Dynamic decision making without expected utility: An operational approach

An extension of the Becker proposition to non-expected utility theory

Perception du risque routier par les adultes rhodaniens – département du Rhône, France

Testing the Descriptive Performance of the Rank-Dependent Utility in the Domain of Health Profiles

This article, written by Senior Technology Editor Dennis Denney, contains highlights of paper SPE 127761, ’Probabilistic Modeling for Decision Support in Integrated Operations,’ by Martin Giese, University of Oslo, and Reidar B. Bratvold, SPE, University of Stavanger, prepared for the 2010 SPE Intelligent Energy Conference and Exhibition, Utrecht, Netherlands, 23-25 March. The paper has not been peer reviewed. A system was designed to assist operational decisions on the basis of real-time sensor readings in a typical scenario: While drilling close to the transition to a high-pressure formation, gas influx is observed. The technology used Bayesian networks and influence diagrams (IDs) to apply the method of decision analysis. The resulting ID was tested with a simulation. Introduction An assumption of integrated operations is that all information provided by the technology will help to make better decisions faster. But for this to happen, information must be presented in an accessible, useful, and decision-relevant format. Decision-analysis tools provide decision makers with logical and consistent recommendations based on the available data. This decision-analysis method was applied to a real case, representative of a typical scenario in drilling operations. The tool enabled good decisions consistently. However, effort is required and challenges exist in the modeling process along with problems regarding the way decision making is treated in the industry. Modeling and Solving A decision tree provides a graphical illustration of all the uncertainties, decisions, and payoffs associated with a decision situation. Although application of decision trees is intuitive for simple problems, the method loses its appeal for complex decisions. A symmetric decision tree grows exponentially with the number of variables in the decision domain, which often makes its use impractical. For complex decisions, the ID can provide a level of insight and transparency that cannot be achieved with the equivalent decision tree. The ID is a compact graphical-model representation for reasoning under uncertainty and was developed to assist structuring and analysis of complex decisions. The ID has two advantages—structuring and probabilistic evaluation. The structuring provides a graphical representation of the inter-relationships among the decision-basis elements (i.e., alternatives, information, and preferences), while the evaluation appraises the resulting decision structure and provides an assessment of its expected utility given the quantified decision basis. The representational framework of an ID captures the probabilistic relationships among decisions (alternatives), key uncertainties (information), and utilities (values or preferences). The ID model comprises four types of nodes. Decision nodes specify a set of alternatives. Chance nodes represent the key uncertainties in the decision domain. Deterministic nodes represent either constants or intermediate calculations. Value nodes represent the criteria used to make the decisions.

Influence diagrams are a powerful graphic representation for decision models, complementary to decision trees. Influence diagrams and decision trees are different graphic representations for the same underlying mathematical model and operations. This article describes the elements of an influence diagram, and shows several familiar decision problems represented as decision trees and as influence diagrams. The authors also contrast the information highlighted in each graphic representation, demonstrate how to calculate the expected utilities of decision alternatives modeled with an influence diagram, provide an overview of the conceptual basis of the solution algorithms that have been developed for influence diagrams, discuss the strengths and limitations of influence diagrams relative to decision trees, and describe the mathematical operations that are used to evaluate both decision trees and influence diagrams. They use clinical examples to illustrate the mathematical operations of the influence-diagram-evaluation algorithm; these operations are arc reversal, chance node removal by averaging, and decision node removal by policy determination. Influence diagrams may be helpful when problems have a high degree of conditional independence, when large models are needed, when communication of the probabilistic relationships is important, or when the analysis requires extensive Bayesian updating. The choice of graphic representation should be governed by convenience, and will depend on the problem being analyzed, on the experience of the analyst, and on the background of the consumers of the analysis.

Stochastic dominance permits a partial ordering of alternatives (probability distributions on consequences) based only on partial information about a decision maker’s utility function. Univariate stochastic dominance has been widely studied and applied, with general agreement on classes of utility functions for dominance of different degrees. Extensions to the multivariate case have received less attention and have used different classes of utility functions, some of which require strong assumptions about utility. The multivariate concave stochastic dominance we investigate is a natural extension of the stochastic order typically used in the univariate case and is consistent with a basic preference assumption. The corresponding utility functions are multivariate risk averse, and reversing the preference assumption allows us to investigate stochastic dominance for utility functions that are multivariate risk seeking. We provide insight into these two contrasting forms of stochastic dominance, develop some criteria to compare probability distributions (hence alternatives) via multivariate stochastic dominance, and illustrate how this dominance could be used in practice to identify inferior alternatives. Connections between our approach and dominance using different stochastic orders are discussed.

Multivariate Concave and Convex Stochastic Dominance

A new and more robust test of QALYs

In many theories of decision under risk (e.g., expected utility theory, rank-dependent utility theory, and prospect theory), the utility of a prospect is independent of other options in the choice set. The experiments presented here show a large effect of the available options, suggesting instead that prospects are valued relative to one another. The judged certainty equivalent for a prospect is strongly influenced by the options available. Similarly, the selection of a preferred prospect is strongly influenced by the prospects available. Alternative theories of decision under risk (e.g., the stochastic difference model, multialternative decision field theory, and range frequency theory), where prospects are valued relative to one another, can provide an account of these context effects.

Chapter 5 - Decision Analysis Fundamentals

Attitude towards risk is important to individual decision making. Rank-dependent utility theory is an appealing framework within which to study decision making under risk. This paper specifies Rank-Dependent Utility (RDU) models in the context of a stated choice experiment of commuter's risky route choice to (a) estimate willingness to pay for travel time, and (b) understand the risk attitudes of sampled respondents and their socioeconomic characteristics. We also allow for unobserved taste heterogeneity within an RDU framework using a mixed multinomial logit model. The findings provide a new set of empirical estimates of the value of travel time savings that allow for travel time variability combined into a single measure, referred to as the value of expected travel time savings.

TWO ALGORITHMS THAT LEARN DNF BY DISCOVERING RELEVANT FEATURES

For the problem of constructing a portfolio of finitely many assets whose return rates are described by a discrete joint distribution, we discuss an approach based on stochastic dominance. The portfolio return rate in this model is required to stochastically dominate a random benchmark, such as an index, or reference portfolio return. We formulate optimality conditions and duality relations for these models and construct equivalent optimization models with utility functions and law invariant coherent measures of risk. Two different formulations of the stochastic dominance constraint–primal and inverse–lead to two dual problems which involve von Neuman–Morgenstern utility functions for the primal formulation and rank dependent (or dual) utility functions for the inverse formulation. We also analyze relations of this approach to value at risk and conditional value at risk. Numerical illustration is provided.

Influence diagrams (IDs) are a popular framework representing a decision maker’s belief and preferences about a sequence of decisions to be made under uncertainty. The quantification of IDs which consists of defining conditional probabilities for chance nodes and utility functions for value nodes is not always obvious. In fact, decision makers cannot always provide exact utilities and in some cases, it is more convincible to describe utilities with interval values than precise ones. This paper is about extending general IDs (with precise single-valued parameters) into IDs with interval-valued utilities. Such extension is interesting because it enables one to model decision making processes in the situation that utilities are represented by interval values. This paper extend Gibbs sampling algorithm to the Bayesian network (BN) containing interval-valued probabilities for approximate inference and propose a method to evaluate IDs with interval-valued utilities based on the BN inference.

Stochastic dominance as an approach to uncertainty in cost accounting