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risk seeking for small-probability gains
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risk seeking for small-probability gains: well, this is risk aversion for small-probability losses. “Overprotection stems partly from the skewed incentives for reviewing committees … are held accountable for failure but not rewarded for success. … the possible risks loom larger than the cost savings. This is because of the disproportionate weighting of rare extreme events — for instance, a risk increase of 0% to 1% may be seen as more alarming than one from 40% to 41%. Institutions may therefore opt to play safe, despite the low probability of such events. … As such, the costs of overprotection raise ethical concerns of their own.” %} Page, Lionel & Katie Page (2017) “Reforms Overdue for Ethical Reviewing,” Nature 544 (13 April 2017) 161. {% decreasing ARA/increasing RRA: shortly after 2011 Australian floods (Brisbane) interviewed home owners. They could choose payment of $10 for sure, or a scratch card costing $10 (sort of lottery game, well known, and giving very high prize with small probability). People with serious damage to their house chose the scratch card more often. So looks like they are more risk seeking. Well, probabilities of scratch card are unknown, so then they are more uncertainty seeking. %} Page, Lionel, David A. Savage, & Benno Torgler (2014) “Variation in Risk Seeking Behaviour Following Large Losses: A Natural Experiment,” European Economic Review 71, 121–131. {% %} Pahlke, Julius, Sebastian Strasser, & Ferdinand M. Vieider (2012) “Risk-Taking for Others under Accountability,” Economics Letters 114, 102–105. {% losses from prior endowment mechanism: this was NOT done. Losses were really implemented and subjects could really lose money, which they could either pay on the spot or work off (€5 per half hour). Every subject was paid three choices, which may generate some income effect, but which was done to minimize the risk for a subject of really losing. Two of 144 lost, €3.50 and €2.00. inverse-S: when people have to decide not only for themselves, but also for the outcomes of someone else, then this accentuates the fourfold pattern. The authors show this by considering gains and losses for 50-50 prospects, and then also for small probabilities. decreasing ARA/increasing RRA: p. 131: for gains they find INCREASING absolute risk aversion, for losses H0 of constant. For gains, the common finding is decreasing absolute risk aversion. The discussion section p. 138 cites increasing risk aversion as the common finding, but the references cited find increasing RELATIVE risk aversion, whereas this paper tests absolute risk aversion (in the chart on p. 129, a constant b/2 is ADDED to all outcomes in the positive shift). %} Pahlke, Julius, Sebastian Strasser, & Ferdinand M. Vieider (2015) “Responsibility Effects in Decision Making under Risk,” Journal of Risk and Uncertainty 51, 125–146. {% %} Palacios-Huerta, Ignacio (1999) “The Aversion to the Sequential Resolution of Uncertainty,” Journal of Risk and Uncertainty 18, 249–269. {% dynamic consistency; Writes that Adam Smith and David Hume already pointed out that we can have, besides instant utility, also utility from anticipated and remembered consumption. Suggests that Smith and Hume meant these concepts to be an internal reward system to avoid dynamic inconsistency. This would be reminiscent of the Machina-McClennen view on dynamic consistency without extraneous commitment device. It may also be that Smith and Hume only meant these emotions to serve good purposes in a general sense, without particularly thinking of dynamic inconsistency. DC = stationarity on p. 242, 248. %} Palacios-Huerta, Ignacio (2003) “Time-Inconsistent Preferences in Adam Smith and David Hume,” History of Political Economy 35, 241–268. {% decreasing ARA/increasing RRA: many refs on power utility and the average power found, in the economics literature. The paper is strange, incorrectly trying to criticize Rabin’s (2000) paradox. Looking at the implausible implication of EU when combined with Rabin’s plausible empirical assumption of 110.510 0 at various wealth levels, the idea to give up EU does not occur to the authors. Instead they, first, add evidence of the same kind as Rabin. That is, they cite many empirical estimations of power utility in the literature that are all based on the EU assumption, and then point out that these findings cannot be reconciled with Rabin’s assumption of the above preference for a range of wealth levels. They do not conclude from this evidence, as does Rabin, that EU is in trouble, but, unable or unwilling to give up EU, they instead turn against Rabin’s assumed preference and conclude that it must not be plausible after all. It is also strange that, in citing findings on powers of utility from the literature, the point so crucial in Rabin’s argument about how large the stakes are, is never mentioned by the authors. %} Palacios-Huerta, Ignacio & Roberto Serrano (2006) “Rejecting Small Gambles under Expected Utility,” Economic Letters 91, 250–259. {% ranking economists %} Palacios-Huerta, Ignacio & Oscar Volij (2004) “The Measurement of Intellectual Influence,” Econometrica 72, 963–977. {% %} Palfrey, Thomas R. & Robert Porter (1991) “Guidelines for Submission of Manuscripts on Experimental Economics,” Econometrica 59, 1197–1198. {% probability elicitation: applied to experimental economics; proper scoring rules %} Palfrey, Thomas R. & Stephanie W. Wang (2009) “On Eliciting Beliefs in Strategic Games,” Journal of Economic Behavior and Organization 71, 98–109. {% %} Palley, Asa (2012) “Great Expectations: Prospect Theory with a Consistent Reference Point” {% %} Palmer, Tim N. & Renate Hagedorn (2006, eds.) “Predictability of Weather and Climate.” Cambridge University Press, Cambridge. {% decreasing ARA/increasing RRA: seems to finds no relation between RRA and income, which suggests constant RRA. %} Pälsson, Anne-Marie (1996) “Does the Degree of Relative Risk Aversion Vary with Household Characteristics?,” Journal of Economic Psychology 17, 771–787. {% Extend quasi-hyperbolic discounting to the continuous case. Axiomatize a discount model with constant discounting before some time point, and after, but the two periods having different discount rates. The switching point can be taken endogenously. %} Pan, Jinrui, Craig S. Webb, & Horst Zank (2014) “Discounting the Subjective Present and Future,” Games and Economic Behavior 89, 43–55. {% %} Pan, Jun (2002) “The Jump-Risk Premia Implicit in Options: Evidence from an Integrated Time-Series Study,” Journal of Financial Economics 63, 3–50. {% information aversion: ostrich effect is a nice term for it. Uses LISS panel to show that loss aversion predicts aversion to info regarding medical tests. %} Panidi, Ksenia (2011) “Ostrich Effect in Health Care Decisions: Theory and Empirics,” working paper. {% questionnaire versus choice utility: argues for introspective psychological data in economics. %} Pantaleoni, Mafio (1913) “Definizione dell’Economia. Una Prolusione,” Erotemi di Economia I, 1–66, Laterza, Bari, Italy. {% Denneberg gaf aan (ik geloof over symmetric integral); alleen ter inzage Koninklijke bib Den Haag %} Pap, Endre (1995) “Null-Additive Set Functions;” Mathematics and its Applications: Vol. 337. Kluwer Academic, Dordrecht. {% %} Papamarcou, Adrianos & Terrence L. Fine (1986) “A Note on Undominated Lower Probabilities,” Annals of Probability 14, 710–723. {% DOI: http://dx.doi.org/10.1016/j.geb.2013.06.010 CBDT : assume functional forms of CBDT and derive, through simulations, properties from that. It is a sort of reversed revealed preference (explained p. 53 1st para). %} Pape, Andreas Duus & Kenneth J. Kurtz (2013) “Evaluating Case-Based Decision Theory: Predicting Empirical Patterns of Human Classification Learning,” Games and Economic Behavior 82, 52–65. {% dynamic consistency People are willing to pay considerably for NOT precommitting. %} Paradiso, Massimo & John D. Hey (2004) “Strategies vs Backward Induction in Dynamic Decision-Making: An Experimental Investigation,” discussion paper. {% Discusses implications of loss aversion for marketing, with a detailed discussion of the conative (action-linked) and other components of loss aversion. %} Paraschiv, Corina & Olivier l’Haridon, (2008) “Loss Aversion: Origin, Components and Marketing Implications,” Recherche & Applications en Marketing 23, 67–83. {% Range-frequency model: assume that you are exposed to a set of stimuli x0,…,xn, which are real numbers with, for convenience, x0 < … < xn. Define the absolute position of xi as (xi‑x0)/(xn‑x0), and the relative position as i/n (my terms). The perceived seize of xi is a weighted average of these two positions.. The absolute position can incorporate differences, but the relative position can only observe orderings, and suggests insensitivity. The model is a mix of an ordinal and a cardinal model. The model implies that we are extra sensitive, and our sensation function is extra steep, in regions where there are many xjs, and we are little senstive in regions with few xjs. The ordinal term pushes our perceptions in the direction of uniformly distributed locations. Makes sense that we are extra sensitive in regions where we have much experience. %} Parducci, Allen (1965) “Category Judgment: A Range-Frequency Model,” Psychological Review 72, 407–418. {% %} Parducci, Allen (1968) “The Relativism of Absolute Judgments,” Scientific American 219 (n. 6, Dec), 84–90. {% Good reference on his range-frequency theory. %} Parducci, Allen (1995) “Happiness, Pleasure, and Judgment: The Contextual Theory and its Applications.” Lawrence Erlbaum Associates, Hillsdale, NJ. {% %} Pareto, Vilfredo (1892) “Considerazioni sui Principii Fondamentali dell’Economia Politica Pura,” Giornalie degli Economisti, Series 2, Vol. V, Aug. 1892. {% Stigler (1950) says that on p. 307 (or p. 119 ff. says Stigler, 1950 in Footnote 201): first person in history to give empirical implication of additive decomposability it seems (according to Stigler, 1950). Mentioned that increase in price of any commodity then implies decrease in demand. Then says that demand is observable, that we can infer the implication just mentioned, and that therefore the utility of a commodity may be assumed to depend, approximately, only on the quantity of the commodity in question. Seems to have noted problem of existence of utility function; i.e., seed of ordinalism. Schumpeter (1954), §5 of Appendix to Ch. 7, suggests that Pareto turned to ordinalism only in 1890, and that “Wieser” preceded him. %} Pareto, Vilfredo (1893) “Considerazioni sui Principii Fondamentali dell’Economia Politica Pura,” Giornalie degli Economisti, series 2, Vol. VII. {% P. 4748 (I think of Vol. I) used interpersonal comparison of utility for welfare purposes. Distinguishes between utility bringing usefulness and fulfilling needs (in principle objective and observable), and utility fulfilling desires (ophelimity, subjective). Pareto seems to say that the two concepts should be identical for a rational person. So then ophelimity is descriptive and usefulness is normative? Cooter & Rappoport, footnote 23, say that Pareto (1896 Vol. I) says that the two concepts should coincide for a rational person, don’t say where. Just before, they referred to p. 3 of Pareto’s work.) %} Pareto, Vilfredo (1896/7) “Cours d’Economie Politique, Vol. I and II.” Rouge, Lausanne. {% Seems to write: “It is an empirical fact that the natural sciences have progressed only when they have taken secondary principles as their point of departure, instead of trying to discover the essence of things … Pure political economy has therefore a great interest in relying as little as possible on the domain of psychology.” (I got this from Bruni & Sugden (2007), who cite Busino (1964) for it on their p. 154.) %} Pareto, Vilfredo (1896/7) letter to Adrien Naville. {% P. 214 (I guess of 1982 reprinted text) seems to claim, as one of his main achievements, that “every psychological analysis is eliminated.” %} Pareto, Vilfredo (1900) “Sunto di Alcuni Capitoli di un Nuovo Trattato di Economia Politica del Prof. Pareto,” Giornale degli Economisti 10, 216–235; 511–549. Reprinted in 1982, “Oeuvres Complètes of V. Pareto,” Droz, Geneva. {% Seems that both the first article in Econometrica and in Review of Economic Studies was an article on Pareto. Showed some implications of additive decomposability of utility, mentioned some economic phenomena that contradict those implications, but still defended it as an approximation. Ch. 3, paragraph 29, utility is relation between man and thing. Paragraph 36b points out that only indifference curves matter, not anything of utility (called ophelimity, meaning it’s what the subject chooses so what apparently pleases him most, but need not be useful in some rational sense, e.g. such as taking heroine. 1927 translation in French seems to be first to define strength of preference on p. 19, according to Fishburn (1970 p. 81). 1971 translation seems to write, on p. 191, that strength of preference judgments by introspection are possible, though not with great precision. Seems that in Ch. 3, §1, he writes on preferences only after learning: “A man who buys a certain food for the first time may buy more of it than is necessary to satisfy his tastes, price taken into account. But in a second purchase he will correct his error, in part at least, and thus, little by little, will end up by procuring exactly what he needs. We will examine this action at the time when he has reached this state. Similarly, if at first he makes a mistake in his reasoning about what he desires, he will rectify it in repeating the reasoning and will end up by making it completely logical.” [italics added here] conservation of influence: seems to have written, on man maximizing something with us researchers being conspicuously vague on what is maximized: “to compare the sensations of a man in different situations, and to determine which of these he would chose. … [S]ince it is customary to assume that man will be guided in his choice exclusively by consideration of his own advantage, of his self-interest, we say that this class is made up of theories of egotism. But it could be made up of theories of altruism (if the meaning of that term could be defined rigorously), or, in general, of theories which rest on any rule which man follows in comparing his sensations. It is not an essential characteristic of this class of theories that a man choosing between two sensations choose the most agreeable; he could choose a different one, following a rule which could be fixed arbitrarily. (Ch.3, §11) %} Pareto, Vilfredo (1906) “Manuele di Economia Politica.” Piccolo Biblioteca Scientifica, Milan. Translated into English by Ann S. Schwier (1971) “Manuel of Political Economy,” MacMillan, London. Translated into French in 1927 as “Manuel d’Economie Politique; 2nd edn.” Giard, Paris. Seems to be in “Oeuvres Complètes,” 12, Droz, Genève, 1964. {% discounting normative: Ch. 14 argues for positive discounting because your identity changes over time, and criticizes six arguments for constant discounting. If those do not apply, then he favors zero discounting. This is taken as the most standard reference for this viewpoint. Seems that he introduced the silly term of the repugnant conclusion for an Archinedean axiom. %} Parfit, Derek (1984) “Reasons and Persons.” Clarendon Press, Oxford, UK. {% Dutch book %} Paris, Jeff B. (2000) “A Note on the Dutch Book Method.” {% Says Rabin is due to loss aversion. %} Park, Hyeon (2016) “Loss Aversion and Consumption Plans with Stochastic Reference Points,” B.E. Journal of Theoretical Economics 16, 303–336. {% Extends Green & Osband (1991) to weighted utility. %} Park, In-Uck (1998) “A Revealed-Preference Implication of Weighted Utility Decisions under Uncertainty,” Economic Theory 11, 413–426. {% %} Park, Joo Heon & Douglas L. MacLachlan (2008) “Estimating Willingness to Pay with Exaggeration Bias-Corrected Contingent Valuation Method,” Marketing Science 27, 691–698. {% utility elicitation: participants choose between 2-dimensional alternatives where the first coordinate describes an amount of money, the second some good such as a new compact disk player or a tennis outfit. They find that double cancellation is rather well satisfied and conclude that an additive representation must hold. P. 280: “Krantz et al. (1971) have shown that, for all effective purposes, if double cancellation is not violated, the system is additive.” That is, they make the well known mistake of not understanding the empirical implications of restricted solvability, clearly explained in Krantz et al. (1971, §9.1). They get the additive value function for money as x to the power .64. IMPORTANT, on risky utility u = strength of preference v (or other riskless cardinal utility, often called value) or risky utility u = transform of strength of preference v: !!!Nice example of cardinal utility obtained from additive conjoint measurement. Give many references to the usefulness of the power family to fit utility.!!! %} Parker, Scott & Bruce Schneider (1988) “Conjoint Scaling of the Scaling of the Utility of Money Using Paired Comparisons,” Social Science Research 17, 277–286. {% Review implications of Keeney (1992). %} Parnell, Gregory S., David W. Hughes, Roger Chapman Burk, Patrick J. Driscoll, Paul D. Kucik, Benjamin L. Morales, & Lawrence R. Nunn (2013) “Invited Review—Survey of Value-Focused Thinking: Applications, Research Developments and Areas for Future Research,” Journal of Multi-Criteria Decision Analysis 20, 49–60. {% DOI: 10.1214/12-AOS971 proper scoring rules: extend locality to also allow dependence on some higher-order derivatives of the score at the event observed. Then more than just the logarithmic function can do it. %} Parry, Matthew, A. Philip Dawid, & Steffen Lauritzen (2012) “Proper Local Scoring Rules,” Annals of Statistics 40, 561–592. {% time preference; referaat of Anne op 15 mei 1996. Argue against Keeler-Cretin idea that benefits must be discounted as strongly as money because one would defer projects for ever otherwise. %} Parsonage, Michael & Henry Neuburger (1992) “Discounting and Health Benefits” (with discussion), Health Economics 1, 71–79. {% %} Parthasarathy, Koduvayur R. (1967) “Probability Measures on Metric Spaces.” Academic Press, New York. {% no. 233: Pascal’s wager. Seems to be discussed by Hacking (1975). %} Pascal, Blaise (1660), Pensées. {% PT, applications: §3.2.2 points out that they have no closed form for equilibrium. §4 describes PT as a descriptive theory. %} Pasquariello, Paolo (2014) “Prospect Theory and Market quality,” Journal of Economic Theory 149, 276–310. {% I thought for some time that they introduced QALYs, together with Torrance, Sackett & Thomas (1973). Later I found that Fanshel & Bush (1970, p. 1050) preceded them. %} Patrick, Donald L., James W. Bush, & Milton M. Chen (1973) “Toward an Operational Definition of Health,” J. Health Soc. Behavior 14, 6–23. {% survey of QALYs; use MAUT techniques to combine dimensions in Health utilities index (vision, hearing, speech, dexterity, mobility, cognition, emotion, pain) and others into a QALY index %} Patrick, Donald L. & Pennifer Erickson (1993) “Health Status and Health Policy: Allocating Resources to Health Care.” Oxford University Press, New York. {% A strange paper. It discusses the publication process from a sort of meta- philosophical perspective, such as what kind of general communication system it is. I did not find concrete suggestions for any of the involved parties on how they could improve their performance. %} Patriotta, Gerardo (2017) “Crafting Papers for Publication: Novelty and Convention in Academic Writing,” Journal of Management Studies 54, 747–759. {% %} Pauker, Stephen G. (1976) “Coronary Artery Surgery: The Use of Decision Analysis,” Annals of Internal Medicine 85, 8–18. {% simple decision analysis cases using EU %} Pauker, Stephen G. & Jerome P. Kassirer (1980) “The Threshold Approach to Clinical Decision Making,” New England Journal of Medicine 302, 1109–1117. {% %} Pauker, Stephen G. & Jerome P. Kassirer (1987) “Decision Analysis,” New England Journal of Medicine 316, 250–258. {% inverse-S: N=16 subjects, CEs (certainty equivalents) elicited for seven one nonzero-outcome prospects. No real incentives (p. 676 last para). The authors then find the best-fitting power utility function and 2-parameter CI family of Prelec (1998) (minimizing squared distance). Find U(x) = x0.66 as best fitting, and usual w. However, for one-nonzero outcomes the joint power of utility and probability weighting is undetermined. Looks like they make a classical mistake here. Find that degree of inverse-S (which is not affected by indeterminacy of power, as in Wakker 2004 Psychological Review) corresponds with lack of controlled processing by the anterior cingulate cortex (do not know what that means, copying it from the abstract). % Paulus, Martin P. & Lawrence R. Frank (2006) “Anterior Cingulate Activity Modulates Nonlinear Decision Weight Function of Uncertain Prospects,” Neuroimage 30, 668–677. {% Z&Z %} Pauly, Mark V. (1968) “The Economics of Moral Hazard: Comment,” American Economic Review 58, 531–537. {% Z&Z %} Pauly, Mark V. (1968) “Overinsurance and Public Provision of Insurance: The Role of Moral Hazard and Adverse Selection,” Quarterly Journal of Economics 88, 44–62. {% %} Payne, John W. (1973) “Alternative Approaches to Decision Making under Risk: Moments versus Risk Dimensions,” Psychological Bulletin 80, 439–453. {% PT falsified %} Payne, John W. (2005) “It Is whether You Win or Lose: The Importance of the Overall Probabilities of Winning or Losing in Risky Choice,” Journal of Risk and Uncertainty 30, 5–19. {% %} Payne, John W., James R. Bettman, Eloise Coupey, & Eric J. Johnson (1992) “A Constructive Process View of Decision Making: Multiple Strategies and Choice,” Acta Psychologica 80, 107–141. {% %} Payne, John W., James R. Bettman, & Eric J. Johnson (1988) “Adaptive Strategy Selection in Decision Making,” Journal of Experimental Psychology: Learning, Memory and Cognition 14, 534–552. {% a review %} Payne, John W., James R. Bettman, & Eric J. Johnson (1992) “Behavioral Decision Research: A Constructive Processing Perspective,” Annual Review of Psychology 43, 87–131. {% %} Payne, John W., James R. Bettman, & Mary-Frances Luce (1996) “When Time Is Money: Decision Behavior under Opportunity-Cost Time Pressure,” Organizational Behavior and Human Decision Processes 66, 131–152. {% This paper does not only describe things going wrong in preference theory but it is constructive in nature: it seeks to offer offer remedies and make preference measurement function again. Schkade during SPUDM ’97 lecture: “Get more out of fewer subjects.” The paper is less focused on the issue of interacting with clients but gives a broad survey of the many biases that can occur during preference measurement. P. 249: “The procedures often involve greater work in the measurement of preferences, with a focus on doing more tasks with fewer respondents.” Paper uses term “design purposes” for prescriptive. P. 247: they argue for using coherence conditions for improving preference elicitation, adding to it that also the process leading to preference should be judged. P. 257, §3.3.1 gives reasons for why people may want to avoid making tradeoffs. P. 259 recommends that anchors be made explicit rather than have them be made by implicit/random factors P. 265: “Nevertheless, we believe that providing procedures and tools that help individuals discover their own preferences is in the best interest of those individuals, even though this may also influence those preferences.” %} Payne, John W., James R. Bettman, & David A. Schkade (1999) “Measuring Constructed Preferences: Towards a Building Code,” Journal of Risk and Uncertainty 19, 243–270. {% %} Payne, John W. & Myron L. Braunstein (1971) “Preferences among Gambles with Equal Underlying Distributions,” Journal of Experimental Psychology 87, 13–18. {% N = 30 & N = 42 & N = 84; hypothetical choice; reflection at individual level for risk: they don’t give data detailed enough to see this. Translating gambles (adding up a constant to all outcomes) through the origin evokes sharp changes in risk attitude, in agreement with the predictions of loss aversion. Gives many refs to early aspiration-level and reference-level ideas. paternalism/Humean-view-of-preference: p. 1055 suggests that utility should not be concavitized but should be left convex for losses if that is what is measured. Criticize Keeney & Raiffa (1976) for such concavitization. %} Payne, John W., Dan J. Laughhunn, & Roy L. Crum (1980) “Translation of Gambles and Aspiration Level Effects in Risky Choice Behavior,” Management Science 26, 1039–1060. {% Supplement findings of their 1980 paper. They now manipulate the reference level, not the outcomes. P. 1054 writes: “The prevailing view about risk attitude in management science research, for both normative and positive models, ignores the aspiration level concept and assumes that decision makers are uniformly risk averse.” %} Payne, John W., Dan J. Laughhunn, & Roy L. Crum (1981) “Further Tests of Aspiration Level Effects in Risky Behavior,” Management Science 27, 953–958. {% Study multiattribute risk aversion; Risk averse for gains, risk seeking for losses %} Payne, John W., Dan J. Laughhunn, & Roy L. Crum (1984) “An Experimental Study of Multiattribute Risky Choice,” Management Science 30, 1350–1361. {% CBDT Players do CBDT optimization in repeated games. %} Pazgal, Amit (1997) “Satisficing Leads to Cooperation in Mutual Interests Games,” International Journal of Game Theory 26, 439–453. {% %} Pazner, Elisa A. (1979) “Equity, Nonfeasible Alternatives and Social Choice: A Reconsideration of the Concepts of Social Welfare.” In Jean-Jacques Laffont (ed.) Aggregation and Revelation of Preferences, Ch. 9, 161–173, North-Holland, Amsterdam. {% Argues against reasonableness of Nash equilibrium; T00032 %} Pearce, David (1984) “Rationalizable Strategic Behavior and the Problem of Perfection,” Econometrica 52, 1029–1050. {% %} Pearl, Judea (1986) “Fusion, Propagation, and Structuring in Belief Networks,” Artificial Intelligence 29, 241–288. {% Book is pro-Bayesian. Reviewed by Dubois & Prade (1990, JMP). %} Pearl, Judea (1988) “Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference.” Morgan Kaufmann, San Mateo CA. {% %} Pearl, Judea (1990) “Reasoning with Belief Functions: An Analysis of Compatibility,” International Journal of Approximate Reasoning 4, 363–389. {% %} Pearl, Judea (1992) “Probabilistic Semantics for Nonmonotonic Reasoning.” In Robert G. Cummins & John Pollock (eds.) Philosophy and AI, Essays at the Interface, 157–187, MIT Press, Cambridge, MA. {% This book is considered a classic. Imagine that we observe only correlations, and find one between C and A. We don’t know if C has causal influence on A or vice versa, because of symmetry. If we also get temporal info, and know that C preceded A, then it seems plausible that C has causal influence on A. (There is always problem of hidden common causes for C and A; soit.) For long time it was believed that with only info on correlations, and not for instance on temporal ordering, we cannot speculate on causal directions because of symmetry. It seems that Pearl discovered a way to speculate nevertheless: if C and B are mutually independent but both are correlated with A, then it is plausible that B and C have causal influence on A and not the other way around. Seems that he started writing on it at end of 1980s. This book collects several of his papers. %} Pearl, Judea (2000) “Causality. Models, Reasoning, and Inference.” Cambridge University Press, New York. {% Measured prior probability for binomial parameter experimentally, e.g., one day he goes out on the street and observes the proportion of women that wear red hats. Collected data over four years. P. 389 describes Venn’s rule of succession. P. 397: “Casual Observations in London Streets and elsewhere” Under this heading: “From a window in Gower street I observe how many vehicles out of the first 20 that pass below are drawn by horses, and then how many of a later sample of 15.” %} Pearson, Egon S. (1925) “Bayes Theorem, Examined in the Light of Experimental Sampling,” Biometrika 17, 388–442. {% Seems to have argued that each scientist should search for “self-elimination in his judgements, to provide an argument which is true for each individual mind as for his own.” This spirit contributes to inclination to take statistics in a non-Bayesian way, such as in the theory of Neyman and Egon Pearson (Karl’s son). %} Pearson, Karl (1892) “Grammar of Science.” {% Explains that Hutton (known for work on geological time), preceding Darwin (1831), had a chapter explaining the principles of selection of the fittest, though maybe not the development of new species. Hutton taught in Edinburgh, where besides Darwin also Patrick Matthew and William Wells lived, two people credited before for having preceded Darwin on the idea of evolution. All these three came after Hutton. %} Pearson, Paul N. (2003) “In Retrospect of: James Hutton (1794) An Investigation of the Principles of Knowledge and of the Progress of Reason, from Sense to Science and Philosophy;”” Nature 425, 16 October 2003, p. 665. {% Seems to discuss f''//f' as a measure for curvature, and to give references to preceding literature, as was told to me by Rich Gonzalez in August 1994. %} Pecaric, Proschan, & Tong, “Convex Functions, Partial Orderings, and Statistical Applications.” {% RDU version of de Finetti’s coherence, containing generalizations of things of Diecidue & Wakker (2002). %} Pedersen, Arthur P. (2014) “Comparative Expectations,” working paper. {% DOI: 10.1038/s41562-017-0219-x An impressive study. For1,507 (!) subjects, six elicitation methods were used to measure risk attitudes, taking essentially a whole day of each subject. Very little consistency was found, both between raw measures of risk aversion (only that; no raw measure fo insensitivity) and between fitted parameters of expected utility or prospect theory. The authors conclude very negatively (P. 5 2nd column 1st para): “What is clear is that scientists’ common practice, namely, measuring risk preferences with one simple behavioural EM (for example, lotteries) and thus creating the fiction that they can capture consistent risk preferences, should stop.” They several times express the constructive view of preference. E.g., abstract last sentence: “Instead, we interpret the results as suggesting that risk preferences may be constructed when they are elicited, and different cognitive processes can lead to varying preferences.” My reaction: I will continue to work on finding consistent risk preferences. One reason is based on normative thoughts: There exists a normative proper risk attitude in every person, e.g. though utility in expected utility. We should do all we can to find it as much as possible. The more so as finding it is something like finding the holy grail. One can then take best decisions for people. This is also why the decision-theory concepts of risk attitude are way more interesting than introspective measures. Another point in my reaction: subjects had to spend almost a day doing the experiment. My experience is that individual choice experiments can last no more than 45 minutes. After that subjects get bored. The subjects here may have gotten bored, so that almost only noise was measured. The literature references in the paper are impressive. P. x+1, 2nd para: “Surprisingly, there is no consensus across science and industry on how risk preferences should be measured.” P. x+1: end of 1st para of 2nd column: many references that compare different measurement methods. P. x+2 penultimate para: the BART measurement deviated most from the others, and this is because, unike the other tasks, it had unknown probabilities, to be learned from sampling (DFE). P. x+4 1st para: BART has very weird results, with risk seeking and loss aversion = 0.43, so, much gain seeking. P. x+2 2nd column 3rd para: They related choice inconsistencies to a cognitive intelligence measure, but found no relation. Report it only in online appendix. P. x+4, 2nd para: “However, numerous studies have demonstrated that individuals’ risk preferences often deviate from EUT and that CPT is often the best model for fitting aggregate choices even if some people are not [typo] best described by EUT and even though there may not be a single best model for fitting individual choices.” P. x+4, 4th para: “Although on average CPT describes the choices better than EUT” P. x+5, 2nd para: “Second, capturing risk preferences in terms of the non-normative components of risky choice (for example, probability weighting and loss aversion)”. That is, the authors take expected utility as normative. P. 5 2nd column 1st para reports the only positive result: “Second, the fact that all levels of analysis reveal exclusively positive correlations may hint at the existence of a general underlying construct.” P. 5 2nd column 1st para expresses the other constructive view of preference. It is not the view that all is arbitrary ad hoc construction and here is nothing down there. The second is that experimenters should influence subjects and construct their risk attitude together with subjects, as architects (“getting more out of fewer subjects”), when the authors write: “In addition, it may be of interest to examine whether decision aids, such as expert advice on how to approach specific decisions, may increase consistency in observed risk preferences.” %} Pedroni, Andreas, Renato Frey, Adrian Bruhin, Gilles Dutilh, Ralph Hertwig, & Jörg Rieskamp (2017) “The Risk Elicitation Puzzle,” Nature Human Behaviour 1, forthcoming. {% Propose to use expo-power in PT, and show some properties. %} Peel, David A. & Jie Zhang (2009) “The Expo-Power Value Function as a Candidate for the Work-Horse Specification in Parametric Versions of Cumulative Prospect Theory,” Economics Letters 105, 326–329. {% I enjoyed this discussion, given to me by Gideon Keren, of the psychological factors underlying positive versus negative outcomes, distinguishing several biases or functional weightings. The authors separate affective from informational, and relate to approach-avoidance. It interested me because if gives psychological background to loss aversion. But sometimes it was hard to follow. For instance, on p. 37: “the tendency to expect the positive is allied with a strongly marked sensivitity for aversive stimuli,” if any part of this claim had been reversed it would have been just as plausible to me. P. 54 middle: negativity effect (overweighting of negative outcomes, both affectively and informationally) is independent of probability at that negative outcome. Yechiam & Hochman (2013) present a sophisticated model explaining loss aversion by attention rather than to utility, with a followup in Yechiam, Retzer, Telpaz, & Hochman (2015). Bilgin (2012) is also relevant. %} Peeters, Guido & Janusz Czapinski (1990) “Positive-Negative Asymmetry in Evaluations: The Distinction between Affective and Informational Negative Effects.” In Wolfgang Stroebe & Miles Hewstone (eds.) European Review of Social Psychology 1, 33–60. {% %} Peijnenburg, Kim (2011) “Life-Cycle Asset Allocation with Ambiguity Aversion and Learning,” Bocconi University, Milano. {% Complete first name is Charles Sanders. information aversion: nonaversion to information (also for nonexpected utility??); note clearly thinks that value of additional knowledge is always positive. See for instance, in reprinted version, note.7.159, p. 86, ll 6-8. Note 142, p. 77 in reprinted version, says that the utility of knowledge consists in its capability of being combined with other knowledge so as to enable us to calculate how we should act. %} Peirce, Charles S. (1876) “Note on the Theory of the Economy of Research.” Reprinted in Arthur W. Burks (1978, ed.) “Collected Papers of Charles Sanders Peirce,” Volume 7, Science and Philosophy, 7, 140–161, Harvard University Press. {% foundations of statistics: proposes an expected utility criterion to assess the value of a test, say the prediction of a tornado. This value is (p.aa l.ab)/(aa + ab + ba + bb) where: p is profit (extra relative to not predicting) gained by correctly predicting it, aa the frequency of correct predictions, l the loss (relative to not predicting) of incorrectly predicting it, ab the frequency of incorrect predictions, and ba + bb the frequency of not predicting the tornado (wrong or right, respectively). So, the true Bayesian solution to evaluate a statistical hypothesis test. %} Peirce, Charles S. (1884) “The Numerical Measure of the Success of Predictions,” Science 4 (Nov. 14) 453–454. {% P. 421 seems to write: “to express the proper state of belief, not one number but two are required, the first depending on the inferred probability, the second on the amount of knowledge on which that probability is based. %} Peirce, Charles S. (1932) “Collected Papers.” Charles Hartstone & Paul Weiss (eds.) Belknap Press, Cambridge, MA. {% There is an incomplete pref. rel. over lotteries satisfing independence and continuity. The paper also considers choices between menus, and investigates cautiousness: defer choice whenever in doubt. Then there must be preference for flexibility. Thus, preference for self-control is distinguished from indecisiveness. %} Pejsachowicz, Leonardo & Séverine Toussaert (2017) “Choice Deferral, Indecisiveness and Preference for Flexibility,” Journal of Economic Theory 170, 417–425. {% Fit EU, RDU, en PT (they write CPT) for 8 macaques, 5 capuchins, and 4 orang-utans, by letting them choose between a sure cookie or a risky-size cookie. Fit power utility under EU (which fitted better than exponential, under EU by p. 157), power utility under RDU (which fitted better than exponential; p. 159), and piecewise linear, with kink at 0, for PT (can’t have more parameters for then unidentifiable; see footnote 8 p. 157). For RDU and PT use 1-parameter T&K (1992) family. When fitting PT, they assume linear utility because otherwise nonidentifiable (footnote 8 p. 157) apart from loss aversion. Find mixed results. %} Pelé, Marie, Marie-Hélène Broihanne & Bernard Thierry, Joseph Call, & Valérie Dufour (2014) “To Bet or not to Bet? Decision-Making under Risk in Non-Human Primates,” Journal of Risk and Uncertainty 49, 141–166. {% %} Peleg, Bezalel & Hans J.M. Peters (2009) “Nash Consistent Representation of Effectivity Functions through Lottery Models,” Games and Economic Behavior 65, 503–515. {% dynamic consistency? %} Peleg, Bezalel & Stef H. Tijs (1996) “The Consistency Principle for Games in Strategic Form,” International Journal of Game Theory 25, 13–34. {% dynamic consistency; reviewed by Shefrin (1998); Goldman (1979, 1980) seems to be an important follow-up. Paper first points out that for Strotz-Pollak solution (so, sophisticated choice; forgone-branch independence [often called consequentialism] is assumed for utility at time t) solution need not always exist. The counterexample is, if I understand right, based on the observation that the consumption chosen at time t is the result of a maximization and need not be continuous, therefore at time t1 a noncontinuous function has to be maximized, if I understand right. Then one can approximate the optimal utility within each distance but the maximum need not exist. (This is in my opinion a technical complication which does not lead me to reject sophisticated choice intuitively.) The authors next proceed to study different approaches than Strotz-Pollak, and propose that the solution should be a subgame perfect equilibrium for the players which makes sense. They point out that being an equilibrium is necessary (I agree given sophisticated choice) but surely not sufficient, e.g., equilibria can violate Pareto optimality. Note that sophisticated choice leads to equilibria. I’m not sure if the authors point that out. P. 392, assumption that utility function at time t does not depend on past consumption, considered in §II, is like forgone-branch independence. I do not understand their claim, at the end of §III, that their definition of stationarity would preclude changing tastes. For example, let U1(x1,x2,x3, ... ) be x1 + x2/2 + x3 + x4/2 + .... then I think that their stationarity leads to dynamic inconsistency and changing tastes; I didn’t study it in much detail. DC = stationarity: 2nd to last sentence of §III is on that topic. It defines stationarity as utility Ut at t being independent of past consumption and Ut(a,b,...) = U1(a,b,...). So it is what I would call forgone-act independence (often called consequentialism) plus a sort of invariance (that DUR automatically has but DUU not) different than stationarity. They are wrong in suggesting that their stationarity would preclude changing tastes, there they seem to confuse things with DC (dynamic consistency). E.g. let U1(a,b,c,d,...) = a + b/2 + c + d/2 + + ..., then DC is violated, at time 1 I may prefer (0,0,1,0,...) to (0,0,0,1,0,...) but at time 2 my preference reverses. %} Peleg, Bezalel & Menahem E. Yaari (1973) “On the Existence of a Consistent Course of Action when Tastes are Changing,” Review of Economic Studies 40, 391–401. {% %} Pelham, Brett W. & William B. Swann, Jr. (1989) “From Self-Conceptions to Self-Worth: On the Sources and Structure of Golbal Self-Esteem,” Journal of Personality and Social Psychology 57, 672–680. {% %} Pelham, Brett W., Tin Tin Sumarta, & Laura Myaskovsky (1994) “The Easy Path from Many to Much: The Numerosity Heuristic,” Cognitive Psychology 26, 103–133. {% An Italian author propagating the ideas of de Finetti. He favors giving more importance to de Finetti’s influence on Friedman, giving many discussion of Mach etc. on observability. %} Pelloni, Gianluigi (1996) “De Finetti, Friedman, and the Methodology of Positive Economics,” Journal of Econometrics 75, 33–50. {% Axiomatize ways of market evaluations, satisfying the conditions in the title. P. 26 4th para: they use utility indifference, meaning CE (certainty equivalents) under EU. P. 38: time consistency (other terms: recursiveness or tower property) means that if you do two-step evaluation over two consecutive periods, or do the two one-blow, should give the same result. Under some conditions it is equivalent to the usual dynamic consistency or time consistency. %} Pelsser, Antoon & Mitja Stadje (2014) “Time-Consistent and Market-Consistent Evaluations,” Mathematical Finance 24, 25–65. {% real incentives/hypothetical choice: for time preferences: seems to be %} Pender, John L. (1996) “Discount Rates and Credit Markets: Theory and Evidence from Rural India,” Journal of Development Economics 50, 257–296. {% Test house money effect and find it confirmed. Use hypothetical choice, with questions of the type “Suppose you had just won such a gamble. Would you play it again?” %} Peng, Jiaxi, Danmin Miao, & Wei Xiao (2013) “Why are Gainers More Risk Seeking,” Judgment and Decision Making 8, 150–160. {% questionnaire versus choice utility; Outcomes were monetary. Data were collected from 346 managers from small and medium size hog farms. Risk attitude was measured by (1) psychometric questionnaires regarding whether they would be open to new products etc. (2) hypothetical CE (certainty equivalent), fifty-fifty, questions. (3) same as (2) but corrected by taking it w.r.t. underlying scale that was derived from strength of preference (as they call it but it is direct assessment such as what is called VAS (visual analog scale) in the health domain), so it was risk attitude à la Dyer & Sarin. CE bias towards EV: most (60%) were risk seeking! Risk attitude from questionnaire correlated significantly with (2) and (3), not with str. of pr. value scale. Exponential utility fitted data better than power. Attitude questions were best predicted by (1); i.e., psychometric questionnaire results. Actual behavior was, however, best predicted by (2) and (3). There was no relation between actual behavior and psychometric scales. %} Pennings, Joost M.E. & Ale Smidts (2000) “Assessing the Construct Validity of Risk Attitude,” Management Science 46, 1337–1348. {% PT, applications, loss aversion, buying strategy of hog farmers; CE bias towards EV: p. 1254 reports only 55% risk averse in CE (certainty equivalent) questions. 50-50 CE questions were asked to 332 Dutch hog farmers. 149 had an “open” production system, where piglets and feeds are bought, piglets are raised to slaughter hogs in three months, and then sold. 183 had a closed system that is similar, only do they breed the piglets themselves iso buying them. In the open system where people buy the piglets, the buying price provides a natural reference point. Of these 149 people, 83 indeed show the S-shaped utility function of PT around that price, with convexity below, and 66 have concave utility. Of the other group of 183, 163 have concave utility without reference point or convex part, and 20 have ref/point concavity. An exceptionally nice illustration of how reference points come about due to small psychological aspects of framing. In the open group with the natural reference point, for gains we have c = 3.53, and for losses c = -0.77 (Pennings, personal communication, email of Friday 23 July 2004.) P. 1261: with log-IPT fitting (contrary to what the paper writes, it is not the IPT family but the log-IPT family, as Smidts, November 2003, personal communication, let me know), the inflection point (reference point!?) of utility is endogenous P. 1272: argue that farmers may not transform 50/50 probabilities because they know them very well from everyday experience. There are many elaborate details on parametric fittings. When the authors write global shape, they refer to the extent to which the function exhibits an S-shape. When they write local shape, they refer to the extent to which the function is concave or not. When they say organizational (strategic) behavior, they mean whether or not the production is open or closed and they relate it to whether or not utility is S-shaped. When they say trading behavior they mean other actions studied in another of their paper, and they relate it to risk aversion/concavity. Given that the choice of production must be complex, and driven by many factors, risk attitude can at most be a minor causal factor. Therefore, I think that the choice of production is the cause of the utility function measured, and not the other way around. I interpret this paper, therefore, as a nice illustration of how framing can drive utility measurement. %} Pennings, Joost M.E. & Ale Smidts (2003) “The Shape of Utility Functions and Organizational Behavior,” Management Science 49, 1251–1263. {% %} Pennock, David M., Steve Lawrence, C. Lee Giles, & Finn Årup Nielsen (2001) “The Real Power of Artificial Markets,” Science 291 (5506; February 9) 987-988. {% free-will/determinism: seems to suggest that indeterminacy at level of elementary particles may suffice to have uncertainty in the world and this making free will possible. So, the author overestimates the implications of physics. %} Penrose, Roger (1997) “The Large, the Small, and the Human Mind.” Cambridge University Press, Cambridge. {% Christiane, Veronika & I %} Pepermans, Ronald, Carole B. Burgoyne, & Anke Müller-Peters (1998) “European Integration, Psychology and the Euro,” Journal of Economic Psychology 19, 657–661. {% Christiane, Veronika & I %} Pepermans, Ronald, Gino Verleye (1998) “A Unified Europe? How Euro-Attitudes Relate to the Psychological Differences between Countries,” Journal of Economic Psychology 19, 681–699. {% %} Perakis, Georgia & Guillaume Roels (2008) “Regret in the Newsvendor Model with Partial Information,” Operations Research 56, 188–203. {% %} Perea, Andrés (2007) “Proper Belief Revision and Equilibrium in Dynamic Games,” Journal of Economic Theory 136, 572–586. {% %} Perea, Andrés (2008) “Minimal Belief Revision Leads to Backward Induction,” Mathematical Social Sciences 56, 1–26. {% %} Perea, Andrés (2007) “A One-Person Doxastic Characterization of Nash Strategies,” Synthese 158, 251–271. {% %} Perea, Andrés (2009) “A Model of Minimal Probabilistic Belief Revision,” Theory and Decision 67, 163–222. {% %} Perea, Andrés (2012) “Epistemic Game Theory: Reasoning and Choice.” Cambridge University Press, New York. {% %} Perea, Andrés (2014) “Belief in the Opponents’ Future Rationality,” Games and Economic Behavior 83, 231–254. {% %} Perlman, Michael D. & Lang Wu (1999) “A Defense of the Likelihood Ratio Criterion for Testing One Sided and Order Restricted Alternatives,” submitted to Journal of Statistical Planning and Inference. {% foundations of statistics; §9 gives many citations arguing against Neyman-Pearson hypothesis testing. Conclusion: “it is better to have no universal criterion than cling to an inappropriate one.” %} Perlman, Michael D. & Lang Wu (1999) “The Emperor’s New Tests” (with discussion), Statistical Science 14, 355–381. {% %} Perlman, Michael D. & Lang Wu (2000) “On the Validity of the Likelihood Ratio and Maximum Likelihood Methods.”. {% %} Perold, André F. (2004) “The Capital Asset Pricing Model,” Journal of Economic Perspectives 18, 3–24. {% %} Perraillon, Marcelo Coca, Ya-Chen Tina Shih, & Ronald A. Thisted (2015) “Predicting the EQ-5D-3L Preference Index from the SF-12 Health Survey in a National US Sample: A Finite Mixture Approach,” Medical Decision Making 35, 888–901. {% Data of households. They also asked for subjective assessment of own risk attitude (“I am willing to take above-average risks” etc.) and related it to investments in stocks. Seems that they found some trivial (p. 136) and some nonintuitive (p. 131) results. %} Perraudin, William R.M. & Bent E. Sorensen (2000) “The Demand for Risky Assets: Sample Selection and Household Portfolios,” Journal of Econometrics 97, 117–144. {% Body length during adolescence (I think age 16) predicts future wage, and not body height during adulthood. %} Persico, Nicola, Andrew Postlewaite, & Dan Silverman (2004) “The Effect of Adolescence Experience on Labor Market Outcomes: The Case of Height,” Journal of Political Economy 112, 1019‑1053. {% History of term “ceteris paribus;” earliest use 1311 after Christ; so not used by Romans or Greecs themselves %} Persky, Joseph (1990) “Retrospectives: Ceteris Paribus,” Journal of Economic Perspectives 4 no. 2, 187–193. {% %} Pesendorfer, Wolfgang (2006) “Wolfgang Behavioral Economics Comes of Age: A Review Essay on Advances in Behavioral Economics,” Journal of Economic Literature 44, 712–721. {% %} Peski, Marcin (2011) “Prior Symmetry, Similarity-Based Reasoning, and Endogenous Categorization,” Journal of Economic Theory 146, 111–140. {% People who score bad on measurements of elementary numerical skills, are also subject to many confusions such as to interpreting numbers or percentages as probabilities; etc. In particular, if Bowl A contains 9 red beans and 91 white, and Bowl B contains 1 red bean and 9 white, they prefer to gamble on red from A because it “gives more chances to win” (ratio bias). A similar finding, called ratio bias, is in Kirkpatrick & Epstein (1992), and in Denes-Raj & Epstein (1994), as the authors indicate. They investigate how these effects are affected by numeracy. Also do Asian-disease-like questions with their usual weakness (20% died need not mean that 80% survived; there may be missing data etc.). Whereas their numeracy score predicts things, more general intelligence scores do not. (cognitive ability related to risk/ambiguity aversion) %} Peters, Ellen, Daniel Västfjäll, Paul Slovic, C.K. Mertz, Ketti Mazzocco, & Stephan Dickert (2006) “Numeracy and Decision Making,” Psychological Science 17, 407–413. {% %} Peters, Hans J.M. (1986) “Bargaining Game Theory.” Ph.D. dissertation, University of Nijmegen, Department of Mathematics. {% %} Peters, Hans J.M. (1986) “Simultaneity of Issues and Additivity in Bargaining,” Econometrica 54, 153–169. {% strength-of-preference representation: through stengths of prefs if one function is concave transform of other. %} Peters, Hans J.M. (1992) “A Criterion for Comparing Strength of Preference with an Application to Bargaining,” Operations Research 40, 1018–1022. {% %} Peters, Hans J.M. (1992) “Axiomatic Bargaining Theory.” Kluwer Academic Publishers, Dordrecht. {% This great paper analyzes Shalev’s model of loss aversion. It does not incorporate probability weighting. Note that the symbol used in this paper corresponds with 1 of Tversky & Kahneman (1992) and Wakker (2010, Ch. 8). So in the notation of this paper, >0 means loss aversion. As several authors have pointed out (Currim & Sarin 1989 p. 24 point ii), the Shalev model cannot accommodate utility being concave for gains and convex for losses. Despite this problem, this paper is still the best presently available in the literature to show what loss aversion means, because it considers variable reference points (the desirability of that latter was pointed out by Wakker 2010, p. 247, §8.8, end of Problem 1). Its conciseness and mathematical style may make it, unfortunately, hard to read for nonmathematicians. %} Peters, Hans J.M. (2012) “A Preference Foundation for Constant Loss Aversion” Journal of Mathematical Economics 48, 21–25. {% DOI 10.1007/978-3-662-46950-7; ISBN 978-3-662-46949-1; ISBN 978-3-662-46950-7 (eBook); %} Peters, Hans J.M. (2015) “Game Theory; A Multi-Leveled Approach” (2nd edn) Springer, Berlin. {% Consider the incomplete preference model of Dubra et al. (2004). Add a bad-outcome aversion axiom: after cancelling all the common worst outcomes with the same prob, the first one decides: the prospect assigning the biggest probability to it is dispreferred. It can be modeled by a set of utility functions that more and more overweigh the low outcome relative to the good one. That is, that go to the nonstandard function that at every lower outcome makes a jump down greater than any before, a sort of extreme lexicographic. %} Peters, Hans, Tim Schulteis & Dries Vermeulen (2010) “Generalized Stochastic Dominance and Bad Outcome Aversion,” Social Choice and Welfare 35, 285–290. {% %} Peters, Hans J.M. & Eric van Damme (1991) “Characterizing the Nash and Raiffa Bargaining Solutions by disagreement Point Axioms,” Mathematics of Operations Research 16, 447–461. {% %} Peters, Hans J.M. & Koos J. Vrieze (1987) “Surveys in Game Theory and Related Topics,” CWI-Tract 39, Center for Mathematics and Computer Science, Amsterdam. {% Show that Yaari’s (1969 result of first decision maker’s u being a concave transform of a second iff first’s certainty equivalents are always smaller, formulated by Yaari only for Euclidean spaces and, if I remember right, differentiability, can easily be extended to general outcomes. The main step in the proof is to show that a convex function on a nonconvex domain can be extended to a convex function on the convex hull of its domain. %} Peters, Hans J.M. & Peter P. Wakker (1987) “Convex Functions on Non-Convex Domains,” Economics Letters 22, 251–255. Link to paper
Peters, Hans J.M. & Peter P. Wakker (1990) “Independence of Irrelevant Alternatives and Revealed Group Preferences” (Extended abstract). In Tatsuro Ichiishi, Abraham Neyman, & Yair Tauman (eds.) Game Theory and Applications, 404–406, Academic Press, New York. Link to paper
Peters, Hans J.M. & Peter P. Wakker (1991) “Independence of Irrelevant Alternatives and Revealed Group Preferences,” Econometrica 59, 1787–1801. Reprinted in William Thomson (2010, ed.) “Bargaining and the Theory of Cooperative Games: John Nash and Beyond,” Ch. 4, Edward Elgar Publisher, Northampton, MA. Link to paper {% revealed preference; A follow-up paper with a simpler counterexample is John (1995, JET). %} Peters, Hans J.M. & Peter P. Wakker (1994) “WARP Does not Imply SARP for More than Two Commodities,” Journal of Economic Theory 62, 152–160. Link to paper
Peters, Hans J.M. & Peter P. Wakker (1996) “Cycle-Preserving Extension of Demand Functions to New Commodities,” Journal of Mathematical Economics 25, 281–290. Link to paper
Peters, Hans J.M. & Horst Zank (2005) “The Egalitarian Solution for Multichoice Games,” Annals of Operations Research 137, 399–409. {% Replicate Fehr-Tyran (2001) and argue that money illusion is less important, rather being a second-order effect. Fehr & Tyran (2014) argue that the authors misinterpret their data. %} Petersen, Luba & Abel Winn (2014) “Does Money Illusion Matter?: Comment,” American Economic Review 104, 1047–1062. {% %} Peterson, Daniel (2011) “Qeauty and the Books: A Response to Lewis’s Quantum Sleeping Beauty Problem,” Synthese 181, 367–374. {% statistics: c lassification in data analysis. %} Petit-Renaud, Simon & Thierry Denoeux (2004) “Nonparametric Regression Analysis of Uncertain and Imprecise Data Using Belief Functions,” International Journal of Approximate Reasoning 35, 1–28. {% Use hypothetical choice. Study relation between inverse-S and cognitive ability (cognitive ability related to likelihood insensitivity (= inverse-S) & inverse-S (= likelihood insensitivity) related to emotions). With affect-rich outcomes (voucher for romantic dinner) there is more likelihood insensitivity than with affect-poor outcomes (reduction of electricity bill). Numerosity (Berlin number task) also seems to reduce likelihood insensitivity (in re-appraisal task.). These results, however, seem to hold only for small probabilities, and not for large. To calculate probability weighting, they assume linear utility, which for moderate stakes is fine. Data-fitting is by minimizing quadratic distance. They confirm inverse S. %} Petrova, Dafina G., Joop van der Pligt, & Rocio Garcia-Retamero (2014) “Feeling the Numbers: On the Interplay between Risk, Affect, and Numeracy,” Journal of Behavioral Decision Making 27, 191–199. {% %} Pfanzagl, Johann (1959) “Die Axiomatischen Grundlagen einer Allgemeinen Theorie des Messens.” Physica-Verlag, Vienna. Elaborated in Pfanzagl, Johann (1968) “Theory of Measurement.” Physica-Verlag, Vienna. {% A marvelous paper, with mature and deep writing on measurement. Advanced results on the bisymmetry axiom, how that axiomatizes subjective expected utility etc. Everything is then restricted to two-outcome acts. For example, Theorem 1 considers bisymmetry, essentially giving SEU there (given reflexivity as explained later in the paper), but does not yet relate to uncertainty. Pfanzagl only uses topological connectedness, not top. separability, so immediately understood that top. separability can be dispensed with. This insight was lost for some time after, due to Debreu (1960) and Gorman (1968) and others who did assume topological separability, but it was rediscovered by Krantz et al. (1971), and was propagated by me and others. Theorem 2 considers bisymmetry (event-commutativity as Chew (1989) called it) for two-outcome acts with different events involved, characterizing that they have the same utility function so that it really is RDU-with-symmetry (SEU for fixed event but additivity of probability need not hold otherwise) when restricted to only binary acts that may relate to different events. Pp. 287-288 discuss what I consider most interesting, DUU, where Pfanzagl then essentially is giving Savage’s (1954) SEU for two states of nature, even for all binary acts. biseparable utility: p. 287 has it, but (see end of 3rd para) only for symmetric nonadditive measures and probability transformations, (w(p) = 1w(1p)), so that no rank-dependent restriction needs to be added. He calls w(p) subjective probability. binary prospects identify U and W: writes: “In spite of that, they permit us to derive all relevant results concerning the scale of utility.” Then he goes on to do biseparable utility for uncertainty, for the special case of a symmetric maybe nonadditive measure although he does not say this explicitly. P. 287 bottom goes on to do the same thing done before for probabilities, now doing it for an event. P. 288 gives all the axioms that axiomatize biseparable utility with a nonadditive symmetric measure. He does not write the model itself, but it is evident from replacing probabilities on the previous page by events. The bottom of the page shows that a violation of symmetry, discussed only for a fifty-fifty event, violates his axioms. Pfanzagl is overly pessimistic in claiming that the construction of utility then is impossible. Nowadays we know that comonotonic versions of axioms will still hold. Wakker & Deneffe (1996) showed that the construction of utility can still be done. P. 288 already describes the nice dynamic interpretation of bisymmetry if the events can be repeated independently that is also in Segal (1993, JME, “order indifference”), Luce (1988, JRU 1, Eqs. 22 and 23), and Luce (1998, JRU, “event commutativity”). Pp. 289-290 discuss constant absolute risk aversion (called consistency) and the crucial role of what is taken as a fixed or variable status quo (he uses this term status quo). There are several discussions of empirical and psychological studies, Mosteller & Nogee (1951), Stevens, etc. Theorem 3, p. 290, characterizes linear/exponential (CARA) family through constant absolute risk aversion. This was done before by Nagumo (1930 p. 78, stating sufficiency, but proof also stating necessity) and Hardy, Littlewood, & Pòlya (1934, Theorem 84, for log-power utility). P. 290: “the amount of money in front of the subject—not of the amount in his pocket.” Paper ends (p. 293) with the currently important warning that we, when studying utility, should be very aware of what initial wealth etc. is. %} Pfanzagl, Johann (1959) “A General Theory of Measurement—Applications to Utility,” Naval Research Logistics Quarterly 6, 283–294. {% Characterizes a functional as being a conditional expected value, with no utility involved (“linear utility”). %} Pfanzagl, Johann (1967) “Characterizations of Conditional Expectations,” Annals of Mathematical Statistics 38, 415–421. {% An elaborated version of his 1959 book, translated by himself, with help (also in content) by Volker Baumann and H. Huber. Download 7.23 Mb. Share with your friends:
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