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?
But is reality being described any less accurately by one of these two phrases?
When comparing two predictions, the better prediction is the one that leads to less surprise.* That means that oftentimes you may treat false positives as much less important than false negatives, or vice versa. To me, the difference between the two is which error they favor- the first is likely to overestimate the chance someone is gay, whereas the second is likely to underestimate it. Given that the damage done by a wrong guess is asymmetric, which error you favor should li...
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).