Let's start with the simplified version of a point I have already made. Suppose we believe that there is a 50% chance that "Brett" committed the attack that Ford alleges. Note that I am now shifting my language somewhat. Under legal reasoning, that would constitute "reasonable doubt." He would be acquitted. Were we to have a serious confirmation process that properly assessed nominees, though, "Brett" would not be confirmed because a 50% chance of such an allegation being true is too high. Some of us want Supreme Court nominees of... unimpeachable character, not ones who just manage to show "reasonable doubt." Reasonable doubt is the standard by which you escape criminal conviction, not the standard by which you secure a lifetime appointment to the Supreme Court. Acquittal does not mean innocence. It means reasonable doubt.
What is the mathematical threshold for reasonable doubt? Um... Uh... There, uh... Yeah. There's a reason lawyers say, "reasonable doubt," rather than "convict if probability of guilt is greater than p where p=.95," just to pull a social science number out of a hat. How would one, or 12, ever put a number like .93 on the probability of guilt in any case? Unless they hang the number entirely on assessment of DNA evidence, or something similar, that kind of quantification is just too hard in too many cases. So, you have legal standards like "reasonable doubt," or, "preponderance of evidence" in civil cases.
Understanding what that means, though, clarifies the silliness of saying, "well, we can't convict Kavanaugh, so he must be confirmed." A 25% Bayesian assessment of the chances of innocence realistically means reasonable doubt, but would you confirm someone to a lifetime appointment on the Supreme Court if there were a 75% chance of that person having committed a horrific crime? 25% 10% Really? Reasonable doubt is not the standard by which decent, intelligent people confirm Supreme Court nominees. Insert comment about who is neither decent nor intelligent here.
This is the time for Bayesian statistical reasoning. Updated assessments of the probability of guilt. Start with Ford's therapist's notes. Is that direct evidence of Kavanaugh's guilt, in legal terms? No, but in Bayesian terms, once you have that piece of information, you update your assessment of the probability of his guilt upwards. Legal versus statistical reasoning. A court wouldn't give a shit about those notes because the therapist wasn't there. It was years later. A statistically trained mind cares. It is more information, indicating that the claim is not just a political attack. Enter Ramirez, the Yale student "allegedly" harassed at a party by "Brett." We now have two separate claims. Does one claim increase the probability that the other claim is true? In Bayesian terms, once I have a second claim, I'm going to update my prior that the first claim is true upwards because it suggests a pattern. In legal terms, one claim is not evidence that the other is true. They're just two separate accusations. Legal versus statistical reasoning.
Remember, though, that the issue here isn't the question of whether or not anyone can secure a criminal conviction. The question is whether or not this is the guy who should be trusted with a lifetime appointment on the Supreme Court. There's no "ruining his life," or any such bullshit. If he doesn't get appointed, he stays a judge on the DC Circuit, which is not exactly a ruined life.
How certain do you want to be about people with that kind of power? "Reasonable doubt" certain, or as certain as possible? There is a time for legal reasoning, and a time for Bayesian reasoning. Bayes' theorem. It's a law too!
As for Bayesian assessments of "Brett's" chances, they're way down. Here's the betting with Ramirez's story now public. At this point, I have no clue.