Decision making under certainty and with multiple objectives: multiattribute value functions

Summary In many situations, multiple objectives are relevant when making a decision. They require the evaluation of alternatives by means of a multiattribute value function. The simplest and most important multiattribute value function is the additive one. Using this value function, the (total) value of an alternative is computed as a weighted sum of (individual) values per attribute. The additive model can only be employed if certain independence conditions between the considered attributes are fulfilled. The weights of the attributes can reasonably be determined using the tradeoff method or the swing method. In the case of the trade-off method, objective weights are derived from the trade-off relationship between two attributes. In the case of the swing method, objective weights are computed from point valuations of different alternatives. The widely used direct-ratio method is fraught with problems. Attribute weights can only be reasonably interpreted with respect to the ranges of the attribute levels. There is no “per se” importance of particular attributes. If the decision maker is incapable of specifying exact weights, the optimal alternative might also be determined on the basis of imperfect information (e.g. the specification of an interval) or at least dominant alternatives can be eliminated. Sensitivity analyses can provide important information on acceptable changes of the objective weights without changing the optimal alternative. Individuals make systematic mistakes when trying to determine their attribute weights. In particular, they do not sufficiently take into account the attribute ranges (see 6. above) and overestimate the weight of an objective if it is split into multiple subordinate objectives.