How much more unlikely is it that I will throw 15 consecutive snake-eyes, than that I will throw 11 consecutive snake eyes?
I should allocate about −170 dB of belief to the likelihood of throwing 11 snake-eyes, and about −232 dB to the likelihood I will throw 15 snake-eyes. The ~60 dB difference indicates the latter event is 6 orders of magnitude more unlikely.
What does it mean if someone thinks the difference is smaller?
If 6 orders of magnitude of improbability are glossed over, that means the person does not comprehend it in gut terms.
To what other event might I allocate −60 dB to? How about flipping a coin 20 times and getting all Heads?
Now we’re getting somewhere. Let us ask ourselves a series of restricted Aumann Questions (on various statements in general knowledge) and calculate our joint belief. The difference between the belief we allocated, and the belief we ought to have allocated, is a measure of our flattened sense of improbability. We can take this into account, and adjust our anchors accordingly. We can, in effect, see how finely-tuned is our sense of improbability.
i.e. Suppose I take a restricted Aumann test of 40 questions regarding various general facts. I assign a joint probability of −150 dB to the survey. If I were better calibrated, my priors ought to have increased this to −100. I now know I must be aware a possible 50 dB gap between my beliefs and reality, I ought to be wary of any parochial adjustment. How wary? I should attach very little confidence to any adjustment under one order of magnitude...
I ran that one in my head and thought, “that’s got to be about a million times less likely.” And indeed it was, 6 orders of magnitude. To some extent, I may just have gotten lucky… but I think that lurking on Less Wrong for the last couple years may have made me appreciate probabilities at a more intuitive level.
Let’s make the debiasing technique more rigorous.
How much more unlikely is it that I will throw 15 consecutive snake-eyes, than that I will throw 11 consecutive snake eyes?
I should allocate about −170 dB of belief to the likelihood of throwing 11 snake-eyes, and about −232 dB to the likelihood I will throw 15 snake-eyes. The ~60 dB difference indicates the latter event is 6 orders of magnitude more unlikely.
What does it mean if someone thinks the difference is smaller?
If 6 orders of magnitude of improbability are glossed over, that means the person does not comprehend it in gut terms.
To what other event might I allocate −60 dB to? How about flipping a coin 20 times and getting all Heads?
Now we’re getting somewhere. Let us ask ourselves a series of restricted Aumann Questions (on various statements in general knowledge) and calculate our joint belief. The difference between the belief we allocated, and the belief we ought to have allocated, is a measure of our flattened sense of improbability. We can take this into account, and adjust our anchors accordingly. We can, in effect, see how finely-tuned is our sense of improbability.
i.e. Suppose I take a restricted Aumann test of 40 questions regarding various general facts. I assign a joint probability of −150 dB to the survey. If I were better calibrated, my priors ought to have increased this to −100. I now know I must be aware a possible 50 dB gap between my beliefs and reality, I ought to be wary of any parochial adjustment. How wary? I should attach very little confidence to any adjustment under one order of magnitude...
I ran that one in my head and thought, “that’s got to be about a million times less likely.” And indeed it was, 6 orders of magnitude. To some extent, I may just have gotten lucky… but I think that lurking on Less Wrong for the last couple years may have made me appreciate probabilities at a more intuitive level.
So does this mean Less Wrong actually works?