A Parametric Representation of Additive Value Functions

This paper introduces a new parameter for measuring deterministic preference tradeoffs between pairs of attributes. In terms of this parameter, necessary and sufficient conditions for a value function to be additive are established. When additivity conditions are satisfied, a set of these parameters is shown to characterize the value function uniquely up to a set of scaling constants. Implications for assessment, for transforming a nonadditive representation into an additive one, and for multiattribute utility functions are presented.