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.e. making the guess incorrectly probably causes far more friction than deliberately not making a correct guess you could make.
I came up with the following payoff matrix:
Bob | |||
Has trait X (p = 0.95) | Doesn't have trait X (p = 0.05) | ||
Alice | Acts as if Bob has trait X | +1 | -100 |
Acts without assumptions about Bob | 0 | 0 |
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).
A related problem: replacing the majority with the norm.
Most Americans are Christians. Given a random American, he/she is more likely to be Christian than anything else. It may be a safe bet to say Merry Christmas (especially since few people are offended by hearing Merry Christmas even if they're not Christian.) So far, that's just reacting rationally to the fact that Christians are a majority.
But it starts to get unsettling when the majority is regarded as the norm -- when people refer to the United States as "a Christian nation," for instance, with a normative rather than a statistical implication. There's a difference in thinking "Most Americans are Christian, but some are not," and thinking "Americans are Christian. (Except for a few aberrations.)" The latter has the connotation that non-Christians are less American.
You can apply this to all kinds of majority/minority things. "Most people are straight, but some are gay" as opposed to "People are straight. Except for some aberrations." "Most mathematicians are men, but some are women" as opposed to "Mathematicians are men. Except for some aberrations." "Many cultures share a similar standard of beauty, but there are some differences" as opposed to "There is one standard of beauty. Except for aberrations."
People are known to have a bias of rounding up high probabilities (treating 90% as practically certain) and rounding down low probabilities (treating 10% as practically impossible.) It's possible that this has an effect on the way we think about minority populations -- we mentally approximate a population that's 95% A and 5% B as "basically" 100% A, and we don't always distinguish in our intuitions between a 5% and a 0.05% population.
Moral of the story: it may be rational to assume that a given person in a group is a member of the majority, but remember to correct for your tendency to slip over the edge from "majority" to "normal" or "standard".
I don't detect a difference between the two universes being described by
except that all things being equal, I would suspect that who uttered the second phrase was more likely to disapprove of homosexuality than who uttered the first phrase. But is reality being described any less accurately by one of these two phrases? How would we go about discovering which phrase was more accurate?