Dear Lotfi, In addition to what I have sent you yesterday (to support your thesis of the "degree of influence" in a causal relation) I would like to take the example of the raincoats for which you ask a "causal" solution. Indeed, the present theories don't seem to be very adequate to solve it. The theory of "weighted strengths" seems more suitable. We have applied to a judicial case (Paul Snow and me)at Amsterdam and St.Louis meetings organized by Peter Tillers.
In short, when we have many factors which influence the occurrence of a given event, we englobe them in a fuzzy set of (known) causal influences;in order to calculate their influence, we have to evaluate two things: 1.Their importance (their "weight")in a _typical_ process of this kind (in other words the membership function of each element in the fuzzy set of causal influences. 2. The force (the "strength") of their influence in the _given_ process. The extent to which the effect is conditioned by all these factors can be evaluated (in a first approximation) by the summ of the weighted strengths of all the known causal factors. We have called this global influence the "propensity" of the effect to occur (but this is another story). If some of the causal factors are not directly related to the effect, a recursive (retroactive) influence can be calculated, as we have shown in the judicial case. In all the cases the occurrence of the effect is a "matter of degree" from the point of view of its causal dependency. In your example, the set of (known) causal influences (which play in every process of increasing sales) is formed by the increased spending on advertising, the adequate weather, bankruptcy of a competitor,improved styling, etc. On each of them we assign a weight in a numerical scale, according to our experience. Then we consider the real influence these factors have in our specific raincoat example (the strengths). Then we calculate the summ of the weighted strenghts. Being a subjective evaluation of an objective reality, there are many shortcomings which prevent an exact evaluation: -the set of causal factors may be incomplete (we ignore some of them); -the real importance they have in a typical process may be ignored too (we rely on our experience in the domain which is more or less sound); -the real influence they have in the given (real) process can be ignored too especially if these factors are hidden (non controllable). Some of these shortcomings can be avoided by "controllability", a key technique which enables one to study the quantitative influence of a cause on a given effect (Iwasaki proposed it some years ago in Artificial Intelligence).
