Where Judgment is used in Science and in Decision Making

In science, measurements of factors with different ratio scales are combined by means of formulas. The formulas apply within structures and involve variables and their relations. Each scale has a zero as an origin and an arbitrary unit applied uniformly in all measurements on that scale but the meaning of the unit remains elusive and only becomes well understood through much practice. The meaning and use of the outcome of any measurement on a ratio scale must in the end be interpreted according to the judgment of an expert as to how well it meets understanding and experience for the situation in which it is being applied or how well it satisfies laws of nature that are always there. Science derives results using numbers objectively, that is, everyone gets the same numbers, but interprets their significance subjectively, that is, how well they serve individual or group goals and understanding.

In decision making, however, because of the diversity of influences with which it is concerned, and the many decisions that may arise, there are no set laws that characterize in fine detail commonly encountered structures as there are in science. Understanding and familiarity with the situation is needed to structure a problem and judgments are needed to capture importance, preference or likelihood. With the Analytic Hierarchy Process (AHP) these judgments are expressed quantitatively on an absolute scale that denotes dominance of one element over another so that a best outcome can be derived by combining and trading off different factors or attributes. In the end after applying the AHP rules of composition a multidimensional scaling problem is reduced to a one-dimensional scale of priorities that are relative sets of numbers which belong to an absolute scale. So in the AHP significance is interpreted subjectively at the beginning of the process through judgments and priority numbers are derived from them objectively, that is, everyone would derive the same results from those judgments.

Priority scales are similar to probabilities; they are not the same as the ratio scales used in science. Ratio scales are like yardsticks. They have a starting point (a zero) and a unit. Priority scales do not. By the term “relative” we mean a priority scale is specially derived for a situation with its factors and alternatives and it is applicable only to that situation. It is not good for all situations and all time; when the situation changes the priorities may change. The ratios of AHP priorities are meaningful: for example, a priority of .50 is twice a priority of .25. In decision making the priority scales are derived objectively after subjective judgments are made, and they reflect the importance of the influences we considered. The process is the opposite of what we do in science when the subjectivity of interpreting what the final number means comes at the end. Of course there has to be validation of the decision process through many examples that show it works to make it a science based on reason, quantity and mathematics.

Finally, in science measurement is applied uniformly using the arbitrary unit from the very small to the very large. This cannot be done for all elements using judgment in decision making. Judgment can only be applied meaningfully to homogeneous groups of elements and when they are not they must be put into different clusters with a common pivot element from one cluster to the next to make it possible to compare them in each cluster and then combine their measurement according to increasing order of magnitude. In science there is no way to compare the significance of very small numbers with very large numbers in a systematic and meaningful way except by speaking of orders of magnitude. The meaning of the unit does not change from one order of magnitude to another, thus leaving interpretation in science subjective and loose.

In another blog we look forward to bringing the two together: science and mathematics with their Cartesian axes and decision making with its priorities that occur in relative form.