Standards of Proof, Statistical Evidence, and the Stakes

Emad Atiq

In criminal cases, the prosecution bears the burden of proving the defendant’s guilt “beyond a reasonable doubt” (“BRD”). But it is not entirely clear what this standard requires. Courts routinely strike down attempts by prosecutors and judges to define (say, in terms of degrees of confidence or the probability of guilt) what counts as reasonable doubt. Moreover, pure statistical evidence is often deemed insufficient for proof beyond a reasonable doubt, even when such evidence suggests an extremely high probability that the defendant is guilty. The BRD standard’s resistance to definition or quantification invites explanation.

Sarah Moss offers an intriguing account: proof beyond a reasonable doubt requires knowledge, and knowledge is similarly resistant to definition and comes apart from probable truth. Moss’s analysis touches on several aspects of legal proof in both criminal and civil trials, but I’ll focus my comments on two suggestions that struck me as especially promising.

Drawing on observations by David Lewis, Moss argues that whether an agent knows P depends on whether the agent is able to rule out a set of “relevant” possibilities inconsistent with the truth of P. The “relevance” of a possibility is determined by, among other things, its salience in a given context. Hence, if belief beyond a reasonable doubt in the defendant’s guilt requires knowledge of the defendant’s guilt, the factfinder must rule out all and only those possibilities of innocence that are contextually relevant/salient. But this suggests that attempts to define “unreasonable doubt” by appealing to irrelevant possibilities (e.g., conspiracy theories involving the government) are counterproductive precisely because (a) such attempts make salient scenarios that the jury wouldn’t otherwise consider in the absence of the instruction, and (b) by making such scenarios salient, the instruction threatens to artificially raise the standard for knowing the defendant is guilty. As Moss puts it:

The problem is that the more we say in an effort to spell out the difference between reasonable and unreasonable doubts, the more we call attention to the possibilities that jurors shouldn’t be considering. As Lewis might have put it, the more we risk “destroying” the knowledge that would have sustained a conviction. (P. 7.)

Notably, the history of the BRD standard seems to support Moss’s explanation of its indefinability.¹

Are the relevant possibilities in a criminal trial—those that have a kind of “natural” salience for the factfinder—an arbitrary set? Not at all. Moss suggests that salience and relevance are partly determined by the stakes in a given context—that is, the practical consequences of believing a falsehood or failing to believe the truth. In fact, this feature of knowledge—its sensitivity to the stakes—plays a central role in Moss’s account of the law’s treatment of statistical evidence.

Moss begins by pointing out that the law doesn’t always deem pure statistical evidence insufficient for establishing guilt or liability (a fact sometimes obscured by the literature on statistical evidence). A paradigmatic example of insufficiency involves 25 attendees of a sports event who are charged with gatecrashing based on the evidence of only one ticket being sold. For any given individual, the odds that she gatecrashed are very high (0.96) but convicting her solely on that basis seems inappropriate despite the high odds, given the salient possibility that she is the one innocent person who bought a ticket. Moss contrasts the scenario with cases where corporate defendants are held civilly liable for causing harm to plaintiffs who purchase defective goods based solely on market share evidence (evidence that the defendant serves 90% of the demand for the goods).²

Moss suggests that this difference is explained by the fact that the stakes determine whether statistical evidence secures knowledge, and the stakes differ in the two scenarios. In the gatecrashers case, the possibility that any given defendant may have bought a ticket looms large, and so knowing that the defendant is guilty requires ruling out the possibility that she bought a ticket (which one cannot do based on statistical evidence alone). The possibility is salient precisely because the case highlights the fact that convicting all 25 individuals is guaranteed to result in a wrongful conviction and because convicting innocent persons is a very bad outcome. By contrast, the possibility that the corporate defendant might not have sold the precise good that caused the plaintiff’s injury does not loom as large, since imposing civil liability on innocent corporations does not seem as morally bad. Moreover, the structure of the market share cases does not guarantee an instance of wrongful liability.

There is much more to Moss’s fascinating discussion than I’ve captured in the above summary, and I encourage others to read Knowledge and Legal Proof in its entirety. But I’ll make three observations based on the points I’ve highlighted.

First, a central challenge for the view that legal proof requires knowledge (one that Moss considers) is the implication that, since knowledge is factive (one cannot know P if P is false), innocent defendants who are convicted of a crime could not possibly have been proven guilty beyond a reasonable doubt. That is, a jury cannot know—and, if Moss is right, believe beyond a reasonable doubt—that a defendant is guilty who happens to be innocent, no matter the strength of the evidence against him. This is so even if the jury might be justified in believing that the defendant is guilty. Moss largely concedes the implication and argues that it is not so theoretically costly, though I suspect intuitions will vary.

Second, some of Moss’s insights about the way that practical stakes influence a standard of proof seem separable from the question of whether legal proof requires knowledge. Suppose BRD invites the factfinder to have not knowledge, per se, but rather a level of confidence in the defendant’s guilt that is morally sufficient given the practical stakes (e.g., convicting the defendant of a specified crime, issuing a sentence of life without parole, and so on). Then, what BRD requires of the factfinder ends up being highly sensitive to context. And this context sensitivity makes offering a general, context-invariant definition of the standard difficult as well as misleading. Moreover, a view along these lines appears to have the same upshot for the gatecrashers case as Moss’s account. The moral stakes—in particular, the risk of a wrongful conviction—rule out convicting the 25 defendants based on pure statistical evidence. ³ Likewise, the view may permit the imposition of liability on corporate defendants based on pure market share data (because the moral stakes aren’t as high). I wonder whether there are reasons for preferring an account of legal proof in terms of knowledge over one that relies on something like “morally sufficient confidence” (the latter avoids the dicey implication I mentioned above).

Third, Moss’s arguments draw attention to features of our ordinary epistemic practices that lawmakers ought to consider but generally don’t. There is a growing body of literature pointing out that a failure to account for the stakes-sensitivity of the standards that govern belief-formation results in biased criminal procedures. If what counts as belief beyond a reasonable doubt depends partly on the practical stakes, then there are arguments to be made in favor of (for instance): (a) reconsidering the practice of shielding jurors from information about the consequences of conviction⁴; (b) greater flexibility in the forms of evidence we consider relevant to prosecuting different kinds of crime⁵; and (c) granting criminal defendants the constitutional right to argue that the jury should reconsider at sentencing any “residual” doubts it may have had during the conviction phase, since doubt that’s unreasonable in the context of a conviction may be quite reasonable in the context of sentencing (a right that the Supreme Court has consistently failed to recognize).⁶

1. The BRD standard was introduced at a time when juries were convinced by a popular literature on conscience that they would be risking their own salvation by falsely convicting, and so juries were willing to entertain any doubt, however fanciful, as a basis for exonerating defendants. On Moss’s telling, the BRD standard emerged to restrict the range of “relevant” possibilities and to lower the standard for knowing in the context of the criminal trial. (P. 9.)
2. Relying on her work on probabilistic knowledge, Moss interprets the civil standard of “proof by a preponderance of the evidence” in terms of knowledge of probable guilt.
3. One upshot of this view that distinguishes it from Moss’s is that if we ratchet up the number of defendants and gatecrashers, the probability of guilt for an arbitrary defendant may be high enough to be morally sufficient for conviction. But I’m not sure that’s a counterintuitive result. Another distinguishing feature of the view is that it explains our intuitions about the gatecrashers case not in terms of the statistical nature of the evidence, but rather in terms of the probability of innocence and its significance in light of the stakes.
4. Sarah Moss, Pragmatic Encroachment and Legal Proof, 30 Philosophical Issues 258 (2021).
5. Lewis Ross, Criminal Proof: Fixed or Flexible, Philosophical Quarterly (2023).
6. Emad Atiq, Reasonable Moral Doubt, 75 N.Y.U. L. Rev. 1373 (2022).