You need to take advantage of the fact that probability is a consequence of incomplete information, and think about the models of the world people have that encode their information. “Meta-probabbility” only exists within a certain model of the problem, and if you totally ignore that you get some drastically confusing conclusions.
I’d think about it like this: suppose that I hand you a box with a slot in it. What do you expect to happen if you put a quarter into the slot?
To answer this we engage our big amount of human knowledge about boxes and people who hand them to you. It’s very likely that nothing at all will happen, but I’ve also seen plenty of boxes that also emit sound, or gumballs, or temporary tattoos, or sometimes more quarters. But suppose that I have previously handed you a box that emits more quarters sometimes when you put quarters in. Then maybe you raise the probability that it also emits quarters, et cetera.
Now, within this model you have a probability of some payoff, but only if it’s one of the reward-emitting boxes, and it also has some probability of emitting sound etc. What you call a “meta-probability” is actually the probability of some sub-model being verified or confirmed. Suppose I put in one quarter in and two quarters come out—now you’ve drastically cut down the models that can describe the box. This is “updating the meta-probability.”
It also has elrich markers, and is being used in a decision theory experiment, and given in association with omnius wording. These indicates it does something nasty.
I guess it will raise the probability a little bit, but out of all eldritch-marked things I’ve ever seen, about 100% have been ornamental. We can’t over-weight small probabilities just because they’re vivid.
Maybe we’re getting different mental images for “eldrich”. I assumed things that’d get me banned to even vaguely describe, not tentackles and pentagrams.
You need to take advantage of the fact that probability is a consequence of incomplete information, and think about the models of the world people have that encode their information. “Meta-probabbility” only exists within a certain model of the problem, and if you totally ignore that you get some drastically confusing conclusions.
So, how would you analyze this problem, more specifically? What do you think the optimal strategy is?
The problem of what to expect from the black box?
I’d think about it like this: suppose that I hand you a box with a slot in it. What do you expect to happen if you put a quarter into the slot?
To answer this we engage our big amount of human knowledge about boxes and people who hand them to you. It’s very likely that nothing at all will happen, but I’ve also seen plenty of boxes that also emit sound, or gumballs, or temporary tattoos, or sometimes more quarters. But suppose that I have previously handed you a box that emits more quarters sometimes when you put quarters in. Then maybe you raise the probability that it also emits quarters, et cetera.
Now, within this model you have a probability of some payoff, but only if it’s one of the reward-emitting boxes, and it also has some probability of emitting sound etc. What you call a “meta-probability” is actually the probability of some sub-model being verified or confirmed. Suppose I put in one quarter in and two quarters come out—now you’ve drastically cut down the models that can describe the box. This is “updating the meta-probability.”
Of comments so far, this comes closest to the answer I have in mind… for whatever that’s worth!
It also has elrich markers, and is being used in a decision theory experiment, and given in association with omnius wording. These indicates it does something nasty.
I guess it will raise the probability a little bit, but out of all eldritch-marked things I’ve ever seen, about 100% have been ornamental. We can’t over-weight small probabilities just because they’re vivid.
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Maybe we’re getting different mental images for “eldrich”. I assumed things that’d get me banned to even vaguely describe, not tentackles and pentagrams.