“#BelieveAllWomen” is a popular slogan nowadays. And like many popular slogans, it is irrational if taken literally. If you believe all women, then you’d have to believe the woman who got Emmett Till lynched, plus all of the women who put these innocent men in jail. It’s safe to say that when pressed, any reasonable person who trots out this slogan would not follow through on its implications. In this sense, it’s a fake belief for most people that claim to hold it.
But the fundamental problem with #BelieveAllWomen is not that it’s a fake, virtue-signaling belief (after all, such beliefs can turn out to be true.) The fundamental problem is that it’s a bad Bayesian prior.
But the fundamental problem with #BelieveAllWomen is not that it’s a fake, virtue-signaling belief (after all, such beliefs can turn out to be true.) The fundamental problem is that it’s a bad Bayesian prior.
A Bayesian prior is the probability––absent any specific evidence––that some belief is true. For instance, let’s say that there is an American man standing behind an opaque curtain. Your task is to guess whether he is shorter than six feet; and all you know is that he is American and male. Your prior credence should be 85.5 percent because that’s the percentage of American men that are under six feet tall. If you receive new information, then your credence level should go up or down accordingly. For instance, if you learn that he is an NBA basketball player, then your credence should decrease to reflect the proportion of American male basketball players that are below six feet, etc.
Thinking like a Bayesian, what should our prior credence in the alleged sexual assault of Christine Blasey Ford be? It shouldn’t be 100 percent, given how many false accusations occur, and it shouldn’t be zero percent, given how many true accusations occur. Believe all women, and believe no women both fail. What about 50 percent? This sounds reasonable at first. Many a cool-headed person has thought to him or herself: all of these people with strong opinions are clearly biased. After all, they weren’t even in the room when the alleged event happened. The truly rational person must believe that either possibility is equally likely.
But a 50 percent prior credence in Ford’s account is as arbitrary as a 50 per cent prior credence in the American man behind the curtain being less than six feet. Where we have data on base rates, such data (insofar as it is trustworthy) should trump our intuition that a 50 percent credence level is rational.
So in order to form a prior credence we should ask: Of all rape allegations that are made, what percentage are false? According to Snopes, that number is between 5 percent and 33 percent, with a greater number of studies showing the 5 percent figure. In order to steelman Kavanaugh’s defenders, let’s take the 33 percent figure. This means that, knowing nothing at all except the fact that Ford is an American woman making a sexual assault accusation, we should believe that there is a 67 percent chance that her accusation is accurate (granted sexual assault accusations are different than rape accusations, but there is better data on rape, so I’ll use it as a proxy.) Note that we should already think that she is more likely to be telling the truth than lying or misremembering, without knowing anything else.
Now we should nudge that credence around in the face of all relevant facts. Some of those facts would push the credence level up and others would push it down. In the former category there are the questions: If she is lying/misremembering, how likely would it be that
- She told her husband this years ago;
- She tried to settle this out of the public spotlight first;
- After decades of living privately, she agreed to derail her and her family’s life and subject herself to being hounded by reporters;
- (Fill-in every detail that we would expect to see given the belief that she’s telling the truth and remembering correctly.)
And on the other side of the equation we have the questions: If she is telling the truth/remembering accurately, how likely would it be that:
- None of her named witnesses have corroborated her account;
- She at one point asserted that two people were in the room and later changed it to four;
- She doesn’t remember whose house it was or how she got there;
- (Fill-in every detail that we would expect to see given the belief that she’s lying or misremembering.)
Of course, how you update your credence level given all the new evidence is up to you, but only because we don’t have data on questions like: what proportion of sexual assault victims who were assaulted at a house party remember how they got to the house 30+ years later; and what proportion of accusers misidentify alleged perpetrators they are already acquainted with; etc. Though the answers to such questions are simple percentages, we will never know them in practice. In principle, however, two good Bayesians with common knowledge cannot agree to disagree.
None of this necessarily bears on questions like, Should Kavanaugh be confirmed?, or What credence level should be required to preclude one from being a supreme court justice?, or Should the presumption of innocence extend to political proceedings?, or Should a 53 year-old be barred from the supreme court for a crime he committed when he was 17? That is, you could agree with everything in this blogpost while strongly believing that he should still be nominated for other reasons. Here, I only deal with the question whether you, as the rational Bayesian that I know you are, should think that it's more likely than not that Ford is telling the truth and remembering correctly.
However you choose to update your credences in the face of new evidence, recall that we used the low-ball estimate of how often accusers are credible. According to Snopes, something like a 95 percent credence level is more appropriate. The social incentive structure of the #MeToo era should lead us to be more wary of opportunists than we might have been a year and a half ago. But still, a 95 percent credence level, as a rough starting point, stacks the deck in Ford's favor so extremely that it should take highly compelling evidence in Kavanaugh’s favor to reduce it to 50 percent. Even a 67 percent prior credence level should lead us to require compelling evidence to come out with 50-50 odds, much less odds that favor Kavanaugh.
The presumption of innocence is essential from the point of view of checking state power––and I'm lucky to live in a nation with due process (however imperfectly it is applied in practice.) But as a rational person who has access to base rates and who wants to form true beliefs about the world in the privacy of his own mind, the presumption of innocence is as useless to me as the presumption of guilt.
Update 9/28: The 95 percent number is likely too high, based on David French's analysis of that statistic in The National Review last week. One study that found roughly 5 percent of accusations to be false also found that 44 percent of allegations were not taken to trial at all, either because of lack of evidence or because the victim withdrew from the process or because the victim mislabelled the event.
Of that 44 percent, how many were true allegations and how many false? Nobody knows. French, on this basis, ends the column by saying "there should be no default presumption that anyone is telling the truth."
True, but there should also be no default presumption that each side is equally likely to be telling the truth. That, I argue, is just as arbitrary as #BelieveAllWomen. In order to get to that view––a 50-50 prior credence––you'd have to assume that all of the 44 percent of allegations not pursued were false, and then add the 5 percent that are proven false, giving you 49 percent of allegations being false. That would get you a 51 (100 minus 49) credence level in favor of the accuser.
It seems highly unlikely that all 44 percent of the allegations not pursued are false––especially given how hard it can be to marshall legally admissible evidence for rape. It seems to me that the starting credences––not from the point of view of legal process, but from the point of view of private belief formation––should still favor the accuser over the accused. By how much? Certainly more than 51-49, and certainly less than 95-5.
The presumption of innocence is essential from the point of view of checking state power––and I'm lucky to live in a nation with due process (however imperfectly it is applied in practice.) But as a rational person who has access to base rates and who wants to form true beliefs about the world in the privacy of his own mind, the presumption of innocence is as useless to me as the presumption of guilt.
Update 9/28: The 95 percent number is likely too high, based on David French's analysis of that statistic in The National Review last week. One study that found roughly 5 percent of accusations to be false also found that 44 percent of allegations were not taken to trial at all, either because of lack of evidence or because the victim withdrew from the process or because the victim mislabelled the event.
Of that 44 percent, how many were true allegations and how many false? Nobody knows. French, on this basis, ends the column by saying "there should be no default presumption that anyone is telling the truth."
True, but there should also be no default presumption that each side is equally likely to be telling the truth. That, I argue, is just as arbitrary as #BelieveAllWomen. In order to get to that view––a 50-50 prior credence––you'd have to assume that all of the 44 percent of allegations not pursued were false, and then add the 5 percent that are proven false, giving you 49 percent of allegations being false. That would get you a 51 (100 minus 49) credence level in favor of the accuser.
It seems highly unlikely that all 44 percent of the allegations not pursued are false––especially given how hard it can be to marshall legally admissible evidence for rape. It seems to me that the starting credences––not from the point of view of legal process, but from the point of view of private belief formation––should still favor the accuser over the accused. By how much? Certainly more than 51-49, and certainly less than 95-5.
