Measurement issues in the evaluation of projects in a project portfolio

A common problem in multicriteria decision analysis is how to value projects in a project portfolio. Recently, there has been some attention given to a practice whereby analysts define a value function on some criterion by setting 0 as the value of the worst project. In particular, Clemen and Smith have argued this practice is not sound as it gives different results from the case where projects are "priced out", and makes a strong implicit assumption about the value of not doing a project. Moreover, it can be shown easily that the optimal choice set is not invariant with respect to rescalings such as those induced by the addition of a new item to the choice set, hence rank reversal can occur when this procedure is used. We provide a measurement theoretic account of the phenomenon and show that whether the admissible transformations of the underlying scale are similarity or affine (or other) transformations depends on the precise details of the value model used. We also provide an axiomatic impossibility result which illustrates an incompatibility between an idea that inaction has a value of zero and the admissibility of constant scale translations. We use our analysis to comment on the view of Clemen and Smith that the baseline problem is best dealt with by assigning project-specific scores for not doing particular projects.