rion weight by the natural log of the criterion score. Thus, y = Priority Score, and, as in Chapter 4, Equation (1) is as follows:
The use of logarithms is neither intuitive nor familiar to most people, but it does express a natural way of thinking. The logarithmic transformation will accomplish the desired scaling, no matter what "natural" scaling is used. All that is necessary to implement this approach is for participants in the priority-setting process to agree that the relative weights represent the relative importance of a criterion. One can then measure the individual score components in any way one desires, as long as measurements are consistent across technologies for a criterion. Weights of 1 yield proportional increases in priority as a component increases. Weights of 2 increase a priority score 20 percent for each 10 percent increase in a criterion score.
To provide an example of how use of relative importance can eliminate worry about how the various components in the criterion scores are measured, let us consider the Phelps and Parente (1990) model. In this model, N = number of people treated annually, P = average cost per procedure performed, Q = average per-capita quantity, COV = the coefficient of variation for the procedure across regions, and e = the demand elasticity. The priority-setting index I for intervention j is:
If one assigns the relative importance weights for each element in Equation (5) as 1, 1, 1, 2, and -1 and takes the logarithm of each, then
Mathematically, the effect of changing the values of the variables on the right side of Equations (5) and (6) can be expressed in terms of percentages. Thus, a 10 percent increase in the number of people treated for intervention j (Nj) raises the value of Ij by 10 percent (and similarly for Pj and Qj); a 10 percent increase in the COVj increases the index by 20 percent; and a 10 percent increase in ej decreases the index by 10 percent.
Using logarithms is an approach that is intended to reflect relative place on a scale of importance. In producing priority scores for each candidate condition or technology, the relative ranking of each procedure will be the same, regardless of how each of the criterion scores is measured. The relative difference in priority scores similarly will be unaffected by changes in the scale used to measure any criterion score.