Dear Lotfi, As I already said I agree completely with the idea of a graduate influence that events have on each other. Your concern is about the "perceptions" of these influences : you talk about "visibility" and "knowledge" which are obviously matter of degree but I go farther and I claim that even "objectively" (that is without an observer)things have a graduate influence. This one combines with our imperfect knowledge providing to the "perception of the causality" a deeper character of uncertainty : we have to evaluate 1)the level of the objective (natural) influence, 2)in the frame of our limited knowledge.
Let us take the raincoat problem (RP). There are many collateral events which "really" (objectively)influence the sale, say A1, A2,...AN, part of which, say M, are known by me (M<N). How can I model their influence ? In your opinion there are two kind of knowledge which play in the model: the "world knowledge"(wk) and the "case-based knowledge (cbk). I agree but in my mind both have to be assigned to each causal event (not to different events). Je m'explique. In the RP example wk is a general knowledge which means that in _general_ the sale of a merchandise depends upon the conditions which make it necessary. It is an _objective_ dependency that I know by experience (and by commonsense). I assign it a great weight of (objective)influence (wi). But not every merchandise depends with the same force upon its necessary conditions. If a chemical attack is announced the sale of gas mask will increase tremendously while an eclipse of the sun will increase in a smaller proportion the number of dark glasses sold. I have then to assign a strength (or force) of the dependency "conditions-sale" particular to my case (RP). This one represents, I think, the "case based influence" (cbi)applied to the "conditions-sale" dependency. I think that the influence of the event "rainy weather" on the sales is due to both factors: it is the cbi weighted by wi, in its simplest form, the product wi*cbi. Now you didn't talk about "influences" but about "knowledge" which translates the objective influences in the subjective realm. But where comes our subjective knowledge from ? You must agree that our source of knowledge is the objective world in which we live and which we perceive with more or less success. It follows that the objective wi becomes a subjective wk and cbi a subjective cbk. The factors of the causal model, wi and cbi are both graduate and so are the subjective factors wk and cbk. The wk differs from the wi and the cbk from the cbi because our knowledge is limited. But they approach each other as our knowledge increases. Each entity which influences the sale can be evaluated in the same manner. Let us take the increase in spending on advertising. It has a general (world) influence which, comparing with the preceding entity is lesser (so that wk-advertising < wk-rainy weather) but in the particular case of raincoat advertising, since I have a good service of advertising the strength cbk could be great. I have again to take the product of both (wk*cbk). I apply the same calculus to all the known dependencies (M). The more M approaches N (all the influent factors), the more my evaluation of the sales will be correct. The question which can be raised about the above proposal is: how can be evaluated all these factors ? First of all I have to remark that the value of a model doesn'lie in its numerical values but in its structure and the way in which this one models the reality. But if the model has to be useful we have to choose a scale of values, say between 0 and 1 for the wk and between -1 and +1 for the cbk (because of the events which oppose to the consequent, as for example an increase of the unemployment which has a _negative_ influence over the increase of the sales) and to assign values in this scale for each of the factors we consider. The influence of each factor upon the consequent can be (in its simplest form) the _algebraic_ sum of all the weighted strengths. In this way we can aggregate contributions of collateral events with positive or negative polarities (to answer to one of your remarks !). I think we experience such degrees of dependencies (causal or not) every time we have to take a decision and to valuate the occurrence of an uncertain event. Usually we perform such a analysis in our minds, rather in a qualitative form. I apologize for such a long mail but I am very interested in this topic. Marianne
