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## Curvature of the probability weighting function (1996)

Venue: | Management Science |

Citations: | 290 - 5 self |

### Citations

6311 | Prospect theory: an analysis of decisions under risk, Econometrica 47
- Kahneman, Tversky
- 1979
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Citation Context ... the choice proportions in the two 1 Data for this survey were collected in collaboration with Amos Tversky. PROBABILITY WEIGHTING FUNCTION 131 FIG. 1. Weighting function proposed in Prospect Theory (=-=Kahneman & Tversky, 1979-=-), which is not defined near the end points. The key properties are the overweighting of small probability and the underweighting of large probability. problems is statistically significant by McNemar... |

1717 | Advances in prospect theory: Cumulative representation of uncertainity.
- Tversky, Kahneman
- 1992
(Show Context)
Citation Context ...gh probability. Weighting functions consistent with the survey data are shown in Fig. 2; empirical support for this shape appeared in three recent choice studies (Camerer & Ho, 1994; Hartinger, 1998; =-=Tversky & Kahneman, 1992-=-; Wu & Gonzalez, 1996). The general question studied in this paper is how the psychophysics of probability influences decision making under risk. In turn, an understanding of the probability weighting... |

1468 | The EM Algorithm and Extensions - McLachlan, Krishnan - 1997 |

683 | Rational choice and the framing of decisions
- Tversky, Kahneman
- 1986
(Show Context)
Citation Context ...n of the model would lead to predicted violations of stochastic dominance.2 Violations of stochastic dominance are difficult to observe empirically unless the stochastic dominance is not transparent (=-=Tversky & Kahneman, 1986-=-; Birnbaum, 1997; Leland, 1998). To avoid predictions of transparent stochastic dominance violations, Kahneman and Tversky proposed a number of editing operations. Here we consider only the case of tw... |

681 |
Nonlinear regression.
- Seber, Wild
- 1989
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Citation Context ...RE and PRE-EU shows the contribution of estimating the extra two weighting function parameters relative to fixing both parameters to 1. least squares estimates are the maximum likelihood estimates11 (=-=Seber & Wild, 1989-=-). The error for this estimation procedure was on the CE scale. Table 3 also presents the proportion reduction in sum of squared error relative to the simple grand mean model and the proportion reduct... |

607 | The psychology of control.
- Langer
- 1983
(Show Context)
Citation Context ...a person may prefer a lottery in which she is PROBABILITY WEIGHTING FUNCTION 139 able to select her own numbers to one in which numbers are assigned to her (such as in the illusion of control work by =-=Langer, 1975-=-). Note that we interpret the illusion of control as due to the probability weighting function rather than due to differences in subjective probability or the value function. In sum, there appear to b... |

571 |
A theory of Anticipated Utility”,
- Quiggin
- 1982
(Show Context)
Citation Context ...pplies because the weight attached to an outcome (w(p) for the higher outcome and 1 2 w(p) for the lower outcome) depends on the rank of that outcome with respect to other outcomes in the gamble (see =-=Quiggin, 1982-=-; Yaari, 1987; Segal, 1989; Wakker, 1989, 1994). Note that Eq. (2) is, after algebraic rearrangement, identical to Eq. (1). One advantage of the rank-dependent approach is that Eq. (2) is easily gener... |

562 |
Lectures on functional equations and their applications,
- Aczel
- 1966
(Show Context)
Citation Context ...f (z) iff (A3) f (tx) 1 f (ty) 5 f (tz). If this functional equation holds for all t . 0, then under some mild continuity conditions, the only nontrivial solution for monotonic f is f (x) 5 axb (A4) (=-=Aczel, 1966-=-). For a discussion of conditions needed for the continuity of w in the context of rank-dependent models see Wakker (1994). Our method of proof is to use CPT with outcomes restricted to one side of th... |

461 |
Regret in decision making under uncertainty.
- Bell
- 1982
(Show Context)
Citation Context ... w (as suggested by Luce, Mellers, and Chang, 1993, and by Hey & Orme, 1994) and a linear weighting function w(p) 5 (b 2 a)p 1 a, with 0 , a , b , 1, end points w(0) 5 0 and w(1) 5 1 (as suggested by =-=Bell, 1985-=-). GOALS OF THE PRESENT STUDY Empirical estimation of the weighting function is not straightforward. In order to assess the shape of the weighting function with standard, nonlinear regression methods ... |

373 |
Measuring utility by a single-response sequential method.
- Becker, DeGroot, et al.
- 2012
(Show Context)
Citation Context ...nts (5 female).5 All participants were graduate students in psychology. They were paid $50 for participating in four 1-h sessions. In addition, an incentive compatible elicitation procedure was used (=-=Becker, DeGroot, & Marschak, 1964-=-); participants’ certainty equivalents were entered into a subsequent auction. In order to have an adequate assessment of an individual’s value and weighting function, we opted for a traditional psych... |

305 | Preference and belief: ambiguity and competence in choice under uncertainty,
- Heath, Tversky
- 1991
(Show Context)
Citation Context ...ve than chance domain 2 iff w1(p) $ w2(p) for all p. For example, a person may prefer to bet on sporting events rather than on the outcomes of political elections holding constant the chance winning (=-=Heath & Tversky, 1991-=-), or a person may prefer a lottery in which she is PROBABILITY WEIGHTING FUNCTION 139 able to select her own numbers to one in which numbers are assigned to her (such as in the illusion of control wo... |

290 |
The Probability Weighting Function”,
- Prelec
- 1998
(Show Context)
Citation Context ...range (.01, .99). Instead, specially designed studies testing the key property of the linear in log odds form (see Appendix) and the key property of the Prelec form (compound invariance as defined in =-=Prelec, 1998-=-) will have to be conPROBABILITY WEIGHTING FUNCTION 141 ducted.4 These functions can also be compared on how they predict responses for extremely small probabilities such as .00001. Note that unless d... |

276 |
Support Theory: A Nonextensional Representation of Subjective Probability,”
- Tversky, Koehler
- 1994
(Show Context)
Citation Context ...sitivity unifies under one explanatory umbrella the curvature of the weighting function, the curvature of the value function, and the subadditivity of probability judgments (Tversky & Kahneman, 1992; =-=Tversky & Koehler, 1994-=-). We see this paper as making three contributions to the psychological understanding of the probability weighting function: methodological, empirical, and theoretical. First, a new nonparametric algo... |

263 | The theory of decision making. - Edwards - 1954 |

230 |
The dual theory of choice under risk,
- Yaari
- 1987
(Show Context)
Citation Context ....50, .75, .95, .99}. There are two problems with their analyses. First, the analysis assumes a linear value function. Even though ‘‘duals’’ to expected utility with linear v have been proposed (e.g., =-=Yaari, 1987-=-; Weibull, 1982) and one of the early resolutions to the St. Petersburg paradox used nonlinear w and linear v (see Arrow, 1951, for a discussion), a nonlinear utility function typically provides a bet... |

229 | Tools for Statistical Inference, Methods for the Exploration of Posterior Distributions and Likelihood Functions. Springer-Verlag, 2nd edition - Tanner - 1993 |

228 |
Investigating generalizations of expected utility theory using experimental data.
- JD, Orme
- 1994
(Show Context)
Citation Context ...proximately two-thirds the subjects. Further, some simple functional forms for w can be rejected on the basis of existing data, e.g., a power w (as suggested by Luce, Mellers, and Chang, 1993, and by =-=Hey & Orme, 1994-=-) and a linear weighting function w(p) 5 (b 2 a)p 1 a, with 0 , a , b , 1, end points w(0) 5 0 and w(1) 5 1 (as suggested by Bell, 1985). GOALS OF THE PRESENT STUDY Empirical estimation of the weighti... |

223 | Transformation and Weighting in Regression, - Carroll, Ruppert - 1988 |

187 | Weighing risk and uncertainty, - Tversky, Fox - 1995 |

185 |
Generalized Expected Utility Theory: The Rank Dependent Model.
- Quiggin
- 1993
(Show Context)
Citation Context ...ing function, and for this example X 5 100, Y 5 25, and p 5 .50. More recently, Tversky and Kahneman (1992) generalized prospect theory using a rank-dependent, or cumulative, representation (see also =-=Quiggin, 1993-=-; Luce & Fishburn, 1991, 1995; Starmer & Sugden, 1989; Wakker & Tversky, 1993). Intuitively, cumulative prospect theory (CPT) generalizes the idea of the editing rule exhibited in Eq. (1) to gambles w... |

183 | Parameter-free elicitation of utility and probability weighting functions.
- Abdellaoui, M
- 2000
(Show Context)
Citation Context ...ual subjects were identified. The results for the median data add to a growing body of evidence that concave value and inverse-S-shaped weighting functions appear to fit median data quite well (e.g., =-=Abdellaoui, 1998-=-; Camerer & Ho, 1994; Tversky & Kahneman, 1992; Wu & Gonzalez, 1996, 1998). Moreover, our analyses showed that a one-parameter weighting function and a one-parameter value function (power) provide an ... |

170 | Between Hope and Fear: The Psychology of Risk”, - Lopes - 1987 |

140 |
Anomalies: Parimutuel betting markets: Racetracks and lotteries.
- Thaler, Ziemba
- 1988
(Show Context)
Citation Context ...eighting functions when gambling in their domain of expertise: the efficiency of parimutuel betting markets suggests that many racetrack betters are sensitive to small differences in odds (see, e.g., =-=Thaler & Ziemba, 1988-=-), and a study of options traders found that the median options trader is an expected value maximizer and thus shows equal sensitivity throughout the probability interval (Fox, Rogers, & Tversky, 1996... |

126 |
The problem of inference from curves based on group data.
- Estes
- 1956
(Show Context)
Citation Context ...elevation. If there is substantial individual variability, then some of the properties that have been observed in previous studies at the aggregate level may not hold at the level of individuals (see =-=Estes, 1956-=-, for a related discussion). In light of these issues we conducted a new study that permits nonparametric estimation of an individual’s value function and weighting function under 4 The critical prope... |

121 |
An axiomatization of cumulative prospect theory.
- Wakker, Tversky
- 1993
(Show Context)
Citation Context ...e recently, Tversky and Kahneman (1992) generalized prospect theory using a rank-dependent, or cumulative, representation (see also Quiggin, 1993; Luce & Fishburn, 1991, 1995; Starmer & Sugden, 1989; =-=Wakker & Tversky, 1993-=-). Intuitively, cumulative prospect theory (CPT) generalizes the idea of the editing rule exhibited in Eq. (1) to gambles with an arbitrary number of outcomes. Thus, cumulative prospect theory does no... |

118 | The New S Language.
- BECKER, CHAMBERS, et al.
- 1988
(Show Context)
Citation Context ...weighted, nonlinear least squares algorithm. 4. If an optimum is found, then stop; otherwise, increment iteration counter i and repeat. The algorithm was implemented in the statistical package Splus (=-=Becker, Chambers, & Wilks, 1988-=-) and made use of the package’s nonlinear least squares algorithm as well as its interpolation algorithm. We used linear interpolation in Step 1. The nonparametric algorithm did not impose monotonicit... |

114 |
Violations of the Betweenness Axiom and Nonlinearity in Probability.
- Camerer, Ho
- 1994
(Show Context)
Citation Context ...for low probability and convex for high probability. Weighting functions consistent with the survey data are shown in Fig. 2; empirical support for this shape appeared in three recent choice studies (=-=Camerer & Ho, 1994-=-; Hartinger, 1998; Tversky & Kahneman, 1992; Wu & Gonzalez, 1996). The general question studied in this paper is how the psychophysics of probability influences decision making under risk. In turn, an... |

101 |
Rank- and sign-dependent linear utility models for finite first-order gambles.
- Luce, Fishburn
- 1991
(Show Context)
Citation Context ...nd for this example X 5 100, Y 5 25, and p 5 .50. More recently, Tversky and Kahneman (1992) generalized prospect theory using a rank-dependent, or cumulative, representation (see also Quiggin, 1993; =-=Luce & Fishburn, 1991-=-, 1995; Starmer & Sugden, 1989; Wakker & Tversky, 1993). Intuitively, cumulative prospect theory (CPT) generalizes the idea of the editing rule exhibited in Eq. (1) to gambles with an arbitrary number... |

98 | Eliciting von NeumannMorgenstern Utilities when Probabilities Are Distorted or Unknown". - Wakker, Deneffe - 1996 |

90 | Risk attitudes and decision weights,
- Tversky, Wakker
- 1995
(Show Context)
Citation Context ...ne common consequence to another). [For details on how generalizations of these effects relate to the probability weighting function see Prelec (1998) and Wu & Gonzalez (1998), respectively (see also =-=Tversky & Wakker, 1995-=-).] The properties of the weighting function identified by Kahneman and Tversky included overweighting of small probabilities, underweighting of large probabilities, and subcertainty (i.e., the sum of... |

88 |
Alternative Approaches to the Theory of Choice in Risk-Taking Situations.
- Arrow
- 1951
(Show Context)
Citation Context ...ugh ‘‘duals’’ to expected utility with linear v have been proposed (e.g., Yaari, 1987; Weibull, 1982) and one of the early resolutions to the St. Petersburg paradox used nonlinear w and linear v (see =-=Arrow, 1951-=-, for a discussion), a nonlinear utility function typically provides a better fit for both risk and nonrisk domains (e.g., Fishburn & Kochenberger, 1979; Galanter & Pliner, 1974; Parker & Schneider, 1... |

87 |
Separating marginal utility and probabilistic risk aversion’, Theory and Decision
- Wakker
- 1994
(Show Context)
Citation Context ...cts was .95, and the lowest R2 (Subject 8) was .75. Subcertainty Recall that subcertainty is defined as w(p) 1 w(1 2 p) , 1, and it can be interpreted as a measure of probabilistic risk aversion (see =-=Wakker, 1994-=-). When w(p) 1 w(1 2 p) is substantially less than 1, the individual tends to avoid risk, whereas when w(p) 1 w(1 2 p) exceeds 1, the individual tends to embrace risk. Subcertainty is related to the e... |

83 |
Foundations of measurement (Vol.
- Krantz, Luce, et al.
- 1971
(Show Context)
Citation Context ...posite goal of specifying a functional form on w independent of the utility function. On the outcomes, this preference condition resembles the Thomsen condition used in additive conjoint measurement (=-=Krantz, Luce, Suppes, & Tversky, 1971-=-). Loosely speaking, the present condition can be interpreted as the Thomsen condition applied to outcomes with an additional restriction imposed on probabilities. The preference condition for the lin... |

79 | Ambiguity aversion and comparative ignorance,
- Fox, Tversky
- 1995
(Show Context)
Citation Context ...ry trial, whereas the same person may not have much expertise about football and would not be able to discriminate subtle differences in gambles based on point spreads (see Heath & Tversky, 1991, and =-=Fox & Tversky, 1995-=-, for a related point). An analogous intrapersonal comparison can be made for attractiveness. A person may find one chance domain more attractive than another, as in the comparison between selecting o... |

77 |
Contrasting rational and psychological analyses of political choice.
- Quattrone, Tversky
- 1988
(Show Context)
Citation Context ...tantial than improving from 30 to 35%. In both of these examples the impact of additional probability depends on whether it is added to a small, medium, or large probability (for related examples see =-=Quattrone & Tversky, 1988-=-). We collected survey data as a preliminary test of these intuitions.1 Fifty-six undergraduates were given the following question: You have two lotteries to win $250. One offers a 5% chance to win th... |

72 |
Two-piece von Neumann-Morgenstern utility functions.
- Fishburn, Kochenberger
- 1979
(Show Context)
Citation Context ... to the St. Petersburg paradox used nonlinear w and linear v (see Arrow, 1951, for a discussion), a nonlinear utility function typically provides a better fit for both risk and nonrisk domains (e.g., =-=Fishburn & Kochenberger, 1979-=-; Galanter & Pliner, 1974; Parker & Schneider, 1988; Tversky & Kahneman, 1992). Second, even if Preston and Baratta had used a nonlinear v they would have been unable to extract a unique estimate of t... |

72 | A belief-based account of decision under uncertainty. - Fox, Tversky - 1998 |

67 | Expression theory and the preference reversal phenomena. - Goldstein, Einhorn - 1987 |

63 |
Option traders exhibit subadditive decision weights,
- Fox, Rogers, et al.
- 1996
(Show Context)
Citation Context ... e.g., Thaler & Ziemba, 1988), and a study of options traders found that the median options trader is an expected value maximizer and thus shows equal sensitivity throughout the probability interval (=-=Fox, Rogers, & Tversky, 1996-=-). Discriminability could also be defined intrapersonally, e.g., an option trader may exhibit more discriminability for gambles based on options trading rather than gambles based on horse races. Attra... |

61 | An experimental measurement of utility. - Mosteller, Nogee - 1951 |

59 |
Intraclass Correlation and the Analysis of Variance.
- Haggard
- 1958
(Show Context)
Citation Context ...risons, there does not appear to be a systematic pattern to these violations. Reliability for the nine repeated gambles was measured by the maximum likelihood estimator of the intraclass correlation (=-=Haggard, 1958-=-). The intraclass correlation on the median data was .99 (the median absolute deviation was $1.50). The median of the 10 intraclass correlations computed on the individual subject data was .96, with a... |

59 | Subjective weighted utility: a descriptive extension of the expected utility model’, - Karmarkar - 1978 |

55 | What determines the shape of the probability weighting function under uncertainty. Working paper, - Kilka, Weber - 1998 |

54 |
Quantitative analysis of qualitative data.
- Young
- 1981
(Show Context)
Citation Context ... at Steps 2 and 3, respectively. signs that a global optimum was found. Step 1 served to change the scale of the data at each iteration; this is in the spirit of ‘‘optimal scaling’’ techniques (e.g., =-=Young, 1981-=-). 8 Interpersonal variability supports this intuition. We computed the interquartile range (IQR) over the 10 subjects for each of the 165 gambles. The IQR tend to be monotonically increasing with the... |

52 |
Violations of the independence axiom in common ratio problems: An experimental test of some competing hypotheses.
- Starmer, Sugden
- 1989
(Show Context)
Citation Context ...Y 5 25, and p 5 .50. More recently, Tversky and Kahneman (1992) generalized prospect theory using a rank-dependent, or cumulative, representation (see also Quiggin, 1993; Luce & Fishburn, 1991, 1995; =-=Starmer & Sugden, 1989-=-; Wakker & Tversky, 1993). Intuitively, cumulative prospect theory (CPT) generalizes the idea of the editing rule exhibited in Eq. (1) to gambles with an arbitrary number of outcomes. Thus, cumulative... |

50 | The influence of probability on risky choice: A parametric examination. - Lattimore, Baker, et al. - 1992 |

49 | From subjective probabilities to decision weights: The effect of asymmetric loss functions on the evaluation of uncertain outcomes and events.
- Weber
- 1994
(Show Context)
Citation Context ...erywhere below the identity line, ‘‘potential-minded’’ for w that is concave and everywhere above the identity line, and ‘‘cautiously-hopeful’’ for the inverse-S-shaped w depicted in Fig. 2 (see also =-=Weber, 1994-=-, for a discussion). The present concepts of discriminability and attractiveness provide a more detailed account of the weighting function, without confounding curvature and elevation. The Lopes frame... |

47 | An experimental study of the auctionvalue of an uncertain outcome’, - Preston, Baratta - 1948 |

46 |
Additive Representations of Preferences.
- Wakker
- 1989
(Show Context)
Citation Context ...outcome (w(p) for the higher outcome and 1 2 w(p) for the lower outcome) depends on the rank of that outcome with respect to other outcomes in the gamble (see Quiggin, 1982; Yaari, 1987; Segal, 1989; =-=Wakker, 1989-=-, 1994). Note that Eq. (2) is, after algebraic rearrangement, identical to Eq. (1). One advantage of the rank-dependent approach is that Eq. (2) is easily generalized to n-outcome gambles. For gambles... |

45 | Additive structure in qualitative data: An alternating least squares method with optimal scaling features - Leeuw, Young, et al. - 1976 |

44 | A note on deriving rank-dependent utility using additive joint receipts. - Luce - 1995 |

42 | Recent tests of generalizations of expected utility theory. - Camerer - 1992 |

40 |
Violations of monotonicity in judgment and decision making. In
- Birnbaum
- 1997
(Show Context)
Citation Context ...to predicted violations of stochastic dominance.2 Violations of stochastic dominance are difficult to observe empirically unless the stochastic dominance is not transparent (Tversky & Kahneman, 1986; =-=Birnbaum, 1997-=-; Leland, 1998). To avoid predictions of transparent stochastic dominance violations, Kahneman and Tversky proposed a number of editing operations. Here we consider only the case of two outcome gamble... |

40 |
An Empirical Test of Ordinal Independence,”
- Wu
- 1994
(Show Context)
Citation Context ... stochastic dominance see Fishburn (1978) and Quiggin (1993). PROBABILITY WEIGHTING FUNCTION 135 plicit editing operations in order to avoid predicted violations of stochastic dominance (however, see =-=Wu, 1994-=-). Much of the technical generalization of prospect theory involves the combination rule of how the value function is combined with the probability weighting function. CPT consists of the sum of two r... |

36 | Nonlinear decision weights in choice under uncertainty. - Wu, Gonzalez - 1999 |

35 |
Anticipated utility: A measure representation approach
- Segal
- 1989
(Show Context)
Citation Context ...tached to an outcome (w(p) for the higher outcome and 1 2 w(p) for the lower outcome) depends on the rank of that outcome with respect to other outcomes in the gamble (see Quiggin, 1982; Yaari, 1987; =-=Segal, 1989-=-; Wakker, 1989, 1994). Note that Eq. (2) is, after algebraic rearrangement, identical to Eq. (1). One advantage of the rank-dependent approach is that Eq. (2) is easily generalized to n-outcome gamble... |

31 | Probabilistic insurance. - Wakker, Thaler, et al. - 1997 |

30 | Violations of branch independence in choices between gambles. Organizational Behavior and Human Decision Processes - Birnbaum, McIntosh - 1996 |

29 | Explaining Distortions in Utility Elicitation Through the Rank-Dependent Model for Risky Choices - Wakker, Stiggelbout - 1995 |

27 | On Handa’s ‘‘new theory of cardinal utility’’ and the maximization of expected return - Fishburn - 1978 |

24 |
Generic utility theory: Measurement foundations and applications in multiattribute utility theory.
- Miyamoto
- 1988
(Show Context)
Citation Context ...ng Eq. (2). This assumption can be evaluated by fitting the more general model w(p)v(X) 1 g(1 2 p)v(Y) (8) which relaxes the restriction on the weighting function but maintains the bilinear form (see =-=Miyamoto, 1988-=-). We estimated the more general model and found that g(1 2 p) of Eq. (8) roughly coincides with 1 2 w(p) of CPT (Eq. (2)). The intraclass correlation, which serves as an index of the fit to the ident... |

24 | Common consequence conditions in decision making under risk - Wu, Gonzalez - 1998 |

19 |
Similarity Judgments in Choice under Uncertainty: A Reinterpretation of the Predictions of Regret Theory."
- Leland
- 1998
(Show Context)
Citation Context ...lations of stochastic dominance.2 Violations of stochastic dominance are difficult to observe empirically unless the stochastic dominance is not transparent (Tversky & Kahneman, 1986; Birnbaum, 1997; =-=Leland, 1998-=-). To avoid predictions of transparent stochastic dominance violations, Kahneman and Tversky proposed a number of editing operations. Here we consider only the case of two outcome gambles involving ei... |

19 |
Is choice the correct primitive? On using certainty equivalents and reference levels to predict choices among ganlbles
- Luce, MeUers, et al.
- 1993
(Show Context)
Citation Context ...er functions fail to fit the data of approximately two-thirds the subjects. Further, some simple functional forms for w can be rejected on the basis of existing data, e.g., a power w (as suggested by =-=Luce, Mellers, and Chang, 1993-=-, and by Hey & Orme, 1994) and a linear weighting function w(p) 5 (b 2 a)p 1 a, with 0 , a , b , 1, end points w(0) 5 0 and w(1) 5 1 (as suggested by Bell, 1985). GOALS OF THE PRESENT STUDY Empirical ... |

17 | Subjectively weighted utility and the Allais paradox - Karmarkar - 1979 |

13 | An experimental test of a general class of utility models: Evidence for context dependency - Chechile, Cooke - 1997 |

12 | Re–modeling risk aversion: A comparison of Bernoullian and rank dependent value approaches - Lopes - 1990 |

10 |
Cross-modality matching of money against other continua
- Galanter, Pliner
- 1974
(Show Context)
Citation Context ...used nonlinear w and linear v (see Arrow, 1951, for a discussion), a nonlinear utility function typically provides a better fit for both risk and nonrisk domains (e.g., Fishburn & Kochenberger, 1979; =-=Galanter & Pliner, 1974-=-; Parker & Schneider, 1988; Tversky & Kahneman, 1992). Second, even if Preston and Baratta had used a nonlinear v they would have been unable to extract a unique estimate of the weighting function bec... |

8 |
The effect on the preference reversal phenomenon of using choice indifferences.
- Bostic, Herrnstein, et al.
- 1990
(Show Context)
Citation Context ...not require participants to generate a certainty equiva144 GONZALEZ AND WU lent. Rather, participants chose certainty equivalents from a menu (for related procedures see Tversky & Kahneman, 1992, and =-=Bostic, Herrnstein, & Luce, 1990-=-). The program presented gambles in random order to each participant over four sessions lasting approximately 1 h each. RESULTS There are many ways to analyze these CE data. The standard approach has ... |

8 | Testing expectation theories of decision making without measuring utility or subjective probability - Coombs, Bezembinder, et al. - 1967 |

5 | The Comparative Statics of Deductible Insurance in Expected- and Non-Expected-Utility Theories. The - Schlee - 1995 |

2 | Models of choice between multioutcome lotteries - Bernstein, Chapman, et al. - 1997 |

2 | On the composition of risk preference and belief. Unpublished manuscript - Tversky, Wakker - 1998 |

1 |
Individualdecision making
- Camerer
- 1995
(Show Context)
Citation Context ...alue function v has been widely studied and applied to a number of areas including economics, finance, marketing, medical decision making, organizational behavior, and public policy (for examples see =-=Camerer, 1995-=-, as well as Heath, Larrick, & Wu, 1999). The probability weighting function, in contrast, has received less empirical and theoretical attention. For a few applications of w in medical decision making... |

1 |
Do subjective weighting functions of generalized expected value theories capture persisting properties of individual decision makers. Universitat
- Hartinger
- 1998
(Show Context)
Citation Context ...and convex for high probability. Weighting functions consistent with the survey data are shown in Fig. 2; empirical support for this shape appeared in three recent choice studies (Camerer & Ho, 1994; =-=Hartinger, 1998-=-; Tversky & Kahneman, 1992; Wu & Gonzalez, 1996). The general question studied in this paper is how the psychophysics of probability influences decision making under risk. In turn, an understanding of... |

1 |
Goals as reference points. Unpublished manuscript
- Heath, Larrick, et al.
- 1999
(Show Context)
Citation Context ...idely studied and applied to a number of areas including economics, finance, marketing, medical decision making, organizational behavior, and public policy (for examples see Camerer, 1995, as well as =-=Heath, Larrick, & Wu, 1999-=-). The probability weighting function, in contrast, has received less empirical and theoretical attention. For a few applications of w in medical decision making and insurance see Wakker and Deneffe (... |

1 |
Conjoint scaling of the utility of money using paired comparisons
- Parker, Schneider
- 1988
(Show Context)
Citation Context ...ar v (see Arrow, 1951, for a discussion), a nonlinear utility function typically provides a better fit for both risk and nonrisk domains (e.g., Fishburn & Kochenberger, 1979; Galanter & Pliner, 1974; =-=Parker & Schneider, 1988-=-; Tversky & Kahneman, 1992). Second, even if Preston and Baratta had used a nonlinear v they would have been unable to extract a unique estimate of the weighting function because their one nonzero out... |

1 | The origin of chance in children - Piaget, Inhelder - 1975 |

1 | A method for obtaining an ordered metric scale - GONZALEZ, Siegel, et al. - 1956 |

1 |
A dual to the von Neumann–Morgentern theorem
- Weibull
- 1982
(Show Context)
Citation Context ..., .99}. There are two problems with their analyses. First, the analysis assumes a linear value function. Even though ‘‘duals’’ to expected utility with linear v have been proposed (e.g., Yaari, 1987; =-=Weibull, 1982-=-) and one of the early resolutions to the St. Petersburg paradox used nonlinear w and linear v (see Arrow, 1951, for a discussion), a nonlinear utility function typically provides a better fit for bot... |