When are additive models valid for evaluating proposed research?

This paper is concerned with a comparison of two broad classes of mathematical models, additive and multiplicative, for selecting the best among a number of competing project proposals addressed to a defined research objective. The analysis is predicated on the view that, though additive models are widely utilized, they are theoretically inferior to multiplicative ones. In an effort to more clearly understand when the use of additive models might be acceptable despite their logical flaws, conditions are investigated under which they yield results that are essentially equivalent to those produced by multiplicative models.