I have a taste for conundrums and paradoxes, and The Legal Analyst discusses lots of them. Here are a couple of fun examples involving problems of proof:
1. The conjunction paradox. The standard of proof in a civil lawsuit — a case arising from a car crash, for example — is the preponderance of the evidence: the plaintiff has to prove his case by a “more likely than not” standard. So imagine a case where there are three contested issues. Maybe it’s an accident case where the plaintiff has to prove (a) that the defendant was negligent, (b) that the negligence was the cause of the accident, and (c) that he has a good, truthful excuse for the fact that the claim appeared to be late under the statute of limitations. The jurors decide that they are around 60% sure that the plaintiff is right about the negligence claim, around 60% sure that he is right about causation, and around 60% sure that he is truthful in his story about the statute of limitations.
Should the plaintiff win this case? (Don’t be too sure of yourself!) Would the plaintiff win this case? In other words, how do you think the jury should and would be instructed to act if it reached these conclusions?
[UPDATE. The plaintiff will probably win, because jurors generally are told to find for the plaintiff so long as they think each element of the case is proven by a preponderance of the evidence. Yet the chance that all of the elements of the plaintiff's case are true is around 22%, which seems to flunk the preponderance standard, creating not only a paradox but some potentially serious problems of policy.
There are various replies to this — that sometimes these probabilities may not be independent, or that sometimes the jury may be choosing between only two possible stories, or that we can draw additional confidence from the fact that (say) six jurors, and not just one, all reached the same conclusions. But many students of the paradox nevertheless conclude that defendants are often held liable when they shouldn't be. See, e.g., Ronald J. Allen and Sarah A. Jehl, Burdens of Persuasion in Civil Cases: Algorithms v. Explanations, 2003 Mich. St. L. Rev. 893. These ideas are discussed more in the book.]
2. Proving the law. Suppose you offer to trade a gun to a drug dealer for a couple of ounces of cocaine. The seller accepts, then announces that he is an undercover FBI agent and leads you off to jail. You are prosecuted under a statute that gives many years of prison to anyone who “uses" a firearm in relation to a drug trafficking offense.
You have two lines of defense. You plan to deny that you ever really offered the gun to the undercover agent; to overcome this denial, the government will have to prove its case beyond a reasonable doubt. So far, so good. But you also have another argument: that the prosecution has misread the statute. You don't “use” a gun if you try to barter it; you only "use" a gun (you plan to argue) by putting it to work as a weapon.
There are lively arguments to make either way on this issue (and I’m not really looking for them here). Assume that the judge thinks it’s close but decides that the statute does cover your case. Well, but wait — how sure must the judge be? Is it necessary that he be convinced beyond a reasonable doubt? If not, why not? (I consider the second question — why — the more difficult and interesting part.)
[UPDATE. The puzzle is that we require a very high level of certainty when it comes to facts in criminal cases, but not when it comes to law; we are willing to award long prison sentences, or for that matter death sentences, on the basis of interpretative decisions that everyone knows may be quite doubtful. Indeed, judges do not generally confess to using any standard of proof or confidence at all when they interpret the law, with the partial, occasional, and unreliable exception of the rule of lenity (the use of which I discuss here).
The best explanation of this state of affairs, perhaps, is that if we required any particular level of confidence before a judge could state the law, there might be many situations where there ends up being no law because there is no interpretation that satisfies the standard of proof. This could have some rather untoward consequences. These ideas, again, are discussed in the book; the most interesting longer treatments, I think, are Gary Lawson, Proving the Law, 86 Nw. U. L. Rev. 859 (1992); Larry Alexander, Proving the Law: Not Proven, 86 Nw. U. L. Rev. 905 (1992).]
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Is there any empirical evidence about the relationship between jurors' (or people in general's) probability estimates of various circumstances and their probability estimates of conjunctions of those circumstances?
Christopher M above addresses your question. The issue is whether the probabilities are independent. It is only mathematically proper to multiply probabilities for independent events.
The three elements here are usually not going to be independent events, since a good portion of the uncertainty will have to do with witness credibility. And witnesses credibility with respect to issue X is not usually independent to his credibility with respect to issue Y.
IANAL, but it seems to me that, as opposed to a question of fact, there is no requirement that a question of law needs to be "proved beyond a reasonable doubt". As long as he (probably) thinks the law applies, he is free to apply it.
It sounds to me a great issue to raise on appeal, however.
p.s. Isn't bartering a gun (without doing to requisite background checks, etc) a crime in itself?
I think the answer is the judge must be convinced of the legal issue by a mere perponderence of certainty.
My thoughts go like this. Everyone knows the Hand inequality B < PL for imposing a duty to make safe. The procedural due process Matthews case essentially uses the same test for LifeLibertyProperty deprivations (importance of right involved and liklihood of improper depravation of that right absent more procedure versus burden on government - yes that's BPL). The same test justifies a "beyond a reasonable doubt" fact-finder burden in criminal cases because the right taken in criminal cases is much heavier than in civil, and the liklihood of factfinder error is, if not roughly the same, a little greater in criminal cases. Setting the standard of proof higher for the factfinder in criminal cases balances both of these increased weights on the other side of the equation.
For issues of law, the same heavier right is at stake in criminal cases compared to civil cases. However, the liklihood of law-decider (judge) error is the same, if not less, than in civil cases (if anything, because criminal statues are subject to greater constitutional clarity standards). This calculus would impose a only a slightly higher burden of legal certainty on the judge in criminal cases, but not a "beyond a reasonable doubt" level of certainty. Further, because criminal defendents get more levels of law-decider review (habeus, bifurcation, etc) than civil defendants, this increased review burden serves to further balance out the equation, bringing the required level of certainty in legal issues much closer to a mere perponderence.
The issue is not merely one of facts, but rather uncertainty about the facts. Presumably, if the facts were known with 100% certainty, the case would be easy. If facts are not uncertain, then there are no probabilities whatsoever.
The question then is what causes uncertainty. Not having direct access to the facts is usually what causes uncertainty. So, we often have to rely on witnesses to determine what the facts are. But then what do you do when you have conflicting testimony? Then it is often a matter of witness credibility for reasons of memory, physical ability (eyesight, hearing, smelling etc.) or honesty.
Issues of witness credibility are not usually independent, even as to facts that are independent. A witness who is willing to lie or has a self-serving memory about X is more likely to lie or have a self-serving memory about Y. A witness with a faulty memory about X is more likely to have a faulty memory about Y. And so on.
It is usually the case that probabilities are not independent, even when the facts themselves are independent.
To add another twist. With accidents, the facts themselves are not likely to be independent. Whether a given action is negligent is likely to be highly related to whether that action is likely to cause harm to another. So, even negligence and causation, ignoring issues of witness credibility for now, are not independent. Now consider the statute of limitations issue. Certainly, a plaintiff willing to lie or who have a self-serving memory about this issue is more likely to be lying or have a self-serving memory about the circumstances surrounding an accident and their descriptions of the defendants actions.
So, to answer the question proposed by Mr. Farnsworth, should the plaintiff win their case? The answer is a definite maybe. It depends on the degree to which our uncertainty is based on independent versus dependent factors.
What do jurors do in real life? Well, for one, jurors in real life do not understand probability theory. So, obviously, they do not consider these issues.
Does that matter? Probably not. All the probabilities that Mr. Farnsworth uses are completely made up. They are purely subjective probabilities that are not subject to empirical verification. You can not run trials with a particular witnesses credibility to determine that they lie or have a self-serving memory approximately 60% of the time. Certainly, such probabilities, even if they were empirically possible to produce, would not be avialable to a jury in a trial. The only way to get such numbers would be to pull them out of your ass (excuse the expression). That jurors would not properly assess made up probabilities is not a big concern to me. Especially since, for the reasons I have noted above, even an expert in probability theory would not be able to decide the case based on the limited information Mr. Farnsworth provided, even if the probabilities were available and 100% certain to be accurate.
2. The prosecution must prove the elements of the offense beyond a reasonable doubt. It need not prove what those elements are.
With modern summary judgment practice, it would be a pretty rare case where the issue of statute of limitations is submitted to the jury. Maybe something having to do with the discovery rule, i.e. when the plaintiff knew or should have known her cause of action had accrued. But even then, it would probably be disposed of one way or another via summary judgment.
I had assumed, based on the phrasing of the question, that the facts were objectively independent (but that the jurors might not recognize that). Your reasoning is right, of course; if there is an X factor (presumably plaintiff credibility), it could most certainly indicate that the three questions were related, and thus change the nature of the result.
Usually those different standards reflect different distributions of power for different types of issues: We might be comfortable giving a court the power to say what the law is generally but feel less comfortable giving the court the power to say what the facts are in a specific case.
Psychologically, however, people are hardwired with several logically invalid tendencies. One of those tendencies would result in jurors wrongly considering the probability of the case as a whole much as they would wrongly try to consider the probability of four coin flips all resulting in heads. "The plaintiff's argument about A sounds plausible as does his case for B and C but there is a fair degree of likelihood that each of them are false so, really, what are the odds of A, B, and C *all* being true?"
For the second case, I would think that the "reasonable doubt" requirement only applies to the defendant's guilt as a matter of fact and not to the judge's (or jury's, since the jury is the ultimate arbiter of both fact and law) belief in the interpretation of the law that they are using. Certainly they must believe in the truth of the interpretation they are using but don't need such a degree of certainty as to believe that there are no other possible reasonable interpretations of the law in question. Thus the judge and jury only need justified belief in the interpretation of the law that they are applying.
1. David Price has a plausible explanation--his understanding of the question is that it is *really* asking the jury for three separate findings. The jury should find A if it believes P(A)>50%, it should find B if it believes P(B)>50%, and it should find C if it believes P(C)>50%; thus, the plaintiff prevails. Others argue that the jury must decide whether the probability of all three events occurring simultaneously is > 50%, making the victor less clear.
Why should we turn this into a metaphysical argument about whether Farnsworth's question *really* resolves to one horn of the dilemma or the other, though? This is only paradoxical because the original question is ambiguous; the solution is for the questioner to be more clear about what he means, not to debate what is *really* meant by the ambiguous question.
The only other way to resolve it is by making historical arguments or policy arguments, but that's never a satisfying way to resolve hypothetical logical paradoxes. (However, I think this is how we should solve ambiguities like this in practice.)
2. I would make the same point about #2. Does the heavy burden of proof apply only to the fact-finding or to interpretations of the relevant statutes as well?
Well, by the terms of the question, it's not clear. I suspect this ambiguity can only be resolved with reference to policy arguments or historical arguments; we're not going to get very far if we argue about what "proof beyond a reasonable doubt" *really* means as a metaphysical matter.
I suspect the point of this exercise is to point out that some questions which appear to be paradoxes aren't actually paradoxes, but are just ambiguous. Resolve the ambiguity by being more precise in defining terms. Or, when it's too late to change the terms, decide based on history or policy preferences, and then stick to that decision later.
AnonVCfan and Prof. Kerr: The issue in the second question is this: We require proof of the facts beyond a reasonable doubt because we think it's really important not to wrongfully convict someone. But if we think that, then why would we allow someone to be convicted when it's less than entirely clear that the criminal statute covers their actions?
There are plausible answers, but Prof. Kerr's doesn't seem adequate. Distribution of power between judge and jury is not the issue here: whether the factfinder is a judge or jury, we impose a "reasonable doubt" standard on the facts but only a preponderance standard on the law (the rule of lenity aside). Why? Either way, we're not sure that the defendant has actually committed a crime.
There's a much larger paradox than the difference in the burden of proof between questions of law and questions of fact in criminal cases. "Ignorance of the law is no excuse", even when it's impossible to know the law because experts in the field can argue endlessly about what it means, and the law is not settled until someone has allegedly violated it and the question is litigated all the way to the Supreme Court - and then, if the justices go 5-4 against the defendant, he goes to prison. The defendant may be a middle-school dropout with an IQ of 80, but he's held responsible for understanding a law that the best legal minds disagree about.
In problem 1, the jury is asked to decide a statute of limitations issue. Why is that for the jury? Isn't the limitations defense a matter of law, for the judge?
Thanks. Sorry if this is obvious to the other lawyers. In my defense, I'm a crim. pro. guy.
for instance: given the evidence presented in, say a car accident case, I could imagine thinking the driver was at fault, thinking the driver wasn't at fault, and not being sure. I really have no sense of how to consider whether, either the driver was 60% at fault, or that I am 60% confident that the driver was at fault. It simply makes no sense to me. It seems to me the whole 'preponderance' or '60%' test is really a scientific-sounding means of saying 'if you aren't sure who is at fault, what does your gut say?' (which, in my mind, shouldn't be legally defensible).
I realize this question may be more philosophical than you intend, but every time I hear of a decisionmaking standard in a civil case (this example: the OJ Simpson civil suit is another one), I really can't get past my discomfort with the concept to wonder about other issues.
sk
In this particular case, I really didn't mean to start a debate about whether either of the issues I've raised is an authentic "paradox." Please pardon my casual usage of the word; I can't see the point in fussing much over it, and "conjunction paradox" is a standard term in the literature. I'm really more interested in the substantive question of why we do things the way we do.
I see an interesting puzzle to think about in the discrepancy between the high confidence we require in factual judgments in criminal cases and the low confidence we require for the legal variety. Orin, who I admire, does not; this may just suggest that he's less easily amused than I am. Vive la difference! If you like thinking about that sort of thing, the book should interest you; if not, perhaps not. But check out the sample chapters to get a better sense of this.
In any event, I do appreciate the time many of you took to speculate or comment on the questions I raised this week. I hope the book will provide fun reading for some of you. And no (for the benefit of whoever kept asking), I'm no relation to Allan Farnsworth. Best, WF
If the plaintiff had to prove two elements, he would win if the jury were 71% sure of each element; three elements, 80% sure; four elements, 85% certain; and five elements, 88% certain.
You quickly arrive at the point where a plaintiff would need to prove each element or each fact by clear and convincing evidence (maybe 80ish% certain?) to win by a preponderance of the evidence. The biggest variable in a trial would be the number of elements in the claim at issue.
It's not much of a puzzle. We have a higher standard for that which is capable of being known with a much greater degree of certainty.
On the one hand we have facts, which by definition posses the potential for being known with a high (but not absolute) degree of certainty. On the other hand we have texts, which are open to a near-infinite number of differing interpretations. We can have opinions, sometimes very strong ones, regarding the relative merits of interpretations but it is impossible to 'know' which interpretation of a text is right. By many theories of language there simply is no single correct interpretation.