prase:
I know you have limited it to repeated judgments about essentialy the same question. I was rather asking why, and I am still not sure whether I interpret it correctly. Is it that the judgments themselves are possibly produced by different parts of brain, or the person's self-evaluation of certainty are produced by different parts of brain, or both? And if so, so what?
We don't really know, but it could certainly be both, and also it may well be that the same parts of the brain are not equally reliable for all questions they are capable of processing. Therefore, while simple inductive reasoning tells us that consistent accuracy on the same problem can be extrapolated, there is no ground to generalize to other questions, since they may involve different parts of the brain, or the same part functioning in different modes that don't have the same accuracy.
Unless, of course, we cover all such various parts and modes and obtain some sort of weighted average over them, which I suppose is the point of your thought experiment, of which more below.
Do you 1) maintain that such stable results are very unlikely to happen, or that 2) even if most of people can be calibrated is such way, still it doesn't justify using them for measuring probabilities?
If the set of questions remains representative -- in the sense of querying the same brain processes with the same frequency -- the results could turn out to be fairly stable. This could conceivably be achieved by large and wide-ranging sets of questions. (I wonder if someone has actually done such experiments?)
However, the result could be replicated only if the same person is again asked similar large sets of questions that are representative with regards to the frequencies with which they query different brain processes. Relative to that reference class, it clearly makes sense to attach probabilities to answers, so, yes, here we would have another counterexample for my original claim, for another peculiar meaning of probabilities.
The trouble is that these probabilities would be useless for any purpose that doesn’t involve another similar representative set of questions. In particular, sets of questions about some particular topic that is not representative would presumably not replicate them, and thus they would be a very bad guide for betting that is limited to some particular topic (as it nearly always is). Thus, this seems like an interesting theoretical exercise, but not a way to obtain practically useful numbers.
(I should add that I never thought about this scenario before, so my reasoning here might be wrong.)
If there are any experimental psychologist reading this, maybe they can organise the experiment. I am curious whether people indeed can be calibrated on general questions.
Please read the post before voting on the comments, as this is a game where voting works differently.
Warning: the comments section of this post will look odd. The most reasonable comments will have lots of negative karma. Do not be alarmed, it's all part of the plan. In order to participate in this game you should disable any viewing threshold for negatively voted comments.
Here's an irrationalist game meant to quickly collect a pool of controversial ideas for people to debate and assess. It kinda relies on people being honest and not being nitpickers, but it might be fun.
Write a comment reply to this post describing a belief you think has a reasonable chance of being true relative to the the beliefs of other Less Wrong folk. Jot down a proposition and a rough probability estimate or qualitative description, like 'fairly confident'.
Example (not my true belief): "The U.S. government was directly responsible for financing the September 11th terrorist attacks. Very confident. (~95%)."
If you post a belief, you have to vote on the beliefs of all other comments. Voting works like this: if you basically agree with the comment, vote the comment down. If you basically disagree with the comment, vote the comment up. What 'basically' means here is intuitive; instead of using a precise mathy scoring system, just make a guess. In my view, if their stated probability is 99.9% and your degree of belief is 90%, that merits an upvote: it's a pretty big difference of opinion. If they're at 99.9% and you're at 99.5%, it could go either way. If you're genuinely unsure whether or not you basically agree with them, you can pass on voting (but try not to). Vote up if you think they are either overconfident or underconfident in their belief: any disagreement is valid disagreement.
That's the spirit of the game, but some more qualifications and rules follow.
If the proposition in a comment isn't incredibly precise, use your best interpretation. If you really have to pick nits for whatever reason, say so in a comment reply.
The more upvotes you get, the more irrational Less Wrong perceives your belief to be. Which means that if you have a large amount of Less Wrong karma and can still get lots of upvotes on your crazy beliefs then you will get lots of smart people to take your weird ideas a little more seriously.
Some poor soul is going to come along and post "I believe in God". Don't pick nits and say "Well in a a Tegmark multiverse there is definitely a universe exactly like ours where some sort of god rules over us..." and downvote it. That's cheating. You better upvote the guy. For just this post, get over your desire to upvote rationality. For this game, we reward perceived irrationality.
Try to be precise in your propositions. Saying "I believe in God. 99% sure." isn't informative because we don't quite know which God you're talking about. A deist god? The Christian God? Jewish?
Y'all know this already, but just a reminder: preferences ain't beliefs. Downvote preferences disguised as beliefs. Beliefs that include the word "should" are are almost always imprecise: avoid them.
Additional rules: