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The value of information and value of control calculations have long been two separate parts of a decision analyst's efforts to extract as much insight as possible from a decision model. This paper unifies these concepts as interventions that modify the structure of the original problem, which have two key properties, purity and quality. Purity is an idealization that leads to Howard canonical form, clarifies the definition of control intervention, and allows us to extend and correct the calculation of the value of control. Quality is a characteristic that leads to generic models of imperfect intervention, which, because of their equivalence to any pure intervention, prevent misguided recommendations when the value of a perfect intervention is high but the value of a somewhat imperfect intervention is low. Quality is a number between 0 and 1 that normalizes and allows comparison of imperfect interventions between applications having very different value scales.

AbstractMany companies set multiple performance targets for their managers and reward them on meeting a threshold value for each target or goal. Examples of such incentive structures abide in the managerial literature and in organizational settings. We show that this incentive structure, while popular, has two main problems: (i) it can induce managers who try to maximize the probability of meeting their performance targets to make decisions that are not compatible with expected utility maximizing decisions, and (ii) it may lead to trade‐offs among the performance objectives that are inconsistent with the corporate value function. In this paper, we propose a method to remedy these two problems, while retaining a target‐based incentive scheme. We define a multiattribute target as a deterministic region in the space of multiattribute outcomes that has two properties: (1) the probability that the outcome of a multiattribute lottery lies within the target region is equal to the expected utility of the lottery, and (2) all outcomes within the target region are preferred to all outcomes outside it. These two properties lead to a new quantity; which we call the 'value aspiration equivalent' that leads managers who maximize the probability of meeting their targets to simultaneously maximize the expected utility, and it also induces trade‐offs that are consistent with the decision maker's value function. Copyright © 2009 John Wiley & Sons, Ltd.

AbstractWe examine multiattribute decision problems where a value function is specified over the attributes of a decision problem, as is typically done in the deterministic phase of a decision analysis. When uncertainty is present, a utility function is assigned over the value function to represent the decision maker's risk attitude towards value, which we refer to as a value‐based approach. A fundamental result of using the value‐based approach is a closed form expression that relates the risk aversion functions of the individual attributes to the trade‐off functions between them. We call this relation utility transversality. The utility transversality relation asserts that once the value function is specified there is only one dimension of risk attitude in multiattribute decision problems. The construction of multiattribute utility functions using the value‐based approach provides the flexibility to model more general functional forms that do not require assumptions of utility independence. For example, we derive a new family of multiattribute utility functions that describes richer preference structures than the usual multilinear family. We also show that many classical results of utility theory, such as risk sharing and the notion of a corporate risk tolerance, can be derived simply from the utility transversality relations by appropriate choice of the value function. Copyright © 2007 John Wiley & Sons, Ltd.

Influence diagrams were first used in 1973 as a way to model political conflicts in the Persian Gulf and measure the value of information collected by the Defense Intelligence Agency. The number of scenarios for events in the region was too large to be represented as a conventional decision tree model. Influence diagrams were initially conceived as a way to create smaller, coalesced decision trees that required fewer probability assessments. However we found that they also facilitated communication between analysts, experts, and policy makers. Influence diagrams later became the basis for new ways of solving decision models.