| 171 |
In other words we are ensuring that the equation R,P R,P is soluble for R provided that there exist R,R such that R,P >R,P >R,P
...The fifth condition is not limiting in any way but needs to be stated
...Definition 5
...Thus we require that variation in one while leaving the other constant gives a variation in effectiveness
...Finally we need a technical condition which will not be explained here,that is the Archimedean property for each component
...We now have six conditions on the relational structure <R x P,>>which in the theory of measurement are necessary and sufficient conditions for it to be an additive conjoint structure
...In our case we can therefore expect to find real valued functions [[Phi]]1 on R and [[Phi]]2 on P and a function F from Re x Re into Re,1:1 in each variable,such that,for all R,R [[propersubset]]R and P,P [[propersubset]]P we have:R,P >R,P <>F [[[Phi]]1 R,[[Phi]]2 P]>F [[[Phi]]1 R,[[Phi]]2 P]Note that although the same symbol >is used,the first is a binary relation on R x P,the second is the usual one on Re,the set of reals
...In other words there are numerical scales [[Phi]]i on the two components and a rule F for combining them such that the resultant measure preserves the qualitative ordering of effectiveness
... |
