Officially, the court’s rationale for this policy of refusing to explain what “reasonable doubt” means hinges on its holding that BARD’s meaning is self-evident and that any attempt to define it would only obscure jurors’ preexisting comprehension of the difference between reasonable and unreasonable doubts (one can perhaps be forgiven for thinking that the fact that jurors frequently ask for clarification of BARD gives the lie to the idea that its meaning is self-evident). What is more likely to be the real reason that American courts discourage judges from defining BARD is that trial judges have sometimes botched the explanation badly and created a situation where appellate courts have felt bound to overturn a conviction because the judge defined reasonable doubt in a way that higher courts found to be insufficiently demanding. In some jurisdictions (Oklahoma for instance), any effort by the judge to define BARD is regarded as a basis for throwing out the verdict. The case establishing that, in Oklahoma, any explanation of “reasonable doubt” is a reversible error is Pannell v. Oklahoma (1982) 640 P.2d: 568. For Wyoming’s similar rule, see Cosco v. Wyoming (1974) 521 P.2d: 1345>. Jurors, then, are left to their own devices to figure out what the standard of proof means. That poses two acute puzzles: a) do different jurors and juries understand it more or less the same way? and b) does such consensus as jurors are able to arrive at reflect a sound grasp of how robust and exacting the court expects a proof leading to a conviction should be?

The problem, then, is not only one of fairness between trials. If jurors in a particular case bring into the jury room very disparate conceptions of the rigorousness of BARD, we might well expect that 12 jurors—confronted with the same evidence—might fail to reach unanimity about whether guilt has been proved. In some jurisdictions (e.g., California), mistrials—due chiefly to lack of juror unanimity—occur in about 12 percent of the cases that go to trial (in certain California counties (Alameda and San Francisco), the three-year average for hung juries is higher than 20 percent (Hannaford-Agor et al. 2002: 7, table 1.1)). If one in every seven trials ends in a hung jury, we are faced with formidable economic and emotional inefficiencies, not only for the defendant but also for the state.

Under such circumstances, it seems difficult to escape the conclusion that a standard of proof exists in name only. BARD is the nominal standard and the phrase “proof beyond a reasonable doubt” is repeated by the judge on multiple occasions in every criminal trial, but its meaning is left entirely to the triers of fact to decipher for themselves. One might conjecture that the presumption of innocence could be called into play in stressing the idea that an acquittal should be the default verdict, absent a robust proof of guilt. Yet this remedy is to little avail, absent informing jurors what sort of proof is required to defeat the presumption of innocence. It is specifically the standard of proof that should identify when that presumption has been defeated. Clearly, BARD—given its failure to clearly differentiate between reasonable doubts and unreasonable ones—does little to ameliorate this conundrum. The presumption of innocence merely says that a defendant should be acquitted unless his guilt has been proved to the relevant standard; it entails nothing whatever about what constitutes such a proof nor even about whether such a proof need be strong or weak.

Clearly, given the centrality of the standard of proof to reaching a just verdict, it seems that we should try to put this situation right by formulating a standard of proof that, unlike BARD, is clear, capable of being explained to, and understood by, jurors and justified (in the sense of capturing our value judgments about the respective costs of errors). The English, who first conceived BARD as a legal standard of proof in the late eighteenth century, have already abandoned it; the bad news is that they have replaced it by an equally unclear standard: “being sure of the guilt of a defendant.” This suffers from all of the arbitrariness of BARD and at least part of the latter’s ambiguity, since it leaves wholly unspecified how sure is “sure.”

The BARD rule is preposterous as a standard of proof because of this subjectivity. Imagine saying to a mathematician that he has proved a certain theorem so long as he has no lingering doubts about it or saying to a scientist that he has proven a certain hypothesis so long as he is convinced that it is highly probable. Such advice would properly be considered a joke in very poor taste. Both the mathematician and the scientist must show their peers that their results have been derived using widely recognized and demanding deductive or inductive proof procedures. The fact that someone has “proved” something to his own satisfaction and that she has no lingering doubts about it leaves wholly open the question whether her “proofs” are legitimate. Similarly, the fact that a juror is strongly persuaded that a defendant committed the crime should impress none of her fellow jurors unless we know something about the kinds of inferences that juror used in arriving at that inculpatory conclusion.

In many legal systems, the trier of fact is expected to submit a written opinion in which she lays out precisely the inferences that led her from the evidence presented in the case to her verdict. All the world (and especially the appellate courts) can see for themselves whether the reasoning was cogent. In Anglo-Saxon trials, by contrast, the jurors are neither informed beforehand about what sorts of inferences they should use nor expected after the fact to articulate their reasoning. All they must attest to, in the case of a conviction, is that they have no lingering “reasonable doubts.”

If this sort of wholesale subjectivity is to be minimized and if we are to avoid a situation in which a juror can report that he has no reasonable doubts even when he has reasoned badly, it would be preferable to have a standard of proof that provided something more concrete by way of describing or exhibiting the features that a legitimate inference to guilt should exhibit. In the next section, I will describe two distinct proposals that have been made recently for informing jurors about the kinds of inference that would legitimately sustain a guilty verdict. Each aims to replace BARD by a standard of proof that focuses on the structure of the arguments jurors need to construct to arrive legitimately at a guilty verdict rather than, as BARD does, on the subjective confidence that jurors should have.

Rethinking the Standard of Proof

A second suggestion for a standard of proof was proposed by the author in his book Truth, Error, and Criminal Law (2006, see esp. ch. 3). It rests on the insight emerging from statistics and the philosophy of science that a powerful test of the truth of any empirical hypothesis, H, is its ability to account for apparent facts or data that would seem utterly unintelligible if H were false. Applied to the legal context, the idea would be that the prosecution’s claim that the defendant is guilty acquires high plausibility just to the extent that some pertinent evidence has been established as prima facie true that can be readily accounted for if the defendant is guilty but that would be highly unexpected if the defendant were innocent. If some of the important features of the case that the guilt hypothesis can make sense of are likewise compatible with a hypothesis of innocence, then the prosecution’s case is insufficiently strong to warrant a conviction. Likewise, if there are any pertinent facts that make sense only on the hypothesis of innocence, then an acquittal is called for. In short, this proposed standard demands that a conviction is warranted if and only if a) the hypothesis of guilt can explain most of the salient facts of the case; and b) the innocence hypothesis can account for no important evidence that is inexplicable on the guilt hypothesis. Just as we say that a scientific hypothesis that makes no surprising, corroborated predictions—unanticipated by its rivals—is not very credible, so a guilt hypothesis not backed up by very surprising evidence in its favor lacks the strong empirical support that should be a sine qua non for a conviction.

While BARD is agnostic about the kinds of inferences necessary for a conviction, American legal practice has often toyed with jury instructions for filling that gap. For instance, until half a century ago, when the court abandoned its time-honored distinction between direct proof and circumstantial proof, jurors in cases involving circumstantial evidence often received this instruction:

However, a finding of guilt as to any crime may not be based on circumstantial evidence unless the proved circumstances are not only (1) consistent with the theory that the defendant is guilty of the crime, but (2) cannot be reconciled with any other rational conclusion… Also, if the circumstantial evidence permits two reasonable interpretations, one of which points to the defend ant’s guilt and the other to innocence, you must adopt that interpretation that points to the defendant’s innocence, and reject that interpretation that points to guilt.

(CALJIC 2.01)

Arguably, this instruction would be as appropriate for noncircumstantial cases as for circumstantial ones.

The Distributionist Conundrum

The hardest of those challenges emerges as soon as we realize that—apart from clarity and a focus on exemplary patterns of inference—there is a third crucial constraint in play in the design of an acceptable criminal