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Health status is inherently a multiattribute construct. We examine multiattribute utility decompositions for the quality-adjusted life year (QALY) utility model commonly employed in medical decision and cost-effectiveness analyses. We consider several independence conditions on preference, including the classical notions of preferential independence and utility independence, as well as new related notions of standard-gamble independence and time-tradeoff independence. The latter conditions are helpful in simplifying standard-gamble utility assessment procedures and time-tradeoff assessment procedures in the presence of multiple health attributes. Under the QALY model, all these conditions are equivalent and result in a purely multiplicative decomposition of utility over health states.

This paper introduces the notion of a multiattribute utility tree. This graphical representation decomposes the von Neumann–Morgenstern utility of a multiattribute consequence into a sum of products of indifference probability assessments of binary gambles. The utility tree displays the sequence of gambles required to elicit the utility value of a consequence. In addition, it enables the analyst to conduct consistency checks on the indifference assessments provided by the decision maker and to change the order of the assessments based on her comfort level. Once the indifference assessments are provided, the utility value of a consequence can be obtained by direct rollback analysis. On a continuous domain, the utility tree decomposes the functional form of a multiattribute utility function into a sum of products of normalized conditional utility functions. Each attribute in the expansion is conditioned on the boundary values of the attributes expanded before it. This formulation provides a general method for deriving the functional form of a multiattribute utility function under a wide variety of conditions. It also leads to several new independence concepts such as "boundary independence," which is a weaker condition than utility independence, and "corner independence," which makes higher-order independence assertions. Reversing the order of the nodes in the tree relates several widely used notions of utility independence found in the literature.

We present a game-theoretic model to explore how uncertainty about terrorist preferences can affect optimal resource allocations for infrastructure protection. We consider a dynamic game with incomplete information, in which the defender chooses how to allocate her defensive resources, and then an attacker chooses which target to attack according to a multiattribute utility function. Our model constructs a prior distribution representing both defender uncertainty about the attacker weights on the various attributes in the attacker utility function and also defender ignorance about unobserved attributes that may be important to the attacker but have not been identified by the defender. The incorporation of unobserved attributes is a novel feature of our model and allows every target to have a positive prior probability of being attacked when the defender is sufficiently uncertain about the attacker preferences. In a dynamic environment, the defender then has an opportunity to jointly update her knowledge about both the attribute weights and unobserved attributes in a Bayesian manner, based on actual (or attempted) attacks observed in a previous period of the game. In general, defender uncertainty has a greater impact on defensive resource allocations in our model than in much of the previous work.

ABSTRACTThere have been a number of multiattribute decision aids developed to aid selection problems. Multiattribute value theory and the analytic hierarchy process are two commonly used techniques. Different systems can result in radically different conclusions if they inaccurately and inconsistently reflect the preference structure of decision makers, or if they are based on inappropriate theoretical models. This study examines the impact of the underlying theoretical model, the method in which preference information is elicited, and the structure of alternatives as influences on the results from using various decision aids. It was found that two systems based on the multiattribute value theory model were just as diverse in their conclusions as were results between AHP and the multiattribute value theory models. Therefore, accuracy of information reflecting decision maker preference is an important consideration. Feedback capable of assuring the decision maker that information provided is consistent is a necessary feature required of decision aids applied to selection problems. The study also found that the way in which information is elicited influenced the result more than did the underlying model. Exact numerical data for complex concepts such as attribute importance and alternative performance on attributes is not necessary, and elicitation procedures that are more natural for the user are likely to be more accurate.

AbstractAn adaptive approach for modelling individual‐level choice among multiattribute alternatives using the binary logit model is presented. The algorithm involves the collection of paired comparison data. In an effort to maximize the amount of information obtainable from each response, it is based on the experimental design criterion of D‐optimality. A simulation study indicates that the proposed algorithm outperforms other sequential selection approaches in terms of estimation accuracy and predictive efficiency under certain circumstances. The results appear to encourage the use of such an adaptive algorithm for individual‐level modelling in light of the potential reduction in data requirements without significant loss in predictive accuracy.

We describe a search problem in which a decision maker (DM) must select among sequentially encountered options. Each option is described by multiple attributes, and the value of an option is given by a separable function of its attribute values. However, the attribute values are not known with certainty, and can only be ascertained in a predefined order, at some fixed cost. During the search the DM can choose to select an option, purchase information about an attribute value, reject (permanently) the current option and continue the search, or terminate the search and accept a status quo outcome. We introduce a threshold policy for this search process, and prove the optimality of this policy for separable value functions. We then furnish a dynamic programming procedure for prescribing an optimal policy for this problem. Finally, we derive analytic solutions to some special cases of the problem, and present a case study that demonstrates a possible use of the proposed approach.

Many methods for creating surrogate swing weights based only on the rank order of the attributes are proposed to avoid the cost and effort of eliciting weights in multiattribute decision analysis. We explore empirically how well eight different methods perform based on a large sample of real-world elicited weights. We use the Euclidean distance from the elicited weights to judge the quality of the surrogate weights as well as three other metrics. The sum reciprocal method gives results, on average, statistically closest to the elicited weights for all metrics used. The equal ratio method using a fixed ratio of 0.716 performs just as well on three of the metrics. The rank sum method, the simplest and one of the oldest methods, performs generally next best. The rank order centroid method, which does well in simulation studies, performs relatively poorly in this evaluation using real-world data.

The construction of a representative multiattribute utility function is important in decision analysis. Existing methods focus mainly on constructions of utility functions on the whole domain of attributes. In some cases, decision makers may provide partial information on their local utility assessments. Therefore, it is a challenging and interesting task to construct utility functions that are compatible with local assessments provided by decision makers. This paper proposes the patchwork construction to accomplish this task. We first define a special local preference structure, the local utility independence and then discuss the patchwork construction that unifies local utility independence on different local domains. The utility function elicited by the patchwork approach under the local utility independence condition is named as the local-utility-independent utility function. Three types of local-utility-independent utility functions on three typical partitions are proposed. These local-utility-independent utility functions have concise and tractable functional forms and indicate intuitive preference structures while matching prior known local utility assessments. Furthermore, the preference structures implied by these three types of local-utility-independent utility functions have a close relationship with the n-switch independence. Sufficient and necessary conditions guaranteeing these local-utility-independent utility functions to indicate n-switch independence are provided, respectively. All three types of local-utility-independent utility functions also have an important application in the approximations of arbitrary utility functions when only some local assessments are provided. As approximations, they are robust and have high accuracy.