Decision-focused transformation of additive value models to improve communication

When using multiobjective decision analysis with an additive value/utility model, we may define local ranges of the value measures that are bounded by the set of alternatives, or we can define global ranges of the value measures that are bounded by our preferences for some future set of alternatives. Local value models use the full value space defined by the alternatives to distinguish between the alternatives. Global value models may identify new objectives and may help us develop better alternatives, but the alternatives do not usually span the full global value space. We present a mathematical transformation of a global value model's single-dimensional value functions and swing weights to a decision-focused value model using the global value, alternative scores, and transformation equations. When the transformation is appropriate, the decision-focused value model can provide useful distinctions to better communicate the trade-offs between alternatives. We prove that the transformation preserves the rank ordering of the alternatives, and we discuss the appropriate conditions for use.