3-8% of Americans are gay (more like 5% in the UK.) That's a true statement. Guessing that an arbitrary person is straight is perfectly kosher, from a Bayesian perspective.
Here's the thing. Most of us would say that being left-handed is a minority trait, while being six-fingered is an anomaly or aberration. About 15% of people are left-handed; about 0.2% of people are six-fingered. Take that as a benchmark. Then being gay is more like being left-handed than it is like being six-fingered.
And, at 20-30%, women scientists should definitely belong in the "left-handed" rather than "six-fingered" category.
If you start thinking of a sizable minority as though it's as rare and strange as a very small minority, then you're making a mistake.
3-8% of Americans are gay (more like 5% in the UK.)
Isn't 5% just 3-8% that forgot to state its error margins?
During discussion in my previous post, when we touched the subject of human statistical majorities, I had a side-thought. If taking the Less Wrong audience as an example, the statistics say that any given participant is strongly likely to be white, male, atheist, and well, just going by general human statistics, probably heterosexual.
But in my actual interaction, I've taken as a rule not to make any assumptions about the other person. Does it mean, I thought, that I reset my prior probabilities, and consciously choose to discard information? Not relying on implicit assumptions seems the socially right thing to do, I thought; but is it rational?
When I discussed it on IRC, this quote by sh struck me as insightful:
I came up with the following payoff matrix:
In this case, the second option is strictly preferable. In other words, I don't discard the information, but the repercussions to our social interaction in case of an incorrect guess outweigh the benefit from guessing correctly. And it also matters whether either Alice or Bob is an Asker or a Guesser.
One consequence I can think of is that with a sufficiently low p, or if Bob wouldn't be particularly offended by Alice's incorrect guess, taking the guess would be preferable. Now I wonder if we do that a lot in daily life with issues we don't consider controversial ("hmm, are you from my country/state too?"), and if all the "you're overreacting/too sensitive" complaints come from Alice incorrectly assessing a too low-by-absolute-value negative payoff in (0, 1).