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 ;

Development of Interactive Support Systems for Multiobjective Decision Analysis under Uncertainty

This paper presents interactive multiobjective decision analysis support systems, called MIDASS, which is a newly developed interactive computer program for strategic use of expected utility theory. Decision analysis based on expected utility hypothesis is an established prescriptive approach for supporting business decisions under uncertainty, which embodies an effective procedure for seeking the best choice among alternatives. It is usually difficult, however, for the decision maker (DM) to apply it for the strategic use in the realistic business situations. MIDASS provides an integrated interactive computer system for supporting multiobjective decision analysis under uncertainty, which assists to derive an acceptable business solution for DM with the construction of his/her expected multiattribute utility fuction (EMUF).expected multiobjective decision analysis, MIDASS, expected multiattribute utility function (EMUF), intelligent decision support systems (IDSS).

Utility Independence of Multiattribute Utility Theory is Equivalent to Standard Sequence Invariance of Conjoint Measurement

Utility independence is a central condition in multiattribute utility theory, where attributes of outcomes are aggregated in the context of risk. The aggregation of attributes in the absence of risk is studied in conjoint measurement. In conjoint measurement, standard sequences have been widely used to empirically measure and test utility functions, and to theoretically analyze them. This paper shows that utility independence and standard sequences are closely related: utility independence is equivalent to a standard sequence invariance condition when applied to risk. This simple relation between two widely used conditions in adjacent fields of research is surprising and useful. It facilitates the testing of utility independence because standard sequences are flexible and can avoid cancelation biases that affect direct tests of utility independence. Extensions of our results to nonexpected utility models can now be provided easily. We discuss applications to the measurement of quality-adjusted life-years (QALY) in the health domain

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

The MODERE Model and The Economic Analysis of Farmers’ Decisions

The MODERE, the Ministry of the Environment Irrigation Decision Model, is a simulation tool which uses mathematical programming methods to reveal the implicit multiattribute objective function lying behind the observed cropping decision. The model takes different criteria such as profit maximization, risk aversion, avoidance of management complexities and so forth into account. In order to determine the feasible combination of attributes of this objective function the model considers the production possibility frontier explicitly as depending on market prices, policy incentives, availability of production factors, water irrigation facilities agronomic vocation and other constraints. Once calibrated the model becomes a powerful tool to assess the impact of different policy scenarios such as subsidies decoupling, water prices modifications, irrigation technique substitution and so on. The MODERE is a preference revelation model purposedly designed to be integrated in the Decision Support Platform which is used by the Spanish Ministry of the Environment to compare the policy scenarios which are relevant to assess the effectiveness and economic impact of the measures designed to reach the environmental objectives of the Water Framework Directive. The model is supported by a comprehensive data base built on purpose for its implementation covering almost all the Spanish Irrigation Districts with high spatial detail. This model is currently one of the important modules of the information and decision support systems developed by the Economic Analysis Unit of the Water Directorate at the Ministry of the Environment in Spain.Agricultural Economics, Water Economics, Simulated Models, Land Economics/Use, Political Economy, Research Methods/ Statistical Methods, Resource /Energy Economics and Policy,

Robustness of Multiple Objective Decision Analysis Preference Functions

This research investigated value and utility functions in multiobjective decision analysis to examine the relationship between them in a military decision making context. The impact of these differences was examined to improve implementation efficiency. The robustness of the decision model was examined with respect to the preference functions to reduce the time burden imposed on the decision maker. Data for decision making in a military context supports the distinction between value and utility functions. Relationships between value and utility functions and risk attitudes were found to be complex. Elicitation error was significantly smaller than the difference between value and utility functions. Risk attitudes were generally neither constant across the domain of the evaluation measure nor consistent between evaluation measures. An improved measure of differences between preference functions, the weighted root means square, is introduced and a goodness of fit criterion established. An improved measure of risk attitudes employing utility functions is developed. Response Surface Methodology was applied to improve the efficiency of decision analysis utility model applications through establishing the robustness of decision models to the preference functions. An algorithm was developed and employs this information to provide a hybrid value-utility model that offers increased elicitation efficiency

Local water markets for irrigation in southern Spain: A multicriteria approach

Spanish authorities have recently approved a new legislative framework for the creation of local water markets to improve allocative efficiency for this scarce resource. This paper analyses the potential impacts of the policy. A utility function for three groups of farmers was elicited, using a method that does not require interaction with the decision‐makers. Utility was measured as a function of the first two moments of the distribution of total gross margin. The utility functions were then used to simulate farmers' responses to changes in the price of water.Resource /Energy Economics and Policy,

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