Representation Approach,” Annals of Operations Research 19, 359–373. Before: Segal, Uzi (1988) “Anticipated Utility: A Measure Representation Approach,” Working paper 8803, University of Toronto, Department of Economics and Institute for Policy Analysis, Toronto, Canada. Rewritten version of Segal, Uzi (1984) “Nonlinear Decision Weights with the Independence Axiom,” Working paper 353, University of California, Department of Economics, Los Angeles, USA. {% second-order probabilities to model ambiguity; dynamic consistency: favors abandoning RCLA.: %} Segal, Uzi (1990) “Two-stage Lotteries without the Reduction Axiom,” Econometrica 58, 349–377. {% %} Segal, Uzi (1992) “The Independence Axiom versus the Reduction Axiom: Must We Have Both?” In Ward Edwards (ed.) Utility Theories: Measurement and Applications, 165–183, Kluwer Academic Publishers, Dordrecht. {% %} Segal, Uzi (1992) “Additively Separable Representations on Non-Convex Sets,” Journal of Economic Theory 56, 89–99. {% restricting representations to subsets; ordering of subsets %} Segal, Uzi (1993) “The Measure Representation: A Correction,” Journal of Risk and Uncertainty 6, 99–107. {% %} Segal, Uzi (1993) “Order Indifference and Rank-Dependent Probabilities,” Journal of Mathematical Economics 22, 373–397. {% %} Segal, Uzi (1994) “A Sufficient Condition for Additively Separable Functions,” Journal of Mathematical Economics 23, 295–303. {% quasi-concave so deliberate randomization %} Segal, Uzi (1994) “Stochastic Transitivity and Quadratic Representation Functions,” Journal of Mathematical Psychology 38, 102–114. {% dynamic consistency; like Border & Segal (1994), it considers the special case of long-run events going to 0 where event E has probability p, its complement Ec has probability 1p, p goes to 0, and all else remains the same. It assumes dynamic consistency only for the optimally-chosen strategy. That is, pref between that strategy and other available strategies should remain unaffected. In addition, it assumes that prefs between optimal strategy and nonavailable strategies should also be unaffected. All other prefs are, however, permitted to change freely after updating. Thus, only the indifference class of optimal choice is EU. Rest is free. Then comes, on p. 214, the question of what those other prefs mean. They are not related to hypothetical choices as in decision analysis or consumer demand theory. They are related to “reconsidered choice” because of earlier mistakes in modeling. In counterfactual nodes the decision maker would have acted believing in the wrong tree. %} Segal, Uzi (1997) “Dynamic Consistency and Reference Points,” Journal of Economic Theory 72, 208–219. {% DOI: HTTP://DX.DOI.ORG/10.1006/jeth.2001.2859 Theorem 1 characterizes a result for partial separability, the weakening of joint independence that only excludes reversals of strict preferences after replacement of common outcomes, a condition studied by Blackorby, Primont, & Russell, and some others. For three or more dimensions, monotonicity, symmetry, indifference monotonicity (kind of same degree of strict monotonicity all along indifference curves), and partial separability hold if and only if there exists a representation that kind of maximizes a kind of additively decomposable multiplicative form with one degenerate origin-point, and min everywhere below the origin-point, or a dual representation, with max. representation above an origin and additive decomposability below. Fig. 1 on p. 137 gives a good idea. The authors equate linearity with the combination of invariance under adding a constant (like constant absolute risk aversion) and multiplying by a positive constant (like constant relative risk aversion), but linearity is stronger. RDU with linear utility satisfies constant absolute and relative risk aversion, but is not a linear functional. %} Segal, Uzi & Joel Sobel (2002) “Min, Max, and Sum,” Journal of Economic Theory 106, 126–150. {% %} Segal, Uzi & Avia Spivak (1987) “Non-Expected Utility Risk Premiums: The Cases of Probability Ambiguity and Outcome Uncertainty,” Journal of Risk and Uncertainty 1, 333–347. {% %} Segal, Uzi, Avia Spivak, & Joseph Zeira (1988) “Precautionary Saving and Risk Aversion: An Anticipated Utility Approach,” Economics Letters 27, 223–227. {% That 1st order risk aversion is 0 under EU, but not under nonEU, was also demonstrated by Montesano (1988). However, that paper is not easy to read. %} Segal, Uzi & Avia Spivak (1990) “First-Order versus Second-Order Risk-Aversion,” Journal of Economic Theory 51, 111–125. {% Schrift pg. 665.; Dutch book; foundations of statistics %} Seidenfeld, Teddy (1979) “Philosophical Problems of Statistical Inference.” Reidel, Dordrecht. {% dynamic consistency; Provides an argument for independence that is well-known among philosophers. %} Seidenfeld, Teddy (1988) “Decision Theory without “Independence” or without “Ordering,” What is the Difference?,” Economics and Philosophy 4, 267–290. {% foundations of statistics %} Seidenfeld, Teddy (1992) “R.A. Fisher’s Fiducial Argument and Bayes’ Theorem,” Statistical Science 7, 358–368. {% dynamic consistency %} Seidenfeld, Teddy (2000) “Substitution of Indifferent Options at Choice Nodes and Admissibility: A Reply to Rabinowicz,” Theory and Decision 4, 305–310. {% dynamic consistency %} Seidenfeld, Teddy (2000) “The Independence Postulate, Hypothetical and Called-off Acts: A further Reply to Rabinowicz,” Theory and Decision 4, 319–322. {% On expert ggregation: show, apparently as first, an analog of Arrow’s impossibility theorem for SEU. That is, there is no aggregation rule where all individuals maximize SEU, so does the group preference relation, there are at least two agents who differ both in subjective probability and in utility, weak Pareto optimality (if all subjects strictly prefer x to y, then so does the group) holds, and it is nondictatorial. %} Seidenfeld, Teddy, Joseph B. Kadane, & Mark J. Schervish (1989) “On the Shared Preferences of Two Bayesian Decision Makers,” Journal of Philosophy 86, 225–244. {% Dutch book; finite additivity Some nice examples. Further that [pointwise monotonicity] and [finite-partition-conditional-preference-monotonicity] follow, but not [countable-partition-conditional-preference-monotonicity]. %} Seidenfeld, Teddy & Mark J. Schervish (1983) “A Conflict between Finite Additivity and Avoiding Dutch Book,” Philosophy of Science 50, 398–412. {% %} Seidenfeld, Teddy, Mark J. Schervish, & Joseph B. Kadane (2009) “Preference for Equivalent Random Variables: A Price for Unbounded Utilities,” Journal of Mathematical Economics 45, 329–340. {% proper scoring rules: seem to show that no proper scoring rules exist for imprecise probabilities (sets of priors). %} Seidenfeld, Teddy, Mark J. Schervish, & Joseph B. Kadane (2012) “Forecasting with Imprecise Probabilities,” International Journal of Approximate Reasoning 53, 1248–1261. {% Reviews preference reversals. %} Seidl, Christian (2002) “Preference Reversal,” Journal of Economic Surveys 16, 621–655. {% Nice references on history of St. Petersburg paradox. Gives results and inequalities on the degree of decreasingness of outcomes for whether or not infinite EU can result. On p. 259 he does transformation of separate-outcome probabilities, normalizing by dividing by the sum of all probability weights. It is well known that this violates stochastic dominance. P. 259 writes that a referee called the author’s attention to Yaari’s dual theory. %} Seidl, Christian (2013) “The St. Petersburg Paradox at 300,” Journal of Risk and Uncertainty 46, 247–264. {% %} Seidl, Christian & Ulrich Schmidt (1997) “Pareto on Intra- and Interpersonal Comparability of Utility,” History of Economic Ideas 5, 19–33. {% survey on nonEU: well, on EU it is P. 208 brings up nice point that bisection may give better results than matching simply because participants spend more time. Conclusion: “The response mode bias exceeds the effect of probability dependence.” utility elicitation; Extensive references are given. Certainty equivalents are compared to probability equivalents, using matching elicitation. Dependency of utility on the probability used is less for probability equivalents but does not disappear. %} Seidl, Christian & Stefan Traub (1999) “Biases in the Assessment of von Neumann-Morgenstern Utility Functions,” Journal of Economics Suppl. 8, 203–239. {% intuitive versus analytical decisions: consider combinations of analytic and intuitive decisions, and give many references on the topic. %} Seifert, Matthias & Andreas Eisingerich (2010) “The Role of Ambiguity and Complexity in Judgmental Forecasting,” {% %} Selart, Marcus, Tommy Gärling, & Henry Montgomery (1998) “Compatibility and the Use of Information Processing Strategies,” Journal of Behavioral Decision Making 11, 59–72. {% Give evidence that probability is the prominent dimension in risky choice. %} Selart, Marcus, Ole Boe, & Tommy Gärling (1999) “Reasoning about Outcome Probabilities and Values in Preference Reversals,” Thinking and Reasoning 5, 175–188. {% %} Selden, Lawrence (1978) “A New Representation of Preferences over ‘Certain x Uncertain’ Consumption Pairs: The ‘Ordinal Certainty Equivalent’ Hypothesis,” Econometrica 46, 1045–1060. {% %} Selden, Lawrence (1979) “An OCE Analysis of the Effect of Uncertainty on Saving under Risk Independence,” Review of Economic Studies 45, 73–82. {% Z&Z %} Selden, Thomas M. (1998) “Risk Adjustment for Health Insurance: Theory and Implications,” Journal of Risk and Uncertainty 17, 167–180. {% %} Selender, Arthur K. & Liang Zou (1994) “Limited Liability and the Underlying Asset Constraint: On the Use of Share-Derivative Contracts to Resolve Agency Problems,” Journal of Economics 59, 149–166. {% %} Selim, Asli (2013) “Is the Description-Experience Gap Real? : A Review of The Decisions from Experience Research,” working paper. {% %} Selim, Asli (2014) “An Examination of Uncertainty from a Psychological and Economic Viewpoint,” Ph.D. thesis, Erasmus School of Economics, Erasmus University, Rotterdam. {% Harsanyi’s aggregation %} Selinger, Stephen (1986) “Harsanyi’s Aggregation Theorem without Selfish Preferences,” Theory and Decision 20, 53–62. {% %} Selten, Reinhard (1965) “Spieltheoretische Behandlung eines Oligopolmodells mit Nachfragetragheit,” Zeitschrift für die Gesamte Staatswissenschaft 12, 301–324. (667–689 kan eventueel worden toegevoegd) {% %} Selten, Reinhard (1967) “Die Strategiemethode zur Erforschung des Eingeschränkt Rationalen Verhaltens im Rahmen eines Oligopolexperimentes,” Beiträge zur Experimentellen Wirtschaftsforschung, J.C.B. Mohr, Tübingen, 136–168. {% Uses “trick” of considering selves at different time points as different agents. %} Selten, Reinhard (1975) “Reexamination of the Perfectness Concept for Equilibrium Points in Extensive Games,” International Journal of Game Theory 4, 25–55. {% %} Selten, Reinhard (1994) “New Challenges to the Rationality Assumption: Comment,” Journal of Institutional and Theoretical Economics 150, 42–44. {% probability elicitation %} Selten, Reinhard (1998) “Axiomatic Characterization of the Quadratic Scoring Rule,” Experimental Economics 1, 43–62. {% Four revolutions in economics: (1) Mathemization; (2) Game theory; (3) Experiments assuming preference optimization; (4) bounded rationality. %} Selten, Reinhard (2014) Lecture in Haifa Jan.24, 2014. {% Christiane, Veronika & I: they pay in probabilities unit. linear utility for small stakes: if payment is not in money but in probability for a prize, then by any rational theory with reduction of compound probabilities and stochastic dominance, participants should maximize expected probability. This point has often been observed under the assumption of subjective expected utility. It is a nice observation, which the paper starts with, that it in fact holds for every probabilistically sophisticated (meaning (additive) subjective probabilities are used and decisions are based on only those; the paper does not use this term) decision maker under the minimal assumptions of preferring the highest probability at a good outcome and reduction of compound probabilities. However, extensive violations are found empirically that are farther apart from expectation maximization than for real money. Payments vary between 0 and 500 pfennig, which is between $0 and $2.50, with one loss gamble for about $1 added. The common ratio effect, the “reference point effect” (I assume loss aversion), preference reversals, and violations of stochastic dominance persist and seem to be even stronger. Backward induction seems to be natural in the paper’s setup. Goeree, Holt, & Palfrey (2003, p. 105 2nd para) also list evidence against paying in probabilities. %} Selten, Reinhard, Abdolkarim Sadrieh, & Klaus Abbink (1999) “Money Does not Induce Risk Neutral Behavior, but Binary Lotteries Do even Worse,” Theory and Decision 46, 211–249. {% revealed preference %} Sen, Amartya K. (1971) “Choice Functions and Revealed Preference,” Review of Economic Studies 38, 307–317. {% %} Sen, Amartya K. (1973) “On Economic Inequality.” Clarendon Press, Oxford. {% P. 390 seems to have written, related to Arrow’s impossibility theorem: “armed with only an n-tuple of individual orderings, we can hardly expect to say much of interest on inequality.” %} Sen, Amartya K. (1974) “Informational Bases of Alternative Welfare Approaches. Aggregation and Income Distribution,” Journal of Public Economics 3, 387–403. {% %} Sen, Amartya K. (1977) “Rational Fools: A Critique of the Behavioral Foundations of Economic Theory,” Philosophy and Public Affairs 6, 317–344. {% P. 121 seems to say that consequences should describe “everything in the real world (except in [the] mind).” %} Sen, Amartya K. (1985) “Rationality and Uncertainty,” Theory and Decision 18, 109–127. {% %} Sen, Amartya K. (1986) “Information and Invariance in Normative Choice.” In Walter P. Heller, Ross M. Starr, & David A. Starrett (eds.) Social Choice Public Decision Making: Essays in Honor of Kenneth J. Arrow, Vol. I, 29–55, Cambridge University Press, Cambridge. {% Survey of welfare theory. %} Sen, Amartya K. (1986) “Social Choice Theory.” In Kenneth J. Arrow & Michael D. Intriligator (eds.) Handbook of Mathematical Economics III, 1073–1181, North-Holland, Amsterdam, Ch. 22. {% This is followed by reply by Broome. %} Sen, Amartya K. (1991) “Utility: Ideas and Terminology,” Economics and Philosophy 7, 277–283. {% %} Sen, Amartya K. (1992) “Inequality Reexamined.” Harvard University Press, Cambridge, MA. {% utility = representational? Argues that internal consistency conditions are unconvincing if not related to external criteria. While essentially true, I disageee with the presentation in this paper. Internal consistency is never all of it, indeed, but still it is worthwhile to study it. The more so as, for any external consistency requirement, one can require further external justification (to every answer one can ask again “why”), so external consistency need not be principally more sound. P. 498: the necessity of bringing in something outside choice behavior is the issue. P. 500, fortunately, uses the terms contraction consistency and expansion consistency instead of Sen’s earlier unfortunate terms property or property yy. Many many examples of all kinds of violations of IIA etc. Download 7.23 Mb. Share with your friends:
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