Cumulative Prospect Theory for Parametric and Multiattribute Utilities

In cumulative prospect theory models, different behavior concerning gains and losses is per-mitted. For gains different decision weights are assigned than for losses, and the shape of utility can reveal loss aversion. Decision analyses concentrate on both, the capacities, which determine the decision weights, and the nature of utility. This paper focuses on linear/exponential, power and multilinear utility for decision models under uncertainty. Simple preference axioms are for-mulated for a representation by a cumulative prospect theory function. All models share the following axioms: weak ordering, continuity, monotonicity and tail independence. We first show that in their presence constant absolute (proportional) risk aversion implies linear/exponential (power) utility. Then, in the multiattribute case, considering (mutual) utility independence, it is shown that the utility function is (additive/multiplicative) multilinear.mathematical economics and econometrics ;

Additive utility in prospect theory

Prospect theory is currently the main descriptive theory of decision under uncertainty. It generalizes expected utility by introducing nonlinear decision weighting and loss aversion. A difficulty in the study of multiattribute utility under prospect theory is to determine when an attribute yields a gain or a loss. One possibility, adopted in the theoretical literature on multiattribute utility under prospect theory, is to assume that a decision maker determines whether the complete outcome is a gain or a loss. In this holistic evaluation, decision weighting and loss aversion are general and attribute-independent. Another possibility, more common in the empirical literature, is to assume that a decision maker has a reference point for each attribute. We give preference foundations for this attribute-specific evaluation where decision weighting and loss aversion are depending on the attributes

Eliciting von Neumann-Morgenstern Utilities when Probabilities Are Distorted or Unknown

This paper proposes a new method, the (gamble-)tradeoff method, for eliciting utilities in decision under risk or uncertainty. The elicitation of utilities, to be used in the expected utility criterion, turns out to be possible even if probabilities are ambiguous or unknown. A disadvantage of the tradeoff method is that a few more questions usually must be asked to clients. Also, the lotteries that are needed are somewhat more complex than in the certainty-equivalent method or in the probability-equivalent method. The major advantage of the tradeoff method is its robustness against probability distortions and misconceptions, which constitute a major cause of violations of expected utility and generate inconsistencies in utility elicitation. Thus the tradeoff method retains full validity under prospect theory, rank-dependent utility, and the combination of the two, i.e., cumulative prospect theory. The tradeoff method is tested for monetary outcomes and for outcomes describing life-duration. We find higher risk aversion for life duration, but the tradeoff method elicits similar curvature of utility. Apparently the higher risk aversion for life duration is due to more pronounced deviations from expected utility

A test of the predictive validity of non-linear QALY models using time trade-off utilities

This paper presents a test of the predictive validity of various classes of QALY models (i.e., linear, power and exponential models). We first estimated TTO utilities for 43 EQ-5D chronic health states and next these states were embedded in health profiles. The chronic TTO utilities were then used to predict the responses to TTO questions with health profiles. We find that the power QALY model clearly outperforms linear and exponential QALY models. Optimal power coefficient is 0.65. Our results suggest that TTO-based QALY calculations may be biased. This bias can be avoided using a power QALY model.Cost-utility analysis, QALYs, power QALY model, predictive validity, time tradeoff, Leex

Eliciting Utility for (Non)Expected Utility Preferences Using Invariance Transformations

This paper presents a methodology to determine the preferences of an individual facing risk in the framework of (non)-expected utility theory. When individual preference satisfies a given invariance property, his utility function is solution of a functional equation associated to a specific transformation. Conversely, there exist transformations characterizing any given utility function and its invariance property. More precisely, invariance with respect to two transformations uniquely determines the individual utility function. We provide examples of such transformations for CARA or CRRA utility, but also with any other utility specification and discuss the example of DARA and IRRA specifications.Utility theory; risk aversion, elicitation of preferences.

Risk Aversion in Cumulative Prospect Theory

This paper characterizes the conditions for risk aversion in cumulative prospect theory where risk aversion is defined in the strong sense (Rothshild Stiglitz 1970). Under weaker assumptions than differentiability we show that risk aversion implies convex weighting functions for gains and for losses but not necessarily a concave utility function. Also, we investigate the exact relationship between loss aversion and risk aversion. We illustrate the analysis by considering two special cases of cumulative prospect theory and show that risk aversion and convex utility may coexist.

Eliciting Utility for (Non)Expected Utility Preferences Using Invariance Transformations

This paper presents a methodology to determine the preferences of an individual facing risk in the framework of (non)-expected utility theory. When individual preference satisfies a given invariance property, his utility function is solution of a functional equation associated to a specific transformation. Conversely, there exist transformations characterizing any given utility function and its invariance property. More precisely, invariance with respect to two transformations uniquely determines the individual utility function. We provide examples of such transformations for CARA or CRRA utility, but also with any other utility specification and discuss the example of DARA and IRRA specifications

A Study in Preference Elicitation under Uncertainty

In many areas of Artificial Intelligence (AI), we are interested in helping people make better decisions. This help can result in two advantages. First, computers can process large amounts of data and perform quick calculations, leading to better decisions. Second, if a user does not have to think about some decisions, they have more time to focus on other things they find important. Since users' preferences are private, in order to make intelligent decisions, we need to elicit an accurate model of the users' preferences for different outcomes. We are specifically interested in outcomes involving a degree of risk or uncertainty. A common goal in AI preference elicitation is minimizing regret, or loss of utility. We are often interested in minimax regret, or minimizing the worst-case regret. This thesis examines three important aspects of preference elicitation and minimax regret. First, the standard elicitation process in AI assumes users' preferences follow the axioms of Expected Utility Theory (EUT). However, there is strong evidence from psychology that people may systematically deviate from EUT. Cumulative prospect theory (CPT) is an alternative model to expected utility theory which has been shown empirically to better explain humans' decision-making in risky settings. We show that the standard elicitation process can be incompatible with CPT. We develop a new elicitation process that is compatible with both CPT and minimax regret. Second, since minimax regret focuses on the worst-case regret, minimax regret is often an overly cautious estimate of the actual regret. As a result, using minimax regret can often create an unnecessarily long elicitation process. We create a new measure of regret that can be a more accurate estimate of the actual regret. Our measurement of regret is especially well suited for eliciting preferences from multiple users. Finally, we examine issues of multiattribute preferences. Multiattribute preferences provide a natural way for people to reason about preferences. Unfortunately, in the worst-case, the complexity of a user's preferences grows exponentially with respect to the number of attributes. Several models have been proposed to help create compact representations of multiattribute preferences. We compare both the worst-case and average-case relative compactness