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AbstractA self‐reflecting signed order is a preference relation that compares relative likes and dislikes for items in a set X by jointly ordering X and a disjoint copy of X. If you would like Jones but not Smith appointed to a committee, and also think it more important to exclude Smith than include Jones, your self‐reflecting signed order records this information. We review basic representational theory for signed orders, then examine them when X is multiattributed. Axioms for additive measurement of multiattribute self‐reflecting signed orders are specified for several X‐structures.

It is well documented that the way a static choice task is "framed" can dramatically alter choice behavior, often leading to observable preference reversals. This framing effect appears to result from perceived changes in the nature or location of a person's initial reference point, but it is not clear how framing effects might generalize to performance on dynamic decision making tasks that are characterized by high workload, time constraints, risk, or stress. A study was conducted to examine the hypothesis that framing can introduce affective components to the decision making process and can influence, either favorably (positive frame) or adversely (negative frame), the implementation and use of decision making strategies in dynamic high-workload environments. Results indicated that negative frame participants were significantly impaired in developing and employing a simple optimal decision strategy relative to a positive frame group. Discussion focuses on implications of these results for models of dynamic decision making.

AbstractResearch indicates that selecting a strategy to best exploit a new technology is a complex decision‐making process. The task involves making a series of decisions with multiple alternatives, each to be evaluated by multiple criteria whose values have high levels of uncertainty. This paper presents a methodology for modelling a new technology decision using decision trees and an optimizing algorithm. A problem of a mining company considering the adoption of new technology is used to illustrate the decision‐making task and modelling methodology. A numerical solution to the case demonstrates the potential of the optimizing technique in strategy selection.

Portfolio decision analysis models support selection of a portfolio of projects with multiple objectives and limited resources. These models often rely on the additive-linear portfolio value function, although empirical evidence suggests that the underlying preference assumptions do not always hold. In this paper we relax these assumptions and derive a more general class of portfolio value functions that deploy symmetric multilinear functions to capture nonlinearities in the criterion-specific portfolio values. These values can be aggregated with an additive or a multilinear function, allowing a rich representation of preferences among the multiple objectives. We develop novel techniques for eliciting these value functions and also discuss the use of existing techniques that are often applied in practice. Furthermore, we demonstrate that the value functions can be maximized for problem sizes of practical relevance using an implicit enumeration algorithm or an approximate mixed-integer linear programming model. Application of the results is illustrated with an example in ecological conservation site selection.

AbstractTwo commonly used elicitation modes on strength of preference, equivalence and ratio judgments, were compared in an experiment. The result from the experiment showed that ratio judgments were less effective than equivalence judgments. Based on an iterative design for eliciting multiattribute preference structures, equivalence judgments outperformed ratio judgments in estimating single‐attribute measurable value functions, while being nearly more effective than ratio judgments in assessing multiattribute preference structures. The implications of the results from the experiment are that multiattribute decision‐making techniques should take advantage of the decision maker's inclination of making effective equivalence trade‐off judgments, and that useful techniques should be devised to incorporate different commonly used techniques, such as multiattribute utility theory and the Analytic Hierarchy Process, to elicit and consolidate equivalence trade‐off judgments.

AbstractStrategic investment decisions entail intertemporal resource allocation. Given relative resource availability and favourable environmental dynamics, effective strategic investment planning is a major determinant of overall corporate financial performance. This paper advances a methodology for optimizing intertemporal investment decisions through a consensus‐oriented process. This process entails identifying the strategic investment factors, their relative importance, and their assumed values relevant to the timing of each investment program. The paper also provides a methodology for determining the system's priority formulation as the model's objective function. This information generates an optimization matrix designated by investment programs and time. This matrix is then optimized through a hierarchical goal‐programming model that maximizes overall strategic investment decisions. The model was applied to a major capital investment program in the state of New York.RésuméLes décisions d'investissements stratégiques impliquent une allocation de ressources intertemporelles. étant donné la disponibilité relative des ressources et de bonnes dynamiques environnementales, une planification efficace des investissements stratégiques est le déterminant principal de l'ensemble des résultats financiers d'une entreprise. La présente recherche propose une méthodologie pour optimiser les décisions d'investissements intertemporels au moyen d'un processus orienté vers le consensus (consensus‐oriented). Ce processus comprend tout d'abord l'identification des facteurs d'investissements stratégiques, puis leur importance relative et leur valeur supposée en rapport avec l'échelonnage dans le temps de chaque programme d'investissement. Elle propose également une méthodologie pour déterminer la formulation de la priorité du système ainsi que la fonction objective du modèle. Cette information conduit à la construction d'une matrice d'optimisation par programmes et par temps d'investissement. Cette matrice est ensuite optimisée grǎce à un modèle de programmation à but hiérarchique qui maximise les décisions globales d'investissements stratégiques. Ce modèle à été appliqué à un programme d'investissement en immobilisations dans l'état de New York.

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.