## Prospect theory: An analysis of decisions under risk (1979)

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Venue: | Econometrica |

Citations: | 3023 - 20 self |

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@ARTICLE{Kahneman79prospecttheory:,

author = {Daniel Kahneman and Amos Tversky},

title = {Prospect theory: An analysis of decisions under risk},

journal = {Econometrica},

year = {1979},

pages = {263--291}

}

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### Citations

1659 |
The Foundations of Statistics
- Savage
- 1954
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Citation Context ...model of rational choice [24], and widely applied as a descriptive model of economic behavior, e.g. [15, 4]. Thus, it is assumed that all reasonable people would wish to obey the axioms of the theory =-=[47, 36]-=-, and that most people actually do, most of the time. The present paper describes several classes of choice problems in which preferences systematically violate the axioms of expected utility theory. ... |

1259 |
Decisions with Multiple Objectives: Preferences and value tradeoffs
- Keeney, Raiffa
- 1976
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Citation Context ...f both insurance and gambling. 1. INTRODUCTION EXPECTED UTILITY THEORY has dominated the analysis of decision making under risk. It has been generally accepted as a normative model of rational choice =-=[24]-=-, and widely applied as a descriptive model of economic behavior, e.g. [15, 4]. Thus, it is assumed that all reasonable people would wish to obey the axioms of the theory [47, 36], and that most peopl... |

1186 |
Judgment under uncertainty: heuristics and biases
- Tversky, Kahneman
- 1990
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Citation Context ...ural analogue to subcertainty.PROSPECT THEORY 289 The decision weight associated with an event will depend primarily on the perceived likelihood of that event, which could be subject to major biases =-=[45]-=-. In addition, decision weights may be affected by other considerations, such as ambiguity or vagueness. Indeed, the work of Ellsberg [10] and Fellner [12] implies that vagueness reduces decision weig... |

356 | Lectures on Functional Equations and their Applications - Aczél - 1966 |

354 |
Essays in the Theory of Risk Bearing
- ARROW
- 1970
(Show Context)
Citation Context ...dominated the analysis of decision making under risk. It has been generally accepted as a normative model of rational choice [24], and widely applied as a descriptive model of economic behavior, e.g. =-=[15, 4]-=-. Thus, it is assumed that all reasonable people would wish to obey the axioms of the theory [47, 36], and that most people actually do, most of the time. The present paper describes several classes o... |

333 |
Le comportement de l’homme rationnel devant le risque: critique des postulats et axiomes de l’ecole Américaine. Econometrica
- Allais
- 1953
(Show Context)
Citation Context ...omenon which we label the certainty effect. The best known counter-example to expected utility theory which e*ploits the certainty effect was introduced by the French economist Maurice Allais in 1953 =-=[2]-=-. Allais' example has been discussed from both normative and descriptive standpoints by many authors [28, 38]. The following pair of choice problems is a variation of Allais' example, which differs fr... |

243 | Decision Analysis: Introductory Lectures on Choices under Uncertainty - Raiffa - 1968 |

223 |
The utility analysis of choices involving risk
- Friedman, Savage
- 1948
(Show Context)
Citation Context ...dominated the analysis of decision making under risk. It has been generally accepted as a normative model of rational choice [24], and widely applied as a descriptive model of economic behavior, e.g. =-=[15, 4]-=-. Thus, it is assumed that all reasonable people would wish to obey the axioms of the theory [47, 36], and that most people actually do, most of the time. The present paper describes several classes o... |

219 |
Liquidity preference as behavior towards risk
- Tobin
- 1958
(Show Context)
Citation Context ...25). To resolve this apparent inconsistency one could invoke the assumption that people prefer prospects that have high expected value and small variance (see, e.g., Allais [2]; Markowitz [30]; Tobin =-=[41]-=-). Since (3,000) has no variance while (4,000, .80) has large variance, the former prospect could be chosen despite its lower expected value. When the prospects are reduced, however, the difference in... |

182 |
Proper risk aversion
- Pratt, Zeckhauser
- 1987
(Show Context)
Citation Context ...arding risky choices. It led the early decision theorists of the eighteenth century to propose that utility is a concave function of money, and this idea has been retained in modern treatments (Pratt =-=[33]-=-, Arrow [4]). In the following sections we demonstrate several phenomena which violate these tenets of expected utility theory. The demonstrations are based on the responses of students and university... |

143 |
Mean-Risk Analysis with Risk Associated with BelowTarget Returns
- Fishburn
- 1977
(Show Context)
Citation Context ... for ambiguity, and by van Dam [46] who attempted to scale decision weights. For other critical analyses of expected utility theory and alternative choice models, see Allais [2], Coombs [6], Fishburn =-=[13]-=-, and Hansson [22]. The equations of prospect theory retain the general bilinear form that underlies expected utility theory. However, in order to accomodate the effects described in the first part of... |

143 |
The Utility of Wealth
- Markowitz
- 1952
(Show Context)
Citation Context ...to lose 4,000, in preference to a sure loss of 3,000, although the gamble has a lower expected value. The occurrence of risk seeking in choices between negative prospects was noted early by Markowitz =-=[29]-=-. Williams [48] reported data where a translation of outcomes produces a dramatic shift from risk aversion to risk seeking. For example, his subjects were indifferent between (100, .65; - 100, .35) an... |

131 |
Reversals of preference between bids and choices in gambling decisions
- Lichtenstein, Slovic
- 1971
(Show Context)
Citation Context ...ituation in which this axiom fails is illustrated by the following problems. PROBLEM 7: A: (6,000, .45), B: (3,000, .90). N = 66 [14] [86]* PROBLEM 8: C: (6,000, .001), D: (3,000, .002). N = 66 [73]* =-=[27]-=- Note that in Problem 7 the probabilities of winning are substantial (.90 and .45), and most people choose the prospect where winning is more probable. In Problem 8, there is a possibility of winning,... |

109 |
Topological methods in cardinal utility theory
- Debreu
- 1960
(Show Context)
Citation Context .... TABLE I PREFERENCES BETWEEN POSITIVE AND NEGATIVE PROSPECTS Positive prospects Negative prospects Problem 3: (4,000, .80) < (3,000). Problem 3': (-4,000, .80) > (-3,000). N=95 [20] [80]* N=95 [92]* =-=[8]-=- Problem 4: (4,000, .20) > (3,000, .25). Problem 4': (-4,000, .20) < (-3,000, .25). N=95 [65]* [35] N=95 [42] [58] Problem 7: (3,000, .90) > (6,000, .45). Problem 7': (-3,000, .90) < (-6,000, .45). N=... |

103 |
Economic theory of choice and the preference reversal phenomenon
- Grether, Plott
- 1979
(Show Context)
Citation Context ...A simpler demonstration of the same phenomenon, involving only twooutcome gambles is given below. This example is also based on Allais [2]. PROBLEM 3: PROBLEM 4: A: (4,000,.80), or B: (3,000). N = 95 =-=[20]-=- [80]* C: (4,000,.20), or D: (3,000,.25). N= 95 [65]* [35] In this pair of problems as well as in all other problem-pairs in this section, over half the respondents violated expected utility theory. T... |

88 | http://links.jstor.org/sici?sici=0022-3808%28198306%2991%3A3%3C401%3ABRDIAL%3E2.0.CO%3B2-Z The Twin Crises: The Causes of Banking and Balance-Of-Payments Problems Graciela L - URL - 1999 |

84 | http://links.jstor.org/sici?sici=0002-8282%28200009%2990%3A4%3C980%3ACAPIPG%3E2.0.CO%3B2-H Does Fairness Prevent Market Clearing? An Experimental Investigation Ernst Fehr; Georg Kirchsteiger; Arno Riedl The Quarterly - URL - 1993 |

83 | http://links.jstor.org/sici?sici=0012-9682%28199207%2960%3A4%3C803%3AAESOTC%3E2.0.CO%3B2-J Incorporating Fairness into Game Theory and - URL - 1993 |

70 |
Adaptation-Level Theory
- Helson
- 1964
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Citation Context ...such as brightness, loudness, or temperature, the past and present context of experience defines an adaptation level, or reference point, and stimuli are perceived in relation to this reference point =-=[23]-=-. Thus, an object at a given temperature may be experienced as hot or cold to the touch depending on the temperature to which one has adapted. The same principle applies to non-sensory attributes such... |

61 | http://links.jstor.org/sici?sici=0034-6527%28198104%2948%3A2%3C289%3ADWPRTA%3E2.0.CO%3B2-3 Understanding the Costs of Sovereign Default: American State Debts in the 1840's - URL - 1996 |

59 | http://links.jstor.org/sici?sici=0033-5533%28199908%29114%3A3%3C817%3AATOFCA%3E2.0.CO%3B2-R NOTE: The reference numbering from the original has been maintained in this citation list. LINKED CITATIONS - Page 4 of 4 - An Experimental Study of the Centipede - URL - 1992 |

47 |
Subjective probabilities inferred from decisions
- Edwards
- 1962
(Show Context)
Citation Context ...ains the expectation principle; hence it cannot account for the many violations of this principle; see, e.g., Table I. The replacement of probabilities by more general weights was proposed by Edwards =-=[9]-=-, and this model was investigated in several empirical studies (e.g.,PROSPECT THEORY 277 [3, 42]). Similar models were developed by Fellner [12], who introduced the concept of decision weight to expl... |

35 |
KOCHENBERGER: "Two-Piece von Neumann-Morgenstern Utility Functions," forthcoming
- FISHBURN, A
(Show Context)
Citation Context ... is not the only type of violation of the substitution axiom. Another situation in which this axiom fails is illustrated by the following problems. PROBLEM 7: A: (6,000, .45), B: (3,000, .90). N = 66 =-=[14]-=- [86]* PROBLEM 8: C: (6,000, .001), D: (3,000, .002). N = 66 [73]* [27] Note that in Problem 7 the probabilities of winning are substantial (.90 and .45), and most people choose the prospect where win... |

33 |
Who accepts Savage’s axiom
- Slovic, Tversky
- 1974
(Show Context)
Citation Context ...ich e*ploits the certainty effect was introduced by the French economist Maurice Allais in 1953 [2]. Allais' example has been discussed from both normative and descriptive standpoints by many authors =-=[28, 38]-=-. The following pair of choice problems is a variation of Allais' example, which differs from the original in that it refers to moderate rather than to extremely large gains. The number of respondents... |

30 |
Distortion of subjective probabilities as a reaction to uncertainty. Quarterly
- Fellner
- 1961
(Show Context)
Citation Context ...le in this context to express decision weights as a function of stated probability. In general, however, the decision weight attached to an event could be influenced by other factors, e.g., ambiguity =-=[10, 11]-=-. We turn now to discuss the salient properties of the weighting function 7r, which relates decision weights to stated probabilities. Naturally, 1T is an increasing function of p, with rr(0) = 0 and r... |

29 |
An Experimental Measurement of Utility
- Mosteller, Nogee
- 1951
(Show Context)
Citation Context ... to propose that utility be defined on gains and losses rather than on final asset positions, an assumption which has been implicitly accepted in most experimental measurements of utility (see, e.g., =-=[7, 32]-=-). Markowitz also noted the presence of risk seeking in preferences among positive as well as among negative prospects, and he proposed a utility function which has convex and concave regions in both ... |

27 |
Utility theory: Axioms versus paradoxes
- MacCrimmon, Larsson
- 1979
(Show Context)
Citation Context ...ich e*ploits the certainty effect was introduced by the French economist Maurice Allais in 1953 [2]. Allais' example has been discussed from both normative and descriptive standpoints by many authors =-=[28, 38]-=-. The following pair of choice problems is a variation of Allais' example, which differs from the original in that it refers to moderate rather than to extremely large gains. The number of respondents... |

23 |
1977]: "Preference for Insuring Against Probable Small Losses: Implications of Risk and Insurance
- SLOVIC, FISCHHOFF, et al.
(Show Context)
Citation Context ...nd gambling for small probabilities, we feel that the present analysis falls far short of a fully adequate account of these complex phenomena. Indeed, there is evidence from both experimental studies =-=[37]-=-, survey research [26], and observations of economic behavior, e.g., service and medical insurance, that the purchase of insurance often extends to the medium range of probabilities, and that small pr... |

16 | http://links.jstor.org/sici?sici=0022-2186%28197608%2919%3A2%3C347%3AFBTWT%22%3E2.0.CO%3B2-5 The Utility of Wealth Harry Markowitz The - URL - 1952 |

15 |
Stability of Choices among Uncertain Alternatives
- McGlothlin
- 1956
(Show Context)
Citation Context ...A: (1,000,.50), and B: (500). N= 70 [16] [84]* PROBLEM 12: In addition to whatever you own, you have been given 2,000. You are now asked to choose between C: (-1,000,.50), and D: (-500). N = 68 [69*] =-=[31]-=- The majority of subjects chose B in the first problem and C in the second. These preferences conform to the reflection effect observed in Table I, which exhibits risk aversion for positive prospects ... |

15 |
Additivity, utility, and subjective probability
- Tversky
- 1967
(Show Context)
Citation Context ...3: (4,000, .80) < (3,000). Problem 3': (-4,000, .80) > (-3,000). N=95 [20] [80]* N=95 [92]* [8] Problem 4: (4,000, .20) > (3,000, .25). Problem 4': (-4,000, .20) < (-3,000, .25). N=95 [65]* [35] N=95 =-=[42]-=- [58] Problem 7: (3,000, .90) > (6,000, .45). Problem 7': (-3,000, .90) < (-6,000, .45). N=66 [86]* [14] N=66 [8] [92]* Problem 8: (3,000, .002) < (6,000, .001). Problem 8': (-3,000, .002) > (-6,000, ... |

14 |
Decisions under uncertainty: Drilling decisions by oil and gas operators
- Grayson
- 1960
(Show Context)
Citation Context ... the percentage who choose each option is given in brackets. PROBLEM 1: Choose between A: 2,500 with probability .33, B: 2,400 with certainty. 2,400 with probability .66, 0 with probability .01; N=72 =-=[18]-=- [82]*266 D. KAHNEMAN AND A. TVERSKY PROBLEM 2: Choose between C: 2,500 with probability .33, D: 2,400 with probability .34, 0 with probability .67; 0 with probability .66. N =72 [83]* [17] The data ... |

13 |
Information integration in risky decision making
- Anderson, Shanteau
- 1970
(Show Context)
Citation Context ...iple; see, e.g., Table I. The replacement of probabilities by more general weights was proposed by Edwards [9], and this model was investigated in several empirical studies (e.g.,PROSPECT THEORY 277 =-=[3, 42]-=-). Similar models were developed by Fellner [12], who introduced the concept of decision weight to explain aversion for ambiguity, and by van Dam [46] who attempted to scale decision weights. For othe... |

11 |
H.: "Portfolio Theory and the Measurement of Risk
- COOMBS
- 1975
(Show Context)
Citation Context ...plain aversion for ambiguity, and by van Dam [46] who attempted to scale decision weights. For other critical analyses of expected utility theory and alternative choice models, see Allais [2], Coombs =-=[6]-=-, Fishburn [13], and Hansson [22]. The equations of prospect theory retain the general bilinear form that underlies expected utility theory. However, in order to accomodate the effects described in th... |

10 |
C.: "Attitudes toward Speculative Risks as an Indicator of Attitudes toward Pure Risks
- WILLIAMS
(Show Context)
Citation Context ...in preference to a sure loss of 3,000, although the gamble has a lower expected value. The occurrence of risk seeking in choices between negative prospects was noted early by Markowitz [29]. Williams =-=[48]-=- reported data where a translation of outcomes produces a dramatic shift from risk aversion to risk seeking. For example, his subjects were indifferent between (100, .65; - 100, .35) and (0), indicati... |

8 |
Decisions under Uncertainty
- HALTER, DEAN
- 1971
(Show Context)
Citation Context ...nstern utility functions for changes of wealth (Fishburn and Kochenberger [14]). The functions had been obtained from thirty decision makers in various fields of business, in five independent studies =-=[5, 18, 19, 21, 40]-=-. Most utility functions for gains were concave, most functions for losses were convex, and only three individuals exhibited risk aversion for both gains and losses. With a single exception, utility f... |

7 | http://links.jstor.org/sici?sici=0022-4367%28197706%2944%3A2%3C237%3APFIAPS%3E2.0.CO%3B2-E NOTE: The reference numbering from the original has been maintained in this citation list. LINKED CITATIONS - Page 3 of 3 - Liquidity Preference as Behavior Towards - URL - 1958 |

7 |
0.: "Utility Theory-Insights into Risk Taking
- SWALM
- 1966
(Show Context)
Citation Context ...nstern utility functions for changes of wealth (Fishburn and Kochenberger [14]). The functions had been obtained from thirty decision makers in various fields of business, in five independent studies =-=[5, 18, 19, 21, 40]-=-. Most utility functions for gains were concave, most functions for losses were convex, and only three individuals exhibited risk aversion for both gains and losses. With a single exception, utility f... |

4 | the Savage Axioms Daniel Ellsberg The Quarterly - Risk, Ambiguity - 1961 |

4 |
Decision-making: An Experimental Approach
- DAVIDSON, SUPPES, et al.
- 1957
(Show Context)
Citation Context ... to propose that utility be defined on gains and losses rather than on final asset positions, an assumption which has been implicitly accepted in most experimental measurements of utility (see, e.g., =-=[7, 32]-=-). Markowitz also noted the presence of risk seeking in preferences among positive as well as among negative prospects, and he proposed a utility function which has convex and concave regions in both ... |

4 |
S.: "The Development of Corporate Risk Policy for Capital Investment Decisions
- SPETZLER
(Show Context)
Citation Context ...ysis, rather than in terms of gains and losses, as people usually do. In this case, the reference point is set to zero on the scale of wealth and the value function is likely to be concave everywhere =-=[39]-=-. According to the present analysis, this formulation essentially eliminates risk seeking, except for gambling with low probabilities. The explicit formulation of decision problems in terms of final a... |

3 |
E.: "Risk Attitudes and Chemical Investment Decisions
- GREEN
- 1963
(Show Context)
Citation Context ...nstern utility functions for changes of wealth (Fishburn and Kochenberger [14]). The functions had been obtained from thirty decision makers in various fields of business, in five independent studies =-=[5, 18, 19, 21, 40]-=-. Most utility functions for gains were concave, most functions for losses were convex, and only three individuals exhibited risk aversion for both gains and losses. With a single exception, utility f... |

3 |
A Measurement Axiomatization for an Essentially Multiplicative Representation of Two Factors
- ROSKIES
(Show Context)
Citation Context ...only twooutcome gambles is given below. This example is also based on Allais [2]. PROBLEM 3: PROBLEM 4: A: (4,000,.80), or B: (3,000). N = 95 [20] [80]* C: (4,000,.20), or D: (3,000,.25). N= 95 [65]* =-=[35]-=- In this pair of problems as well as in all other problem-pairs in this section, over half the respondents violated expected utility theory. To show that the modal pattern of preferences in Problems 3... |

2 |
REINMUTH: "Comparing Imputed and Actual Utility Functions in a Competitive Bidding Setting
- BARNES, E
- 1976
(Show Context)
Citation Context |

2 |
The Appropriateness of the Expected Utility Model
- HANSSON
- 1975
(Show Context)
Citation Context ...lems illustrates the certainty effect with non-monetary outcomes. PROBLEM 5: A: 50% chance to win a three- B: A one-week tour of week tour of England, England, with certainty. France, and Italy; N=72 =-=[22]-=- [78]* PROBLEM 6: C: 5% chance to win a three- D: 10% chance to win a oneweek tour of England, week tour of England. France, and Italy; N=72 [67]* [33] The certainty effect is not the only type of vio... |

2 |
C.: "Another Look at Inconsistency in Financial Decision-Making," presented at
- DAM
- 1975
(Show Context)
Citation Context ...l empirical studies (e.g.,PROSPECT THEORY 277 [3, 42]). Similar models were developed by Fellner [12], who introduced the concept of decision weight to explain aversion for ambiguity, and by van Dam =-=[46]-=- who attempted to scale decision weights. For other critical analyses of expected utility theory and alternative choice models, see Allais [2], Coombs [6], Fishburn [13], and Hansson [22]. The equatio... |

1 |
Ambiguity and the Savage Axiorms
- ELLSBERG
- 1961
(Show Context)
Citation Context ...le in this context to express decision weights as a function of stated probability. In general, however, the decision weight attached to an event could be influenced by other factors, e.g., ambiguity =-=[10, 11]-=-. We turn now to discuss the salient properties of the weighting function 7r, which relates decision weights to stated probabilities. Naturally, 1T is an increasing function of p, with rr(0) = 0 and r... |

1 |
R.: "From Bismark to Woodcock: The "Irrational" Pursuit of National Health Insurance
- FUCHS
- 1976
(Show Context)
Citation Context ...urance programs that offer limited coverage with low or zero deductible over comparable policies that offer higher maximal coverage with higher deductibles-contrary to risk aversion (see, e.g., Fuchs =-=[16]-=-). Another type of insurance problem in which people's responses are inconsistent with the concavity hypothesis may be called probabilistic insurance. To illustrate this concept, consider the followin... |