Curated. I’ve tried to think about similar topics—silencing of different kinds of information can also lead to information cascades, for example. This was a simple toy model that I had properties I’d never put into an explicit model before—if signalling always looks like at least a 3:1 ratio of args in your side’s favour, then random chance is gonna mean some people (even if 3:1 is the ground truth) will have lopsided info and have to lie, and that’s a massive corruption of those people’s epistemologies.
Yes, indeed I did. A bunch of the beginning was nice to see again, it’s good for people to reread that stuff, and for any newer users who haven’t done it for the first time yet.
I wasn’t so much enjoying one political footnote which seemed mostly off-topic or something, until the line at the end saying
If I’m doing my job right, then my analogue in a “nearby” Everett branch whose local subculture was as “right-polarized” as my Berkeley environment is “left-polarized”, would have written a post making the same arguments.
which I really like as a way of visualising needling the truth between political biases in any environment.
The post is very readable and clearly explained, plus lots of links for context, which is always great.
I mostly feel confused about quantifying how biased the decisions are. If you have 9 honest rolls then that’s log_2 of 9 = 3.2 bits. But if you roll it 9 times and hide the 3 rolls in a certain direction, then you don’t have log_2 of 6 = 2.6 bits. That would be true if you had 6 honest rolls (looking like 2:2:2) but 3:3:0 surely is not the same amount of evidence. I’m generally not sure how best to understand the effects of biases of this sort, and want to think about that more.
But if you roll it 9 times and hide the 3 rolls in a certain direction, then you don’t have log_2 of 6 = 2.6 bits. That would be true if you had 6 honest rolls (looking like 2:2:2) but 3:3:0 surely is not the same amount of evidence. I’m generally not sure how best to understand the effects of biases of this sort, and want to think about that more.
The general formula is −∑obsP(obs)logP(obs), where obs is the observation that you see. You need to calculate P(obs) based on the problem setup; if you are given the ground truth of how the 9 rolls happen as well as the algorithm by which the 6 dice rolls to reveal are chosen, you can compute P(obs) for each obs by brute force simulation of all possible worlds.
Curated. I’ve tried to think about similar topics—silencing of different kinds of information can also lead to information cascades, for example. This was a simple toy model that I had properties I’d never put into an explicit model before—if signalling always looks like at least a 3:1 ratio of args in your side’s favour, then random chance is gonna mean some people (even if 3:1 is the ground truth) will have lopsided info and have to lie, and that’s a massive corruption of those people’s epistemologies.
Yes, indeed I did. A bunch of the beginning was nice to see again, it’s good for people to reread that stuff, and for any newer users who haven’t done it for the first time yet.
I wasn’t so much enjoying one political footnote which seemed mostly off-topic or something, until the line at the end saying
which I really like as a way of visualising needling the truth between political biases in any environment.
The post is very readable and clearly explained, plus lots of links for context, which is always great.
I mostly feel confused about quantifying how biased the decisions are. If you have 9 honest rolls then that’s log_2 of 9 = 3.2 bits. But if you roll it 9 times and hide the 3 rolls in a certain direction, then you don’t have log_2 of 6 = 2.6 bits. That would be true if you had 6 honest rolls (looking like 2:2:2) but 3:3:0 surely is not the same amount of evidence. I’m generally not sure how best to understand the effects of biases of this sort, and want to think about that more.
The general formula is −∑obsP(obs)logP(obs), where obs is the observation that you see. You need to calculate P(obs) based on the problem setup; if you are given the ground truth of how the 9 rolls happen as well as the algorithm by which the 6 dice rolls to reveal are chosen, you can compute P(obs) for each obs by brute force simulation of all possible worlds.