Puzzles About Proof.

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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