Extending the method of mathematically controlled comparison to include numerical comparisons

The method of mathematically controlled comparison has been used for some time to determine which of two alternative regulatory designs is better according to specific quantitative criteria for functional effectiveness. In some cases, the results obtained using this technique are general and independent of parameter values and the answers are clear-cut. In others, the result might be general, but the demonstration is difficult and numerical results with specific parameter values can help to clarify the situation. In either case, numerical results with specific parameter values can also provide an answer to the question of how much larger the values might be. In contrast, a more ambiguous result is obtained when either of the alternatives can have the larger value for a given systemic property, depending on the specific values of the parameters. In any case, introduction of specific values for the parameters reduces the generality of the results. Therefore, we have been motivated to develop and apply statistical methods that would permit the use of numerical values for the parameters and yet retain some of the generality that makes mathematically controlled comparison so attractive.