Note: This post discusses sexual assault. If you've read this note and want to continue reading, go back, read the headline, and then read the next line as if it followed directly, because it's a real zinger.
That he knew nothing and that Bill Cosby is a rapist.
It's odd to see people come to Bill Cosby's defense in public forums. I can understand it to some extent when it is people who are very close to him personally - people who wrongly assume that they couldn't possibly be friends with a rapist, that they would know somehow. I've said before when discussing intimate partner abuse in relation to Jian Ghomeshi, that we all know abusers and we don't know who the abusers are. I'm fairly sure that rapists are quite a bit less common than intimate partner abusers, but they aren't down to that 1 in 10,000 level that they'd need to get to before you could start comfortably assuming that you may never have really interacted with one.
Here's a great link to what was originally a blog post on "Obsession with Regression", which seems to be a fantastic blog in general. If you want, you can also find a response to objections to the model that were raised in the comments in this post.
The short version is that if you make some reasonable assumptions about how many people commit sexual assault and how often people accuse other people of sexual assault, you can make a model that shows how likely it is that someone committed a sexual assault given that they've been accused by N people. Even when you start with assumptions that make it more likely than not that a person is innocent when N=1, the chance they are innocent drops massively at N=2, and goes to pretty much zero at N=3. The model doesn't give me an accurate value for N=30, but I'm pretty sure it's into the if-this-played-out-on-every-known-planet-in-the-universe-every-day-since-the-beginning-of-time-they-wouldn't-be-innocent-once range.
Of course when you get probabilities like that, you have to think about other things that could be influencing them. What if, for example, a rich and powerful person with an axe to grind against Cosby paid all of these women off?
I'm not going to tell you that scenario is literally, actually impossible. What I am going to say is that if you want to defend Cosby, you are totally backed into a corner and must use that scenario. I said the same thing about Ghomeshi with eight accusers. You need to posit a conspiracy. I went into the model and set the chance of a person who has not committed an assault being accused to an obscene 10% and the probability that the accused was innocent at just five accusers was already down to 20%. At 30 it was going to be back in no-chance range.
The plausibility of such a conspiracy is not something we can build a mathematical model of, but it's a pretty big stretch. Here's a worthwhile question to ponder if you are ever thinking of orchestrating such a conspiracy: Given that you found 30 people who are willing to take money in exchange for leveling false rape accusations, what do you think the odds are that all of these mercenaries are going to say infallibly loyal to you over the next weeks, months or years as this thing plays out? Because if all I know about someone is that they will take money to falsely accuse someone of rape, my confidence in them to stick to their end of a bargain is actually going to be pretty low. Another: What if you ask someone to participate and they say no? What if they tell the media that you asked them to participate as the conspiracy starts to unfold?
I've seen those who know Cosby explicitly play the conspiracy defense, but that's not the favoured defense I see on internet message boards by people who don't know Cosby. Instead what I've been seeing is the assertion that we can't condemn Cosby because we don't have facts.
So here is the best part about having a statistical model to point to: it is a reminder that thirty accusations is fact. There aren't "no facts" there is the fact that thirty women have come forward and accused Cosby of sexually assaulting them.
I think that many of us have been warned about the tendency to overvalue eye-witness evidence of crimes. Bayesian analysis shows us that we should not weight the accuracy of a witness over other probabilities in a case. What got totally lost in my Critical Thinking 101 class, though, is the other side of the coin where we actively discount the value of evidence given by witnesses and victims that are less socially powerful than the person they are giving evidence against.
If Bill Gates were to come forward to talk about being sexually assaulted by Bill Cosby, you can bet we'd all listen. It would be very hard to find anyone saying, "Enh, Bill Gates must just be making it up for attention," or "Someone must have bought him off." That sounds logical, because obviously Bill Gates has no need of attention or money - it is very hard to think of any way someone could motivate him to make that accusation falsely. But this isn't logic based. It would also be hard for someone to say that he must be confused or mistaken, though presumably being ultra-wealthy does not protect you from that.
What statistical models like this should remind us is that we cannot let our biases about people override the fact that their coming forward is evidence in itself. Let's think about people as a system. Let's think about where they would grow tendrils if they were slime mold. Would the slime mold grow that many tendrils to the false-rape-accusation-oatmeal solution?
We should listen to the story of a single woman and give it credence - as much credence as that of a man. We should listen to the story of a single poor person and given it as much credence as that of a rich person. We should do that same for people divided by color, disability, and even mental illness.
But thirty people? There is no credence involved. Thirty people saying that someone sexually assaulted them is better than DNA on a murder weapon and fingerprints on the doorknob. It's better than a video of the crime happening with a high resolution shot of the perpetrator looking right at the camera in good lighting and audio of them repeatedly talking about themselves in the third person. Thirty accusations is better proof than you have of nearly any fact you depend upon in your life.
It is possible to imagine a world in which everything I know to this date is true but Bill Cosby did not commit a sexual assault. Hey, maybe Bill Cosby never committed a sexual assault because Bill Cosby never actually existed! Maybe everything is a lie! Frankly, if you are going to suggest that Bill Cosby is innocent, I think you might as well be suggesting you are a brain in a jar or that Descartes' "demon" has falsified the whole thing for you. It's really pretty much as likely.