tag:blogger.com,1999:blog-3726083.post6685835967426850656..comments2023-10-10T09:46:13.964-04:00Comments on Tillers on Evidence and Inference: Three Questions about the Conjunction ParadoxAnonymoushttp://www.blogger.com/profile/03081983465036974432noreply@blogger.comBlogger8125tag:blogger.com,1999:blog-3726083.post-59087000577574539142010-11-23T09:39:34.410-05:002010-11-23T09:39:34.410-05:00Stipulation: Dan = DonStipulation: Dan = DonAnonymoushttps://www.blogger.com/profile/03081983465036974432noreply@blogger.comtag:blogger.com,1999:blog-3726083.post-7822845359154463992010-11-22T11:44:19.203-05:002010-11-22T11:44:19.203-05:00Hello again. I see you have been busy during what ...Hello again. I see you have been busy during what we here in NZ have been calling "night time".<br /><br />I think your analysis is very helpful. Yes, the product rule applies to facts needed to establish an element. And yes, the chances of establishing all the elements can be no greater than the chance of establishing the least likely of them - in fact it should be the same as the least likely element.<br /><br />So I think I agree with all your steps. Didn't mean to suggest you agreed with the "paradox".<br /><br />I notice my name has become "Dan", no doubt because that's how you pronounce it? Or am I being unfair on Texans?Don Mathiashttp://www.nzcriminallaw.blogspot.comnoreply@blogger.comtag:blogger.com,1999:blog-3726083.post-46015093210456894222010-11-22T09:18:09.430-05:002010-11-22T09:18:09.430-05:00Step 3: If we wish to assess the chances of the co...Step 3: If we wish to assess the chances of the combination of F-1 that instantiates E-1 (Fact 1 instantiating Element 1), F-2 that instantiates E-2, ... F-n instantiating E-n, and if we think of "establishing F-1 ... F-n" as a series of possible events [e.g., chances of getting the jury in a civil action to declare that all F-1 ... F-2 are more probably than not true], we must ask, not what is the pre-existing probability of F-1, of F-2, etc., but, for example, what is the probability of F-1 [e.g., "jury decision that James is dead"] given the evidence available to the proponent (and given the evidence available to the opponent, given the rhetorical skills of the proponent and opponent, and a wide array of factors and circumstance).<br /><br />Step 4 (conclusion): If Step 3 is correct, a product rule of some kind may apply to the "probability of a claim," but the product rule that is applied won't look much like the one L.J. Cohen describes. For example, the probabilities of proving the individual instantiating facts -- F-1, etc. -- will vary enormously. And isn't that as it should be? The conjunction paradox is a parlor trick.<br /><br />N.B. Nothing important in the above argument changes if we focus on the chances of the underlying instantiating facts F-1...F-n. For example, the probability of "death of James" depends (in part) on the available evidence (which may, of course, be sparse initially; but that is neither here nor there).<br /><br />&&&&<br /><br />These thoughts of mine were precipitated by the above exchange with Dan Mathias.<br /><br />&&&&<br /><br />Is the solution this simple? Am I missing something?Anonymoushttps://www.blogger.com/profile/03081983465036974432noreply@blogger.comtag:blogger.com,1999:blog-3726083.post-48425018365597159972010-11-22T09:17:52.244-05:002010-11-22T09:17:52.244-05:00Progress(?) (at last!) toward a satisfying solutio...Progress(?) (at last!) toward a satisfying solution of L.J. Cohen's conjunction paradox:<br /><br />Step 1: The elements of a claim, charge, or affirmative defense are not events that have some probability of happening -- such as probability of .95 [for example] of "death" in murder cases or probability > .5 of "foreseeability" in negligence cases. Essential elements (to some legally-required level of persuasion) are not events or possible events at all. They are legal requirements for the validity of a claim, charge, or affirmative defense.<br /><br />Step 2: If the product rule is to be applied at all, it must be applied to the possible facts that a proponent seeks to establish in order to establish some legal claim, charge, or defense. But it is meaningless to ask, "What is the inherent probability of some element such as 'death.'" (It is no good, in short, to pretend that such possible facts are possible facts like the event "face 1 of an evenly-balanced six-sided die turns up".)<br />[go to next comment, below]Anonymoushttps://www.blogger.com/profile/03081983465036974432noreply@blogger.comtag:blogger.com,1999:blog-3726083.post-13666478923699109462010-11-22T09:17:05.142-05:002010-11-22T09:17:05.142-05:00Progress(?) (at last!) toward a satisfying solutio...Progress(?) (at last!) toward a satisfying solution of L.J. Cohen's conjunction paradox:<br /><br />Step 1: The elements of a claim, charge, or affirmative defense are not events that have some probability of happening -- such as probability of .95 [for example] of "death" in murder cases or probability > .5 of "foreseeability" in negligence cases. Essential elements (to some legally-required level of persuasion) are not events or possible events at all. They are legal requirements for the validity of a claim, charge, or affirmative defense.<br /><br />Step 2: If the product rule is to be applied at all, it must be applied to the possible facts that a proponent seeks to establish in order to establish some legal claim, charge, or defense. But it is meaningless to ask, "What is the inherent probability of some element such as 'death.'" (It is no good, in short, to pretend that such possible facts are possible facts like the event "face 1 of an evenly-balanced six-sided die turns up".)<br /><br />Step 3: If we wish to assess the chances of the combination of F-1 that instantiates E-1 (Fact 1 instantiating Element 1), F-2 that instantiates E-2, ... F-n instantiating E-n, and if we think of "establishing F-1 ... F-n" as a series of possible events [e.g., chances of getting the jury in a civil action to declare that all F-1 ... F-2 are more probably than not true], we must ask, not what is the pre-existing probability of F-1, of F-2, etc., but, for example, what is the probability of F-1 [e.g., "jury decision that James is dead"] given the evidence available to the proponent (and given the evidence available to the opponent, given the rhetorical skills of the proponent and opponent, and a wide array of factors and circumstance).<br /><br />Step 4 (conclusion): If Step 3 is correct, a product rule of some kind may apply to the "probability of a claim," but the product rule that is applied won't look much like the one L.J. Cohen describes. For example, the probabilities of proving the individual instantiating facts -- F-1, etc. -- will vary enormously. And isn't that as it should be? The conjunction paradox is a parlor trick.<br /><br />N.B. Nothing important in the above argument changes if we focus on the chances of the underlying instantiating facts F-1...F-n. For example, the probability of "death of James" depends (in part) on the available evidence (which may, of course, be sparse initially; but that is neither here nor there).<br /><br />&&&&<br /><br />These thoughts of mine were precipitated by the above exchange with Dan Mathias.<br /><br />&&&&<br /><br />Is the solution this simple? Am I missing something?Anonymoushttps://www.blogger.com/profile/03081983465036974432noreply@blogger.comtag:blogger.com,1999:blog-3726083.post-8055059708835467282010-11-22T08:06:42.120-05:002010-11-22T08:06:42.120-05:00The proposition "If that [proof of each eleme...The proposition "If that [proof of each element of a civil claim to a balance of the probabilities] is proved for each element, then liability is established. There is no need for the fact finder to ask, 'Gosh, what were the chances of the elements occurring together? because they did." does not respond to the question of the trial lawyer, "Gosh, what are the chances I can prove this claim?" but, then, neither does the application of the product rule as described by L.J. Cohen -- in part because the chances the lawyer's chance of persuading the jury to the requisite degree of probability that each element of the claim is valid depends in part on the evidence available to support (and oppose) the claim, and not on some chance taken out of the air -- say .5 or any other number -- that each element will be adjudged true or valid. Am I missing something? But the product rule (modified for dependencies) may apply - yes? - to the lawyer's calculation of the lawyer's chances of convincing the jury (by a preponderance, in a civil case) of the validity or truth of the various elements of the claim. Am I missing something? Of course factors other than evidence -- e.g., the pre-existing attitudes of the jurors, the rhetorical skills of the opposing lawyer, etc. -- will affect that assessment. In any event, L.J. Cohen's conjunction paradox turns out to be a parlor room trick.Anonymoushttps://www.blogger.com/profile/03081983465036974432noreply@blogger.comtag:blogger.com,1999:blog-3726083.post-68357287622819991482010-11-22T04:13:07.421-05:002010-11-22T04:13:07.421-05:00Don, interesting comment. N.B. I don't endorse...Don, interesting comment. N.B. I don't endorse the conjunction paradox. I state it. There is something wrong with it. I want to defeat. To that end: your following comment is interesting: "If that [proof of each element of a civil claim to a balance of the probabilities] is proved for each element, then liability is established. There is no need for the fact finder to ask, “Gosh, what were the chances of the elements occurring together?” because they did."Anonymoushttps://www.blogger.com/profile/03081983465036974432noreply@blogger.comtag:blogger.com,1999:blog-3726083.post-45506002509025990792010-11-21T17:19:06.606-05:002010-11-21T17:19:06.606-05:00It would be great if all our errors could be calle...It would be great if all our errors could be called paradoxes!<br /><br />Your questions presuppose that there is a conjunction paradox in the way legal decisions on liability are made. But there isn’t really (although I know it’s well recognised in the literature). Consider how the fact finder will address the liability question: if there are three elements to be proved, and if each (as you want to avoid discussing conditional probabilities) is independent of the others, then the fact finder will consider the evidence relevant to each in turn and will evaluate whether, in a civil case, each is proved on the balance of probabilities. If that is proved for each element, then liability is established. There is no need for the fact finder to ask, “Gosh, what were the chances of the elements occurring together?” because they did.<br /><br />There is nothing paradoxical about the probability that n independent events will occur together being less than the probability that (n – 1) of them will occur together if none of them are certain to occur. It accords with common sense.<br /><br />As to your questions:<br />1. The fact finder will assess the credibility of a witness by taking into account veracity, objectivity and perception in a way that is more like moving a point back and forth on a scale of credibility, than like multiplying probabilities.<br />2. I don’t know about the literature – just about everything has been said by someone sometime, surely (yes yes, “don’t call me Shirley”).<br />3. The elements of affirmative defences should be found by asking whether the evidence for them reaches the necessary standard of proof, again without any paradox arising.<br /><br />Where the elements are independent, legal fact finders go straight to the evidence on each element and assess its strength without reference to the probability that that evidence would exist jointly with the evidence for some other element.<br /><br />I think that before a huge argument starts about how to deal with the alleged paradox, it is appropriate to sort out whether there really is a paradox arising from the way facts are determined in law.Don Mathiashttp://www.nzcriminallaw.blogspot.comnoreply@blogger.com