Dear Lotfi, First, thanks for your comments about my book (for other on the UAI mailing list, it just came out a few weeks ago with MIT Press.) It was a long gestation period; I'm glad it's finally out!
With regard to causality, Judea and I (just as many philosophers in the past few decades) focus on determining if A caused B, where A and B are two events that actually happened. We assume that we are given all the relevant information (in our case "relevant information" means everything that actually happened, together with the causal model, roughly speaking, the counterfactual information regarding what would have happened had things been different). There is no uncertainty here at all. It still turns out to be nontrivial to get a definition of what it means for A to be a cause of B in this case. Our definition is relative to a model. In one model A would be declared a cause of B; in a different model, it wouldn't. So for me to answer your raincoat examples, I'd need to know about all the relevant events and how they might have affected sales. You might say that by assuming I have all the relevant information, I have removed all the difficulty from the problem. All I can say is that (a) the problem still seems quite nontrivial even with this assumption, as many examples in law and philosophy show, and (b) if you're uncertaint about the model, you can have a probability on models (or use some other representation of uncertainty if you like) and determine how likely it is for A to be a cause of B. Finally, with regard to bivalence, the answer is yes: in a particular model, A is either a cause of B or its not. But note that B may have many causes; A1, A2, A3, and A4 can all be causes of B. Moreover, in the second paper I referred to, with Hana Chockler, we define a notion of "degree of responsibility" which is not bivalent. If A is not a cause of B, then A's degree of responsibility is 0; if A is a cause of B, then A's responsibility is positive, but can be anywhere in the interval (0,1]. For example, if there is a vote for the W wins 11-0, then each of the voters (according to our definition) is a cause of W's victory; however, they each have degree of responsibility 1/6 (since you have to change 5 votes before their votes become critical; the 6 in the denominator is 5+1). On the other hand, if the vote is 6-5, then all 6 voters for have degree of responsibility 1. This is a crude notion of responsibility; I'm currently working on an arguably more refined version with Tzachi Gilboa, an economist. However, it does have a number of reasonable properties. I hope that helps things a little. - -- Joe Lotfi A. Zadeh wrote: > Dear Joe: > > First, I should like to congratulate you on fathering a > beautiful baby. Your book " Reasoning About Uncertainty," is > outstanding in all respects. My hat off to you. I have not seen the > papers referred to in your message and naturally am curious about how > you would handle my "raincoats" example. Specifically, the question is > to what degree the increase in advertising causes the increase in > sales. Is causality a bivalent concept in your approach? If it is, then > I cannot see how you can address what is usually the case, namely, an > event is caused by a multiplicity of other events, some visible and some > not. > > With warm regards. > > Sincerely, > > Lotfi > > P.S. It is hard to formalize what sits in our heads when what sits in > our heads is hard to fathom. This is the problem with formalization of > causality .
