So there was a post that was critiquing the epistemological framework of Bayesianism (i.e. using probability theory and its laws as a basis for rationality) saying that it’s “just common sense”. This may seem so in rationalist communities, but in the wider world, a lot of people don’t follow such common sense. As the witty catchphrase goes, common sense isn’t all that common. And I’m beginning to doubt that it’s even all that common in rationalist communities.
This is one of the reasons why we have religious scientists. Many scientists think that the scientific method is just something you do to publish in academic journals, and not something more like a reliable framework for attaining and updating your beliefs about the world. So they might adhere to a concept like Popperian falsifiability when designing experiments but then go home and pray to Nocturnal for good luck.
Anyway, I’ve been noticing a lot of articles and such over the past few days about charges of sexual harassment. Like Philosophy Has A Sexual Harassment Problem. Or this Mr. Deity video that a friend posted on my Facebook and this response. And then there’s the sexual harassment problem at my employer, which has scheduled extra trainings for us as a result.
So the first problem I see, putting on my little rationality cogsci hat on, is that human beings think in groups. And the largest subgroup that humans can be divided into is male and female. This will of course lead to a bunch of motivated cognition, charges of hyperskepticism, and confirmation bias flying off the shelves like they’re on sale at Wal-Mart.
That’s why y’all motherfuckers need Bayes:
- Banish talk like “There is absolutely no evidence for that belief”. P(E | H) > P(E) if and only if P(H | E) > P(H). The fact that there are myths about Zeus is evidence that Zeus exists. Zeus’s existing would make it more likely for myths about him to arise, so the arising of myths about him must make it more likely that he exists. A related mistake I made was to be impressed by the cleverness of the aphorism “The plural of ‘anecdote’ is not ‘data’.” There may be a helpful distinction between scientific evidence and Bayesian evidence. But anecdotal evidence is evidence, and it ought to sway my beliefs.
- Banish talk like “I don’t know anything about that”. See the post “I don’t know.”
- Banish talk of “thresholds of belief”. Probabilities go up or down, but there is no magic threshold beyond which they change qualitatively into “knowledge”. I used to make the mistake of saying things like, “I’m not absolutely certain that atheism is true, but it is my working hypothesis. I’m confident enough to act as though it’s true.” I assign a certain probability to atheism, which is less than 1.0. I ought to act as though I am just that confident, and no more. I should never just assume that I am in the possible world that I think is most likely, even if I think that that possible world is overwhelmingly likely. (However, perhaps I could be so confident that my behavior would not be practically discernible from absolute confidence.)
- Absence of evidence is evidence of absence. P(H | E) > P(H) if and only if P(H | ~E) < P(H). Absence of evidence may be very weak evidence of absence, but it is evidence nonetheless. (However, you may not be entitled to a particular kind of evidence.)
- Many bits of “common sense” rationality can be precisely stated and easily proved within the austere framework of Bayesian probability. As noted by Jaynes in Probability Theory: The Logic of Science, “[P]robability theory as extended logic reproduces many aspects of human mental activity, sometimes in surprising and even disturbing detail.” While these things might be “common knowledge”, the fact that they are readily deducible from a few simple premises is significant. Here are some examples:
- It is possible for the opinions of different people to diverge after they rationally update on the same evidence. Jaynes discusses this phenomenon in Section 5.3 of PT:TLoS.
- Popper’s falsification criterion, and other Popperian principles of “good explanation”, such as that good explanations should be “hard to vary”, follow from Bayes’s formula. Eliezer discusses this in An Intuitive Explanation of Bayes’ Theorem and A Technical Explanation of Technical Explanation.
- Occam’s razor. This can be formalized using Solomonoff induction. (However, perhaps this shouldn’t be on my list, because Solomonoff induction goes beyond just Bayes’s formula. It also has several problems.)
- You cannot expect that future evidence will sway you in a particular direction. “For every expectation of evidence, there is an equal and opposite expectation of counterevidence.”
- Abandon all the meta-epistemological intuitions about the concept of knowledge on which Gettier-style paradoxes rely. Keep track of how confident your beliefs are when you update on the evidence. Keep track of the extent to which other people’s beliefs are good evidence for what they believe. Don’t worry about whether, in addition, these beliefs qualify as “knowledge”.
If everyone is using the same framework, then charges of hyperskepticism, or hypo-skepticism ( not enough skepticism), should be more easily handled — just like my math teachers would say — by showing my work.
So if I were to apply Bayesianism to this sexual harassment boondogle, I would first establish my prior by analyzing my background knowledge. What do all of these problem areas — the atheist/skeptic community, the military, philosophy departments, the tech community — have in common? They are all heavily male-dominated. This creates a scarcity mentality and the men would behave the same way that any other human behaves in a scarcity context: Aggression, objectification (i.e. the thing that’s “scarce” being seen as “valuable“), selfishness/lack of empathy, and other deviant and competitive behavior.
More background knowledge, where are we more likely to find psychopaths: In jail or in leadership positions? You guessed it… definitely leadership positions. Jail selects for criminals, not psychopathy! Couple this with the odd relationship between psychopathy, testosterone, and social dominance, and we have a pretty dangerous combo. Mix a high likelihood for psychopathy with scarcity mentality, and I would have to put a bit higher prior on the likelihood for sexual harassment in these male-dominated areas than in the general population.
One of the critiques of Bayesianism is that prior probabilities are subjective. But probability is in the mind and is (mostly) subjective.
So what would I consider a prior for someone with some level of status in a male-dominated community (i.e. the background knowledge) engaging in some form of sexual harassment? I’d say around 5%. This means that if I were to survey the population of maybe 100 people with some level of status in a male-dominated community, I predict that around 5 of them would be unquestioningly guilty of sexual harassment. Considering that the actual population is much higher than 100, it seems about reasonable. Especially since the majority of victims are usually victimized by a minority, and of that minority the majority are repeat offenders.
Here’s where we get to the divergent assertions of hyperskepticism/hypo-skepticism.
So let’s say that C is “claim of harassment” and H is “actually sexually harassed someone”. This means that P(C | H) is the probability of there being a claim of sexual harassment given that one has actually sexually harassed someone. What we want to find out is P(H | C), the probability that someone has sexually harassed someone given a claim of sexual harassment, which is equal to P(C | H) * P(H) / [P(C | H) * P(H)] + [P(C | ~H) * P(~H)]
Now, a claim of sexual harassment is not itself definitive proof of sexual harassment. Just like testing positive for breast cancer is not itself definitive proof of breast cancer. Even if 100% of claims of sexual harassment given actual sexual harassment are true, this does not mean that someone is definitely guilty of sexual harassment if accused, as counterintuitive as that sounds. A claim of sexual harassment correlating with sexual harassment is a conditional probability; what we want is to update the prior probability of sexual harassment. What we want to find is P(H | C).
On the other hand, collecting multiple independent claims of harassment counts as evidence, and you should update your prior accordingly. The more claims that are made, the more times you update. Even if the prior’s rate of increase might start to plateau. This might not be scientific evidence, or not the type of evidence that might bring one to felony charges, but it’s Bayesian evidence nonetheless.
We then have to look at alternative hypotheses, which are represented by ~H. What is P(C | ~H), or the probability that someone would file a claim given that they weren’t sexually harassed? Maybe it was an actual misunderstanding, or the woman is being vindictive, or any other possible explanation for ~H. But I would certainly say that P(C | H) > P(C | ~H). By how much is the most important factor.
Another point of view I like to look at is from the “absence of evidence” view. If one claims that P(C | H) is 100%, this necessarily means that P(~C | H), or the probability of not having a claim of sexual harassment given that said person actually did sexually harass someone is 0%. And I’m reasonably certain that people have been sexually harassed and not filed a claim for whatever reason (fear, rape culture, etc.), so P(~C | H) is definitely greater than 0%.
So if my prior is 5%, and I think that P(C | H) > P(C | ~H), then this means that P(H | C) > P(H). And the amount that P(H | C) > P(H) is determined by how much P(C | H) > P(C | ~H). Let’s assume that P(C | H) is 90% [forcing P(~C | H) to be 10%] and P(C | ~H) is 1%. This means that P(H | C) is equal to 31%. That’s just for one claim. If there’s another claim, then (depending on the relationship between the two claims) this possibly moves my new prior of 31% to 73%. Of course this is assuming a 90% conditional probability, and I think that looking at it from the view of P(~C | H), it should be lower. Even so, with a conditional probability of 50%, it still moves my prior from 5% to 20%; add another claim and it goes to 50%.
With all of the furor brewing over false accusations, and not enough/too much skepticism about claims of sexual harassment, it seems pretty obvious that “[rationalist] common sense” is not prevailing where it should. Sure, you can assert that “extraordinary claims require extraordinary evidence” but you can only prove that by using Bayes.