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I guess I was more focused on parts of the paper that suggest that Clermont is not committing himself to the application of the MIN rule to non-vague cases.<br /><br />Of course, I can't compete with Woody and Marshall.Sam Ricklesshttps://www.blogger.com/profile/16662254589824229160noreply@blogger.comtag:blogger.com,1999:blog-36951752.post-49918802701459942702012-06-04T14:53:16.684-04:002012-06-04T14:53:16.684-04:00Sam: Thanks for the clarification. I agree that t...Sam: Thanks for the clarification. I agree that the paper only makes the point on which I'm focusing in passing, but I do think it's crucial. The relevant discussion is at p. 36, where he says: "If we can never convert the likelihood of a claim to one or zero, then all we can say is that the defendant is liable to a certain degree. Thus, when we can never know with certainty what happened, a likelihood of occurrence is not different from a degree of misfeasance: now likelihood of occurrence is not a classical probability, it is a fuzzy set."<br /><br />I read that to be saying, as I characterized the point in the blog post, that necessarily imperfect knowledge of some past event is equivalent to membership in a fuzzy set. And for my Annie Hall moment: I've discussed this with Kevin and he agrees that this is what he was saying. But now he's not so sure it's right and is working on a narrower version.Michael C. Dorfhttps://www.blogger.com/profile/02021009233932690926noreply@blogger.comtag:blogger.com,1999:blog-36951752.post-33745051262034303942012-06-04T14:31:34.787-04:002012-06-04T14:31:34.787-04:00Mike: I apologize for saying that I thought that o...Mike: I apologize for saying that I thought that one or both of you was confused. What I should have said instead is that I am confused. If I am responsible for confusing myself, then I owe you a second apology. But let me share with you briefly why I am confused.<br /><br />Here's a quote from Clermont's paper (p. 27): "For random uncertainty in a bivalent world, then the probabilistic operator will give the right answer...If one tries to deal with the variedly uncertain real world, a more inclusive approach to conjunction becomes generally appropriate. In a fuzzy world, the product rule retreats to a specialized role, applying only when the independent values of x and y happen to be randomly uncertain without being vague." [See also p. 36: "I therefore contend that the supposed paradoxes rest on applying a multiplicative rule of classical probability to a problem it cannot handle. It can handle only randomly uncertain estimates of independent events in a binary world, because it is built on the assumption of an excluded middle."]<br /><br />Applying this to your hypo, we should say that the product rule, rather than MIN, applies. This is because whether the defendant was the assailant and whether the pie came from the assailant are not vague issues. Fuzziness does not apply, so the MIN rule does not apply.<br /><br />On the other hand, on pp. 29-30, Clermont applies his thesis to the law. First, he considers simple cases involving one non-fuzzy element (identity) and one fuzzy element (fault). There he says that MIN applies. So far so good (at least on the assumption that fault is fuzzy, which is not clear to me, but never mind). But he then argues that MIN "still should apply even if both percentages measure only random uncertainty" (p. 30). Here's the argument.<br /><br />"A 60% chance of the weakest link [here: identity] represents the chance that all the other elements are more likely than not to exist. Because a 70% chance of fault is good enough for liability, we should not further account for that chance of finding complete fault. To multiply the chances, getting 42%, would be double counting, as it represents the chances of fully establishing both identity and fault. Establishing every element to 100% is not what the law calls for, and so the chances of doing so are irrelevant."<br /><br />There's something I'm not getting here. This argument assumes that what we are interested in is liability, not fault. But then the second element is whether the perpetrator is liable (not whether the perpetrator is at fault), and by hypothesis if a 70% chance of fault is sufficient for liability, then the probability of the perpetrator being liable is 1. So it's no wonder that the right answer here is .60 rather than .42. The product rule predicts this as much as the MIN rule does.<br /><br />Generalizing, it's not clear from this example what Clermont would say about your hypo (where there is no translation of degree of fault into all-or-nothing liability). In your case, you really have two non-fuzzy issues to resolve, and, according to what Clermont writes on p. 27, it sure looks like the product rule applies. Does he have an argument (other than the one on p. 30) that MIN applies to it instead? <br /><br />Again, maybe I'm missing something, but it's not clear to me whether, and if so how, Clermont's article applies fuzzy logic to the retrospective assessment of non-vague terms. <br /><br />Thanks for the reading recommendations. I'll take a look at them when I have a free moment.Sam Ricklesshttps://www.blogger.com/profile/16662254589824229160noreply@blogger.comtag:blogger.com,1999:blog-36951752.post-44535169453973190092012-06-04T07:55:34.801-04:002012-06-04T07:55:34.801-04:00Sam: Clermont is not confused, nor am I. I know t...Sam: Clermont is not confused, nor am I. I know that I am not confused about what Clermont is saying because I have read his paper carefully and talked to him about it. He confirms that I have correctly understood him. I know that Clermont himself is not confused because nothing you say in your comment contradicts what his paper says.<br /><br />Now, although Clermont is not confused, he may very well be wrong. Indeed, I think he probably is wrong. His crucial claim--and the one that I thought I had described clearly in my post but apparently not--is that while classical probability theory applies to making prospective predictions regarding non-vague terms, fuzzy logic applies not only to vague terms but also to making retrospective assessments of non-vague terms so long as we can never truly know what their values will turn out to have been. As I said in the post, I am skeptical of that claim, but there is no confusion here.<br /><br />Assuming that my skepticism is warranted and the product rule should apply, the question you raise (which I also raised in my post), how do we explain the failure of the legal system to employ the product rule? That question has generated a large literature, with some of the best contributions coming from Charlie Nesson, Ron Allen, and Alex Stein. They and others explore the possibilities you suggest--as well as others.Michael C. Dorfhttps://www.blogger.com/profile/02021009233932690926noreply@blogger.comtag:blogger.com,1999:blog-36951752.post-68139200391060249632012-06-04T01:00:59.356-04:002012-06-04T01:00:59.356-04:00I only skimmed the Clermont article, but I am thin...I only skimmed the Clermont article, but I am thinking that either he is confused or you are (or both). Maybe Clermont argues for the strong conclusion you describe, but what he says appears to establish no more than that the law's treatment of the standard of proof in civil cases that involve more than one element is explained by fuzzy logic *only when (at most?) one of the elements is vague*. Fuzzy logic applies to *vague* terms, such as "tall" and "heap". Fuzzy logic is consistent with, and fully accommodates, both classical logic and classical probability theory in the case of non-vague terms. Now Clermont may think that vagueness is everywhere. But it isn't. In your hypo, for example, it is not vague whether the defendant was the masked assailant and it is not vague whether the pie that struck the plaintiff's face came from the assailant or from the truck. In such a case, classical logic and classical probability theory apply. So if the probability that the defendant was the assailant is .60 and the probability that the pie came from the assailant is .60, then the probability that the pie came from the assailant and that the assailant was the defendant is .36. <br /><br />Clermont thinks that his MIN rule (which replaces the product rule) applies when there are two elements, one of which is vague. His example of a vague legal concept, I believe, is *fault*. But here I think the jury is out (forgive the pun). It may be that *fault* in many cases is not vaguely defined at all. The devil here is in the details. And then what are we supposed to do in cases in which only one element is vague and five elements are not? It seems to me that the product rule should apply to the non-vague elements. <br /><br />Clermont's main thesis is descriptive, not prescriptive, namely that the law actually embraced the tenets of fuzzy logic before logicians caught up with the law. This strikes me as very likely mistaken. I find one of the following two hypotheses far more likely: (1) those lawyers, legal theorists and judges who rejected the product rule for independent elements were simply innumerate (lawyers are smart, but how many of them at that time had received rigorous training in logic and probability theory?), or (2) those who rejected the product rule for independent elements did so for purely pragmatic reasons, judging that it would be too difficult for the typical juror to apply the product rule, or that jurors might nullify if faced with a rule that delivers results that appear to them to be counterintuitive (because of their own innumeracy, or because of Kahneman-Tversky effects).<br /><br />It seems to me that (2) is more likely. The reason is that the rule that jurors are asked to apply, wrongheaded as it is, (a) has a veneer of plausibility and (b) is far easier to apply in practice than the product rule. One reason for (b) is that all that a juror needs to determine about any one element is whether its probability is greater than .50; but the product rule requires the assignment of a numerical probability value (or a range of values) to each element.Sam Ricklesshttps://www.blogger.com/profile/16662254589824229160noreply@blogger.comtag:blogger.com,1999:blog-36951752.post-8453918691865874412012-06-03T17:16:12.419-04:002012-06-03T17:16:12.419-04:00To me, the court’s decision rests on the equal pro...To me, the court’s decision rests on the equal protection analysis; and federalism is merely a plus factor in this “unique case.” Obviously, the court did not think federalism concerns rose to the level of a 10th Amendment violation. Therefore, individual plaintiffs could have prevailed only on the EP ground – the sole claim they asserted in their lawsuit. <br /><br />The court’s language makes clear that EP is the basis of its ruling. 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