In the run-up to the Senate confirmation vote on Justice Brett Kavanaugh, those opposing the nominee soon developed the following argument:

1. “If Brett Kavanaugh assaulted Christine Blasey Ford, he should disqualified.”
2. “Seeing as this is a job interview and not a criminal trial, a more-likely-than-not standard is appropriate.”
3. “Probabilistically speaking, given that an accusation has been leveled, Brett Kavanaugh is more likely than not to have assaulted Christine Blasey Ford.”

Therefore:

     4. “Brett Kavanaugh should be disqualified.”

The argument was rarely presented in such stark terms, but it or something very close seemed to undergird a lot of the anti-Kavanaugh animus on display these past few weeks. Over at Vogue, for instance, Michelle Ruize insinuated the pivotal third premise with her assertion that Christine Blasley Ford was unlikely to be “mixed up” because “only 2 to 10 percent of sexual assault reports are false.” And, she concluded:

Ruize didn’t directly express the second premise, but many others did, including Senator Dianne Feinstein, who became a #resistance icon almost overnight.

And in their own sometimes irresponsible rush to proceed with the confirmation, conservatives attacked all three premises with abandon. The first was dismissed as “nihilistic nonsense” by Dennis Prager, who argued that “the charges against Judge Kavanaugh should be ignored.” The second was dismissed as “no mere job interview” by Alan Dershowitz, who argued that “even in the court of public opinion, basic fairness should preclude conviction without clear evidence.”

And the third was given a thoughtful but ultimately unpersuasive rebuttal by National Review’s David French, who argued that because 45 percent of rape cases never go to trial due to insufficient evidence, there may be far more false accusations than official statistics reveal. “If you believe this data,” French concedes, “it’s easy to see why people are so outraged when a skeptic says that an alleged victim hasn’t come forward with compelling evidence. After all, it’s a statistical fact. Women are almost always telling the truth. It’s science.” But the data is unreliable because we don’t really know how many false allegations get made, therefore “there should be no default presumption that anyone is telling the truth.”

It’s obvious why the burden of proof should be lower in a Senate confirmation hearing than a criminal trial, and really, really obvious why attempted rape should preclude someone from sitting on the highest court in the land. But French’s argument deserves more scrutiny, for it ends up validating one of the core assumptions underlying #CancelKavanaugh: the idea that statistical evidence should play any role whatsoever when adjudicating sexual assault claims.

“Reality. . . .is complex,” French says, “and that complex reality demands individual adjudication and individual assessments.” Alright, but suppose the statistical reality were less complex. Suppose we knew for sure that at least 51 percent of rape allegations were true absent specific information. Would it still make sense to bracket this data point, using only the individualized assessments to which French refers?

On one way of thinking, the answer is clearly No. “Preponderance of evidence” is often interpreted to mean “more likely than not” or “over a 50 percent chance,” so since statistics tell us the overall likelihood that a particular event occurred, they should of course factor into our decision about whom to believe.

In particular, statistics can give us a baseline estimate of how likely the relevant parties are to be telling the truth—a “default presumption,” in French’s words—which can then be revised as new facts come to light. This process is sometimes called Bayesian updating, and throughout the Kavanaugh drama several commentators found it useful for framing their arguments. “Did Kavanaugh do it? Math helps us decide,” declared Eric Saund, enlisting Bayes’ Rule to show how different people could come to different conclusions with the same evidence depending on their “prior assumptions”—for example, the assumption that women rarely make false accusations.

Quillette’s Coleman Hughes took this reasoning a step further, arguing that we should in fact have a presumptive bias in favor of Ford:

That “without” caveat is a big one, but before examining the non-statistical evidence against Ford’s claims, let’s zoom in on the numbers Hughes cites. Their range illustrates part of the problem with French’s earlier naysaying: Even if rape statistics do have a huge margin of error, it doesn’t follow that we should be totally agnostic about who is more likely to be telling the truth. Supposing (implausibly!) that one third of accusations are false, the odds still favor Ford by quite a lot. Add the fact that Ford must have known she would face blowback for coming forward with the fact that rape is notoriously underreported, and her story becomes extremely credible. To be sure, there were several case-specific details that pushed its credibility down, especially Leland Keyser’s denial that she ever knew Brett Kavanaugh. But memories are fallible, not least memories 36 years old, and for all intents and purposes, this remained a “he said, she said” case from the beginning.

As a result, the “prior assumptions” described by Saund were really all anybody had to go on—which meant the percentage of true accusations was bound to be a deciding factor for many Americans. And because that number almost certainly exceeded 50 percent, it made perfect sense to believe Ford and disbelieve Kavanaugh—going by the available data, he probably did assault her.

But notice, these statistics would have been the same even if the alleged incident had never occurred. Stipulate for the moment that Kavanaugh is in fact telling the truth, and Ford is misremembering what took place at that summertime soirée. It would still be the case that most women who allege sexual assault are telling the truth. Indeed, the only way statistics could fail to vindicate Ford would be if we somehow knew that the majority of rape accusations that lack corroborating evidence are false. But we don’t know that, and given how many cultural and legal barriers exist to reporting sexual assault, there’s not much reason to assume it either.

And that’s the problem: Once an accusation was made, it became impossible for Kavanaugh to overcome the presumption of credence on which his prosecution soon hinged. If the majority of unsubstantiated rape allegations are true—and to be clear, they probably are—“believe all women” is not just a catchy slogan but a rational imperative: In each such case, believing the accuser maximizes your chances of being right regardless of the accusation’s truth value. But if justified belief was enough to derail a SCOTUS confirmation, politically motivated actors would have had a strong incentive to gin up lies about every potential nominee they dislike, precisely because the odds always tilt in the accuser’s favor. “This is going to destroy the ability of good people to come forward,” Lindsey Graham warned in his fiery soliloquy to the Senate Judiciary Committee. Had a majority of Senators accepted such probabilistic logic, he would have certainly been right.

In other words, statistical evidence incentivizes false accusations because its presence only depends on the accuser coming forward, not on the accused individual committing a crime. By contrast, things like DNA forensics and eyewitness testimony do depend on the actions of the accused. If you weren’t at the bank when it was robbed, chances are your hair won’t turn up in a forensics report. And if you weren’t at the party Christine Blasey Ford described, chances are nobody would remember seeing you there. Whereas statistical evidence does not vary in response to choices made by individual agents (in the sense that no single act of wrongdoing will change that wrongdoing’s overall frequency), this second sort of evidence varies directly with such choices—meaning it doesn’t automatically materialize whenever an accusation gets made.

Therein lies the importance of corroborating before convicting, in both public opinion and the law. If allegations are never taken seriously on statistical grounds alone, partisans can’t use them as an immediate veto, which suggests a strong consequentialist case for bracketing our priors and evaluating sexual assault claims only on their individual merits. The question is not, pace French, whether rape statistics are reliable; it’s whether rape statistics should be allowed to resolve every he-said-she-said dispute in the accuser’s favor, thereby entrenching all such accusations—true and false—as tools of political warfare.

To which 50 U.S Senators correctly replied: Not on my watch.

But we should be clear about why they’re correct. The reason is not, as Trump asserted Monday, that Kavanaugh was proven innocent, or that Ford was proven wrong. Nor is it that the totality of the evidence discredited the allegations against Kavanaugh; statistically speaking they were more likely than not to be true even without corroboration.

No, the reason the Senators were correct is that while total evidence is always the right standard for deciding what to believe, it’s not always the right standard for deciding what to do. Think of evidence obtained in a wrongful search and seizure. Juries are instructed to disregard such evidence not because it’s false or misleading (in many cases it’s neither), but because letting it influence the trial would encourage more misconduct in the future. A similar problem applied with Kavanaugh: Statistics really did bolster his accuser’s credibility, but letting them influence the confirmation process would have established such a horrible precedent that the lack of corroboration had to spell the end of her case. The alternative was complete chaos, a scenario in which merely uttering j’accuse could tank a SCOTUS nominee—and quite a bit else, if the precedent kept metastasizing.

Thus when Susan Collins stated that she did not believe the “more likely than not” standard had been met, she was implicitly advancing a particular interpretation of that standard. For her, “preponderance of evidence” meant case-specific, non-statistical evidence, of which there was very little. It did not mean what it apparently meant to many liberals, whose more holistic view included facts about probability in addition to facts about Ford and Kavanaugh. Failure to distinguish between these interpretations—and the competing rationales behind them—is part of what made the controversy so intractable, with each side talking past the other as Saturday’s vote drew near.

It wasn’t all language games, of course. Some argued that in the #MeToo era confirming Kavanaugh would effectively delegitimize the Supreme Court unless he could prove his innocence beyond all shadow of a doubt. The concern was understandable, but the conclusion was not, for the simple reason that not confirming Kavanaugh was every bit as likely to induce Dreyfusian polarization and undermine the Court’s legitimacy. By the time Collins announced her vote, conservatives had already closed ranks around Kavanaugh, whose perceived mistreatment at the hands of Democrats seems to have caused widespread “radicalization” among the GOP base. In this opaque evidentiary climate, both outcomes were guaranteed to enrage half the country—but only one avoided a system-smashing incentive structure.

If the goal was to minimize damage, mission accomplished.