On equivalent target-oriented formulations for multiattribute utility

Targets are used quite often as a management tool, and it has been argued that thinking in terms of targets may be more natural than thinking in terms of utilities. The standard expected-utility framework with a single attribute (such as money) and nondecreasing, bounded utility is equivalent to a target-oriented setting. A utility function, properly scaled, can be expressed as a cumulative distribution function (cdf) and related to the probability of meeting a target value. We consider whether the equivalence of the two approaches extends to the case of multiattribute utility. Our analysis shows that a multiattribute utility function cannot always be expressed in the form of a cumulative distribution function and, furthermore, cannot always be expressed in the form of a target-oriented utility function. However, in each case equivalence does hold for certain well-known classes of utility functions. In general, our results imply that although interpreting utility as a cdf and thinking about achieving targets works fine in the case of a single attribute, this approach should be used with caution in the multiattribute case, with cdf representations requiring more caution than target-oriented representations.