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random incentive system: discusses that
Oct. 21, 1997: uses decision cost model, and not nonEU model, to explain deviations from EU, in context of random incentive system. Finds that incentives do not matter much for simple choices but do for complex ones. This result is not surprising, but it is useful to have it demonstrated clearly. I think, actually, that the underlying decision-cost model is not very useful here.
Decision time is taken as index for decision complexity. For low incentives, increased complexity gives less EV maximization (so less risk seeking I assume); then also more violations of RCLA. This shows that incentives do not just reduce noise, but can have systematic effects; a point emphasized much by the author.
For high incentives, no differences are found.
P. 1402: refs that find that EV explains much of decisions. For calculating decision costs, the paper takes EV as the correct model, as first approximation. The discussion on p. 1401-1402 is defensive. True that any other model assumed can be criticized, but so can EV be just as much.
The example on p. 1402 shows that satisfying preference axioms such as independence need not always be better than all else. This can be shown trivially by doing EU minimization (stoch. dom. then needs rediscussion). It is a trivial point rather than a good argument against the pragmatic principle of taking preference-condition optimization as index of goodness of decisions.
Concluding sentence: “The results of this experiment suggest that decision time is a potentially rich explanatory and dependent variable, and so should not be an omitted one.” %}

Wilcox, Nathaniel T. (1993) “Lottery Choice: Incentives, Complexity and Decision Time,” Economic Journal 103, 1397–1417.


{% %}

Wilcox, Nathaniel T. (2007) “Stochastically More Risk Averse: A Contextual Theory of Stochastic Discrete Choice under Risk,”


{% error theory for risky choice; pp. 200-201 point out that results about the core theory may depend on the error theory assumed. %}

Wilcox, Nathaniel T. (2008) “Stochastic Models for Binary Discrete Choice under Risk: A Critical Primer and Econometric Comparison.” In James C. Cox & Glenn W. Harrison, (eds.) Risk Aversion in Experiments; Research in Experimental Economics 12, 197–292, Emerald, Bingley.


{% Usual probabilistic choice theories do not preserve the more risk averse than relation. This paper proposes a probabilistic choice theory that does, and shows that it fits data well in the Hey & Orme (1994) data set. %}

Wilcox Nathaniel T. (2011) “ ‘Stochastically More Risk Averse:’ A Contextual Theory of Stochastic Discrete Choice under Risk,” Journal of Econometrics 162, 89–104.


{% probability communication: Seems to write that pie charts (as area of probability wheel) are among the most criticized ways to display numerical results. Seems that people can’t judge angles well. %}

Wilkinson, Leland (2005) “The Grammar of Graphics;” 2nd edn. Springer, Berlin.


{% %}

Wilkinson, Nick (2007) “An Introduction to Behavioral Economics A Guide for Students.” Palgrave, The MacMillan Press, London.


{% Good reference on Dirichlet priors; i.e., the multinomial versions of beta priors. %}

Wilks, Samuel S. (1962) “Mathematical Statistics.” Wiley, New York


{% %}

Willard, Stephen (1970) “General Topology.” Addison Wesley, Reading MA.


{% Generalizes Scotts method for solving linear inequalities. Shows that a finite system of axioms cannot do in general. I think that KLST refer to Suppes for such a result but dont remember details now. %}

Wille, Uta (2000) “Linear Measurement Models—Axiomatizations and Axiomatizability,” Journal of Mathematical Psychology 44, 617–650.


{% %}

Willems, Edwin P. (1969) “Risk is a Value,” Psychological Reports 24, 81–82.


{% On compromise effect and other things. %}

Willemsen, Martijn C. (2002) “Explaining Asymmetries in Preference Elicitation: The Role of Negative Attributes in Judgment and Choice,” Ph.D. dissertation, Eindhoven University.


{% Upward and downward matching give different results. Give further references, for example, to Massaro (1975). %}

Willemsen, Martijn C. & Gideon Keren (2002) “The Meaning of Indifference in Choice Behavior: Asymmetries in Adjustments Embodied in Matching,” Eindhoven University.


{% Seems to use the Tradeoff method %}

Willer, Dave, Dept. of Sociology, University of South Carolina


{% P. 577 uses the term pure risk for loss prospects, and speculative risks for mixed prospects, citing earlier insurance literature on these terms.
P. 578 column 1-2 suggests inertia for what leads to loss aversion.
Seems to find risk seeking for losses;
N = 51. Hypothetical choice. Paper chooses matching. P. 581 explains some that pilots had considered choice list (“multiple choices”) also. They were not systematically different, but, as the author points out, crude.
Did not do pure translation of prospects.
P. 578 mentions inertia factor.
Risk averse for gains, risk seeking for losses: p. 582 last para finds, to the surprise of the authors, risk seeking for loss gambles.
P. 584 finds correlation 0.39 between risk attitude for losses and for mixed prospects. Suggests a bit that some reflection, although loss aversion intervenes.
P. 585: finds no correlation between risk attitude questions and insurance attitude questions.
P. 585: insurance is about losses. %}

Williams, C. Arthur Jr. (1966) “Attitudes toward Speculative Risks as an Indicator of Attitudes toward Pure-Risk,” Journal of Risk and Insurance 33, 577–586.


{% present value; DC = stationarity; p. 855 bottom discussion of Axiom IV.
Dutch book: do it in intertemporal context, with Axiom III (marginal consistency; p. 853) the additivity axiom. Use term temporal consistency for Koopmans stationarity. Thus, they axiomatize net present value, i.e., discounted value, with however the discount factor subjective. %}

Williams, C. Arthur Jr. & J.I. Nassar (1966) “Financial Measurement of Capital Investments,” Management Science 12, 851–864.


{% Does what its title says. %}

Williams, Lawrence E. & John A. Bargh (2008) “Experiencing Physical Warmth Promotes Interpersonal Warmth,” Science 322, 24 Oct, 606–607.


{% inverse-S: people overvalue longshots and undervalue favorites in horse-betting. Suggest its a result of adverse selection faced by bookmakers, regarding bettors with superior information. %}

Williams, Leighton V. & David Paton (1997) “Why is there a Favourite-Longshot Bias in British Racetrack Betting Markets?,” Economic Journal 107, 150–158.


{% Aangeraden door Voorbraken, leerling Jan Bergstra %}

Williams, Peter M. (1976) “Indeterminate Probabilities.” In Marian Przelecki, Klemens Szaniawski, & Ryszard Wojcicki (eds.) Formal Methods in the Methodology of Empirical Sciences, 229–246, Ossolineum and Reidel, Dordrecht.


{% a.o. Dempsters rule of combination %}

Williams, Peter M. (1978) “On a New Theory of Epistemic Probability;” Review of Shafer, Glenn (1976) “A Mathematical Theory of Evidence.” Princeton University Press, Princeton NJ, British Journal for the Philosophy of Science 29, 74–85.


{% foundations of probability %}

Williamson, Jon (2005) “Bayesian Nets and Causality. Philosophical and Computational Foundations.” Oxford University Press, Oxford.


{% foundations of statistics %}

Williamson, Jon (2010) “In Defence of Objective Bayesianism.” Oxford University Press, Oxford.


{% foundations of statistics %}

Williamson, Jon (2011) “Objective Bayesianism, Bayesian Conditionalisation and Voluntarism,” Synthese 178, 67–85.


{% value of information, in the LaValle sense of increase in expected utility, is related to an index of concavity of utility. %}

Willinger, Marc (1989) “Risk Aversion and the Value of Information,” Journal of Risk and Insurance 56, 320–328.


{% time preference: a poets way of, first, defining time discounting, and then negating it, suggesting that time is not ordered linearly;
Tijd en ruimte
Het perspectief, gezichtsbedrog
voor mens en dier, of beter nog:
gezichtsverlies,
maakt alles kleiner wat verdwijnt,
zodat de ruimte kleiner schijnt
dan ze echt is.

Had ook de tijd maar perspectief:


steeds kleiner werden elke grief,
en elk verdriet,
tot stipjes aan de horizon
waar niemand meer om huilen kon,
maar t gaat niet zo.

Tijd is een weg in een groot woud


dat iedereen gevangen houdt
in schemering,
tijd is een pad waar je verdwaalt
en door jezelf wordt ingehaald,
een heksenkring. %}

Wilmink, Willem (19??)


{% foundations of quantum mechanics: brings together objective probabilities in quantum mechanics and subjective, decision-based, probabilities. %}

Wilson, Alastair (2013) “Objective Probability in Everettian Quantum Mechanics,” British Journal for the Philosophy of Science 64, 709–737.


{% anonymity protection %}

Wilson, Edward O. (1992) “The Diversity of Life.” Cambridge, MA. (Later edn. 1994, Penguin, London.)


{% Book on ants %}

Wilson, Edward O. (1979) “On Human Nature.” Bantam, New York.


{% Investigate loss aversion if it concerns payments for others. It exists if just evaluating gains and losses of others, but may disappear if social and environmental contexts are added. %}

Wilson, Robyn S., Joseph L. Arvai, & Hal R. Arkes (2008) “My Loss Is Your Loss … Sometimes: Loss Aversion and the Effect of Motivational Biases,” Risk Analysis 28, 929–938.


{% Mental contamination is, roughly, making errors in judgments. It is a very broad domain. The authors explicitly exclude one special class, incorrect application of rules such as in mathematical mistakes. What remains is still very broad. Figure 1 mentions four requirements to avoid mental contamination if unwanted mental processing is triggered: 1. Awareness of unwanted processing 2. Motivation to correct 3. Awareness of the direction and magnitude of the bias 4. Ability to correct. They discuss the literature through these four steps. %}

Wilson, Timothy D. & Nancy Brekke (1994) “Mental Contamination and Mental Correction: Unwanted Influences on Judgments and Evaluations,” Psychological Bulletin 116, 117–142.


{% intuitive versus analytical decisions; Students can choose between different jams and different courses to enrol. Some are encouraged to evaluate attributes, others are not. The latter take decisions more in agreement with recommendations of experts (taste specialists in the first case, and more experienced students or teachers in the second case). It suggests that the deliberate thinking only worsens the decision relative to intuitive deciding.
Pp. 182-183 gives nice list of explanations: verbalizing can worsen nonverbal memories, and deliberate thinking can worsen natural adaptive systems (as for me when typing where the fingers find the letters without me being able to state their places verbally). This paper is alternative to Dijksterhuis et al. (2006), with the criterion for goodness not self-reported degree of satisfaction, but extraneous. %}

Wilson, Timothy D. & Jonathan W. Schooler (1991) “Thinking too Much: Introspection Can Reduce the Quality of Preferences and Decisions,” Journal of Personality and Social Psychology 60, 181–192.


{% Find that verbal expressions of probability are more information-sensitive and to better predict betting than numerical probabilities, maybe because numerical probabilities may invoke ad hoc rules. %}

Windschitl, Paul D. & Gary L. Wells (1996) “Measuring Psychological Uncertainty: Verbal versus Numerical Methods,” Journal of Experimental Psychology: Applied 2, 343–364.


{% This book seems to be a classic on statistics in psychology and biology.
Chapter 3 seems to discuss that t-test is still OK if the distribution does not deviate much from normality, citing Box (1954). %}

Winer, Ben J., Donald R. Brown, & Kenneth M. Michels (1962) “Statistical Principles in Experimental Design.” McGraw-Hill, inc., New York. (3rd edn. 1991.)


{% probability elicitation;
inverse-S: p. 792 top finds it, with overestimation of low probabilities and underestimation of high. Seems that people improve with training.
P. 785: people had to assess both density function and distribution function. They found the former easier, and did not understand well how the two are related. %}

Winkler, Robert L. (1967) “The Assessment of Prior Distributions in Bayesian Analysis,” Journal of the American Statistical Association 62, 776–800.


{% probability elicitation %}

Winkler, Robert L. (1967) “The Quantification of Judgment: Some Methodological Suggestions,” Journal of the American Statistical Association 62, 1105–1120.


{% probability elicitation %}

Winkler, Robert L. (1969) “Scoring Rules and the Evaluation of Probability Assessors,” Journal of the American Statistical Association 64, 1073–1078.


{% probability elicitation %}

Winkler, Robert L. (1971) “Probabilistic Prediction: Some Experimental Results,” Journal of the American Statistical Association 86, 675–685.


{% simple decision analysis cases using EU: Example 5.10, gives a nice didactical illustration with all that is there being properly balanced (with collecting info analyzed in §6.4 and §6.5). It is a simplified version of an actual analysis done by Grayson (1960, 1979). %}

Winkler, Robert L. (1972) “An Introduction to Bayesian Inference and Decision Theory.” Holt, Rinehart and Winston, New York.


{% probability elicitation %}

Winkler, Robert L. (1986) “On “Good Probability Appraisers” .” In Prem K. Goel & Arnold Zellner (eds.) Bayesian Inference and Decision Techniques. Elsevier, Amsterdam.


{% Argues that ambiguity should not be modeled through nonadditive probabilities, but rather should be incorporated in utility. P. 289: “Although ambiguity about probabilities is the ambiguity of concern in this article, I would argue that the influence of this ambiguity on decision-making behavior generally operates through preferences. Thus, attention should be focused on the preference side of modeling rather than on probabilities. The preference side involves the consequences in the decision model and the value function or utility function over those consequences.”
P. 295: “M.B.A. students studying decision analysis are often quite surprised at how risk averse their assessed utility functions are and at how much they must give up in expected value to accommodate their assessed risk attitudes. This realization often leads them to move towards less risk-averse positions, and the same might happen with respect to ambiguity.” %}

Winkler, Robert L. (1991) “Ambiguity, Probability, Preference, and Decision Analysis,” Journal of Risk and Uncertainty 4, 285–297.


{% proper scoring rules: without aiming to be complete, this paper gives a survey of proper scoring rules and some of their properties in the first 26 pages. §5, for instance, explains that scores obtained for different events are not directly comparable. The rest is comments and discussions. %}

Winkler, Robert L. (1996) “Scoring Rules and the Evaluation of Probabilities,” Test 5, 1–60.


{% probability elicitation;
Consider what happens with subjective probabilities when elicited through quadratic scoring rule if utility is nonlinear, but assuming expected utility. For the convex (“risk-seeking”) U(x) = x2, for subjective p = 0.33 and smaller, it is best to report r=0. Symmetrically, for subjective p = 0.67 and higher, it is optimal to report r=1. Between p = 0.33 and p = 0.67, the optimal reply is linear, being r = 0.5 at p = 0.5. For the concave (“risk-averse”) U(x) = 1  ex, the reported optimal probability r is an inverse-S curve of the “true” subjective probability p, illustated in Figure 3 p. 146, that propect-theory advocates will like. (inverse-S) %}

Winkler, Robert L. & Allan H. Murphy (1970) “Nonlinear Utility and the Probability Score,” Journal of Applied Meteorology 9, 143–148.


{% proper scoring rules %}

Winkler, Robert L. & Roy M. Poses (1994) “Evaluating and Combining Physicians Probabilities of Survival in an Intensitive Care Unit,” Management Science 39, 1526–1543.


{% %}

Winkler, Robert L. & James E. Smith (2004) “On Uncertainty in Medical Testing,” Medical Decision Making 24, 654–658.


{% %}

Winston, Gordon C. (1980) “Addiction and Backsliding: A Theory of Compulsive Consumption,” Journal of Economic Behavior and Organization 1, 295–324.


{% Z&Z; McFadden (AER 2006, p. 20, says that N = 1996 %}

Winter, Joachim, Rowilma Balza, Frank Caro, Florian Heiss, Byung-Hill Jun, Rosa L. Matzkin, & Daniel McFadden (2006) “Medicare Prescription Drug Coverage: Consumer Information and Preferences,” Proceedings of the National Academy of Sciences 103, 7929–7934.


{% Shows that people in bad health find life-prolonging treatment more acceptable, and explain it through diminishing sensitivity of prospect theory. %}

Winter, Laraine & Barbara Parker (2007) “Current Health and Preferences for Life-Prolonging Treatments: An Application of Prospect Theory to End-of-Life Decision Making,” Social Science & Medicine 65, 1696–1707.


{% probability communication: diverse sample of U.S. parents and guardians (n = 407), either standard information about influenza vaccines or risk communication using absolute and incremental risk formats. Participants randomized to the risk communication condition combined with the values clarification interface were more likely to indicate intentions to vaccinate (β = 2.10, t(399) = 2.63, p < 0.01). %}

Witteman, Holly O., Selma Chipenda Dansokho, Nicole Exe, Audrey Dupuis, Thierry Provencher, & Brian J. Zikmund-Fisher (2015) “Risk Communication, Values Clarification, and Vaccination Decisions,” Risk Analysis 35, 1801–1819.


{% Study loss aversion and utility curvature for qualitative health states, subsequently quantified in a nontrivial manner. They find loss aversion confirmed, but linear iso S-shaped utility. %}

Wittenberg, Eve, Eric P. Winer, & Jane C. Weeks (2003) “Empirical Support for Prospect Theory among Health State Valuations of Advanced Cancer Patients,” Massachussetts General Hospital, Harvard Medical School, Boston, MA.


{% Seems to say: “The procedure of induction consists in accepting as true the simplest law that can be recopnciled with our experiences.” 6.363 %}

Wittgenstein, Ludwig (1922) “Tractatus Logico Philosophicus.” Routledge, London.


{% conservation of influence: through illusion of control. %}

Wohl, Michael J.A. & Michael E. Enzle (2002) “The Deployment of Personal Luck: Illusory Control in Games of Pure Chance,” Personality and Social Psychology Bulletin 28, 1388–1397.


{% The Wold three parts were recommended to me as good surveys by Ward Edwards on September 15, 1997. %}

Wold, Herman O. (1943) “A Synthesis of Pure Demand Analysis. Part I,” Skandinavisk Aktuarietidskrift 26, 85–118.


{% Cardinal utility is measured by “unit of measurement” method. That is, if x and y are two commodity bundles, then a “unit of measurement,” i.e., another commodity bundle u, is chosen, and real numbers s,t, such that su~x, tu~y. Then s/t is a measure for the utility proportion of x and y. Under homotheticity this is independent of the choice of unit of measurement.
First to derive existence of utility function through certainty equivalents in Theorem I, based on a continuity-like axiom V. (Before existence of utility function was simply assumed.)
Ref aan me gegeven door Karl Vind op 10 maart 1994. %}

Wold, Herman O. (1943) “A Synthesis of Pure Demand Analysis. Part II,” Skandinavisk Aktuarietidskrift 26, 220–263.


{% %}

Wold, Herman O. (1944) “A Synthesis of Pure Demand Analysis. Part III,” Skandinavisk Aktuarietidskrift 27, 69–120.


{% Note itself does not do more than show that repeated choice is a different thing than one-shot. Wolds rejoinder is more interesting. It points out that if EU is ot be applied only in single-shot then it is very hard to test empirically. %}

Wold, Herman O. (1952) “Ordinal Preference or Cardinal Utility?” (with discussion), Econometrica 20, 661–664.


{% This paper addresses the intriguing question of whether we can have utility over past events (even though we cannot influence them anymore) and, then, how much we discount those. Unfortunately, the model used is out of the blue and not well defined. An interest point is that, although we cnanot influence the past, we can still have uncertainty about it. Under nonEU this can probably be used to derive past utility from revealed preference through choices of receiving info about the past or not. Most examples in this paper concern another phenomenon: past events influence current utility instrumentally. But that is a different point. %}

Wolf, Charles (1970) “The Present Value of the Past,” Journal of Political Economy 78, 783–792.


{% utility elicitation: of vNM utility function for money;
decreasing ARA/increasing RRA: they studied one participant, a dealer in U.S. government securities. First they used hypothetical gamble questions, and also discussed preference axioms, with the dealer. The dealer said he wanted to satisfy constant RRA. (Maybe he did that only because it was easy for his way of thinking?) After these hypothetical choices, they studied his real bids. In his real bids he was more risk averse. There, however, seem to be many distorting factors. Evidence supported increasing RRA, but not significantly. %}

Wolf, Charles & Larry Pohlman (1983) “The Recovery of Risk Preferences from Actual Choices,” Econometrica 51, 843–850.


{% ratio bias. Describe denominator neglect in probability estimation of joint events, and ways to reduce it, done in an experiment. %}

Wolfe, Christopher R. & Valerie F. Reyna (2010) “Semantic Coherence and Fallacies in Estimating Joint Probabilities,” Journal of Behavioral Decision Making 23, 203–223.


{% Chickens like less one whole kernel of corn than when it is divided into four pieces. %}

Wolfe, J.B. & M.D. Kaplon (1941) “Effect of Amount of Reward and Consummative Activity on Learning in Chickens,” Journal of Comparative Psychology31, 353–361.


{% %}

Wolfers, Justin & Eric Zitzewitz (2004) “Prediction Markets,” Journal of Economic Perspective 18, 107–126.


{% SG higher than others: SG gives higher utility than TTO. %}

Wolfson, Allan D., John C. Sinclair, Claire Bombardier, & Allison McGreer (1982) “Preference Measurements for Functional Status in Stroke Patients: Inter-Rater and Inter-Technique Comparisons.” In Robert L. Kane & Rosalie A. Kane (eds.) Values and Long-Term Care, Lexicon Books, Lexicon, MA.


{% Treats topics such as Cournot competition while explaining the formal assumptions such as strict concavity of the profit function. %}

Wolfstetter, Elmar (1999) “Topics in Microeconomics.” Cambridge University Press, Cambridge.


{% utility = representational: argues for importance of emotions and psychological inputs in economics, giving many citations. There are no concrete directions for predictions.
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