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48
Weighing Risk and Uncertainty
, 1995
"... Decision theory distinguishes between risky prospects, where the probabilities associated with the possible outcomes are assumed to be known, and uncertain prospects, where these probabilities are not assumed to be known. Studies of choice between risky prospects have suggested a nonlinear transform ..."
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Cited by 111 (9 self)
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Decision theory distinguishes between risky prospects, where the probabilities associated with the possible outcomes are assumed to be known, and uncertain prospects, where these probabilities are not assumed to be known. Studies of choice between risky prospects have suggested a nonlinear transformation of the probability scale that overweights low probabilities and underweights moderate and high probabilities. The present article extends this notion from risk to uncertainty by invoking the principle of bounded subadditivity: An event has greater impact when it turns impossibility into possibility, or possibility into certainty, than when it merely makes a possibility more or less likely. A series of studies provides support for this principle in decision under both risk and uncertainty and shows that people are less sensitive to uncertainty than to risk. Finally, the article discusses the relationship between probability judgments and decision weights and distinguishes relative sensitivity from ambiguity aversion.
On the Intuition of RankDependent Utility
, 2000
"... Among the most popular models for decision under risk and uncertainty are the rankdependent models, introduced by Quiggin and Schmeidler. Central concepts in these models are rankdependence and comonotonicity. It has been suggested in the literature that these concepts are technical tools that hav ..."
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Cited by 34 (0 self)
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Among the most popular models for decision under risk and uncertainty are the rankdependent models, introduced by Quiggin and Schmeidler. Central concepts in these models are rankdependence and comonotonicity. It has been suggested in the literature that these concepts are technical tools that have no intuitive or empirical content. This paper describes such contents. As
New paradoxes of risky decision making
 Psychological Review
"... During the last 25 years, prospect theory and its successor, cumulative prospect theory, replaced expected utility as the dominant descriptive theories of risky decision making. Although these models account for the original Allais paradoxes, 11 new paradoxes show where prospect theories lead to sel ..."
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Cited by 24 (11 self)
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During the last 25 years, prospect theory and its successor, cumulative prospect theory, replaced expected utility as the dominant descriptive theories of risky decision making. Although these models account for the original Allais paradoxes, 11 new paradoxes show where prospect theories lead to selfcontradiction or systematic false predictions. The new findings are consistent with and, in several cases, were predicted in advance by simple “configural weight ” models in which probabilityconsequence branches are weighted by a function that depends on branch probability and ranks of consequences on discrete branches. Although they have some similarities to later models called “rankdependent utility, ” configural weight models do not satisfy coalescing, the assumption that branches leading to the same consequence can be combined by adding their probabilities. Nor do they satisfy cancellation, the “independence ” assumption that branches common to both alternatives can be removed. The transfer of attention exchange model, with parameters estimated from previous data, correctly predicts results with all 11 new paradoxes. Apparently, people do not frame choices as prospects but, instead, as trees with branches.
An Index Of Loss Aversion
 Journal of Economic Theory
, 2000
"... Under prospect theory, three components influence the risk attitude of a decision maker: the utility function, the probability weighting function, and loss aversion. Loss aversion reflects the observed behavior of decision makers' being more sensitive to losses than to gains, resulting in a utility ..."
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Cited by 23 (2 self)
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Under prospect theory, three components influence the risk attitude of a decision maker: the utility function, the probability weighting function, and loss aversion. Loss aversion reflects the observed behavior of decision makers' being more sensitive to losses than to gains, resulting in a utility function that is steeper for losses than for gains. Much of the empirically observed risk aversion is due to loss aversion. This paper proposes an index of loss aversion. It also demonstrates how the degree of loss aversion of two decision makers can be compared and how its influences on comparative risk aversion can be examined. The main result characterizes comparative loss aversion in terms of preferences.
An Axiomatization of Cumulative Prospect Theory for Decision under Risk
 Journal of Risk and Uncertainty
, 1999
"... Cumulative prospect theory was introduced by Tversky and Kahneman so as to combine the empirical realism of their original prospect theory with the theoretical advantages of Quiggin’s rankdependent utility. Preference axiomatizations were provided in several papers. All those axiomatizations, howev ..."
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Cited by 18 (2 self)
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Cumulative prospect theory was introduced by Tversky and Kahneman so as to combine the empirical realism of their original prospect theory with the theoretical advantages of Quiggin’s rankdependent utility. Preference axiomatizations were provided in several papers. All those axiomatizations, however, only consider decision under uncertainty. No axiomatization has been provided as yet for decision under risk, i.e., the case in which given probabilities are transformed. Providing the latter is the purpose of this note. The resulting axiomatization is considerably simpler than that for uncertainty.
Coalescing, Event Commutativity, and Theories of Utility
 JOURNAL OF RISK AND UNCERTAINTY, 16:87–114 (1998)
, 1998
"... Preferences satisfying rankdependent utility exhibit three necessary properties: coalescing (forming the union of events having the same consequence), statusquo event commutativity, and rankdependent additivity. The major result is that, under a few additional, relatively noncontroversial, neces ..."
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Cited by 14 (3 self)
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Preferences satisfying rankdependent utility exhibit three necessary properties: coalescing (forming the union of events having the same consequence), statusquo event commutativity, and rankdependent additivity. The major result is that, under a few additional, relatively noncontroversial, necessary conditions on binary gambles and assuming mappings are onto intervals, the converse is true. A number of other utility representations are checked for each of these three properties (see Table 2, Section 7).
Qualityadjusted lifeyears (QALY) utility models under expected utility and rank dependent utility assumptions
 Journal of Mathematical Psychology
, 1999
"... Qualityadjusted life years (QALY) utility models are multiattribute utility models of survival duration and health quality. This paper formulates six classes of QALY utility models and axiomatizes these models under expected utility (EU) and rankdependent utility (RDU) assumptions. The QALY models ..."
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Cited by 13 (1 self)
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Qualityadjusted life years (QALY) utility models are multiattribute utility models of survival duration and health quality. This paper formulates six classes of QALY utility models and axiomatizes these models under expected utility (EU) and rankdependent utility (RDU) assumptions. The QALY models investigated in this paper include the standard linear QALY model, the power and exponential multiplicative models, and the general multiplicative model. Emphasis is placed on a preference assumption, the zero condition, that greatly simplifies the axiomatizations under EU and RDU assumptions. The RDU axiomatizations of QALY models are generally similar to their EU counterparts, but in some cases, they require modification because linearity in probability is no longer assumed, and rank dependence introduces asymmetries between the domains of betterthandeath health states and worsethandeath health states. 1999 Academic Press This paper concerns the foundations of qualityadjusted life years (QALY) utility models. QALY utility models are widely used in the expected utility analysis of health decisions because they provide an outcome measure that integrates the duration and quality of survival. Before discussing the specifics of these models, it will be helpful to motivate the discussion by describing the role played by QALY utility models in health decision analysis (Weinstein et al., 1980; Sox, Blatt,
On the Composition of Risk Preference and Belief
, 2004
"... Prospect theory assumes nonadditive decision weights for preferences over risky gambles. Such decision weights generalize additive probabilities. This article proposes a decomposition of decision weights into a component reflecting risk attitude and a new component depending on belief. The decomposi ..."
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Cited by 9 (3 self)
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Prospect theory assumes nonadditive decision weights for preferences over risky gambles. Such decision weights generalize additive probabilities. This article proposes a decomposition of decision weights into a component reflecting risk attitude and a new component depending on belief. The decomposition is based on an observable preference condition and does not use other empirical primitives such as statements of judged probabilities. The preference condition is confirmed by most of the experimental findings in the literature. The implied properties of the belief component suggest that, besides the oftenstudied ambiguity aversion (a motivational factor reflecting a general aversion to unknown probabilities), perceptual and cognitive limitations play a role: It is harder to distinguish among various levels of likelihood, and to process them differently, when probabilities are unknown than when they are known.
Temporal Resolution of Uncertainty and Recursive NonExpected Utility Models
 ECONOMETRICA
, 2000
"... ..."
A note on Wakker's Cardinal Coordinate Independence
 MATHEMATICAL SOCIAL SCIENCES
, 2004
"... Peter P. Wakker has forcefully shown the importance for decision theory of a condition that he called "Cardinal Coordinate Independence". Indeed, when the outcome space is rich, he proved that, for continuous weak orders, this condition fully characterizes the Subjective Expected Utility model with ..."
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Cited by 7 (4 self)
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Peter P. Wakker has forcefully shown the importance for decision theory of a condition that he called "Cardinal Coordinate Independence". Indeed, when the outcome space is rich, he proved that, for continuous weak orders, this condition fully characterizes the Subjective Expected Utility model with a finite number of states. He has furthermore explored in depth how this condition can be weakened in order to arrive at characterizations of Choquet Expected Utility and Cumulative Prospect Theory. This note studies the consequences of this condition in the absence of any transitivity assumption. Complete preference relations satisfying Cardinal Coordinate Independence are shown to be already rather wellbehaved. Under a suitable necessary order denseness assumption, they may always be represented using a simple numerical model.