I have a question for those more familiar with the discussions surrounding this problem: is there anything really relevant about the sleeping/waking/amnesia story here? What if instead the experimenter just went out and asked the next random passerby on the street each time?
It seems to me that the problem could be formulated less confusingly that way. Am I missing something?
is there anything really relevant about the sleeping/waking/amnesia story here? What if instead the experimenter just went out and asked the next random passerby on the street each time?
Yes, I think that there is something very important about the memory loss/waking.
I don’t think many people here would take the “1/2” approach; they would reason “Since if the die came up 1, there would be 400 interviews, and I am being interviewed, it almost certainly came up 1″.
What if instead the experimenter just went out and asked the next random passerby on the street each time?
I’m confused about how that’s supposed to have the same relevant features, so the answer to your question is probably “Yes”.
Are you suggesting the following?: Flip a coin. Go out and ask a random passerby what the probability is that the coin came up heads.
If so, you’ve entirely eliminated Beauty’s subjective uncertainty about whether she’s been woken up once or more than once, which is putatively relevant to subjective probability.
The exact equivalent of the original problem would be as follows. You announce that:
(1) You’re about to flip a coin at some secret time during the next few days, and the result will be posted publicly in (say) a week.
(2) Before the flip, you’ll approach a random person in the street and ask about their expectation about the result that’s about to be posted. After the flip, if and only if it lands tails, you’ll do the same with one additional person before the result is announced publicly. The persons are unaware of each other, and have no way to determine if they’re being asked before or after the actual toss.
So, does anyone see relevant differences between this problem and the original one?
I’m guessing you already understood this, but as a person accosted and informed of this procedure, I know it’s more likely that I heard about it because the result was tails (than I was to hear about it before the toss). Those experiments that resulted in heads, I (most likely) never got to hear about.
So in asking if there’s any relevant thing that’s different, you expect a halfer to come forth and explain himself. Unfortunately, I’m not one. But it does seem to me that the only possible important difference is that Beauty knows about the experiment before the coin is tossed; but perhaps the amnesia compensates exactly for that.
As far as your “an instrument sold by a (so far completely ignorant) third party that pays off $100 if the announced result is tails”, then of course Beauty would value it exactly as your interviewees, provided she knew that the offer was to be made at every interview.
Well you also have to note in the problem description that a particular person is asked, and ask what should their guess be (so far you just got as far as the announcement).
Well, yes, I should also specify that you’ll actually act on the announcement.
But in any case, would anyone find anything strange or counterintuitive about this less exotic formulation, which could be readily tried in the real world? As soon as the somewhat vague “expectation about the result” is stated clearly, the answer should be clear. In particular, if we ignore risk aversion and discount rate, each interviewee should be willing to pay, on the spot, up to $66.66 for an instrument sold by a (so far completely ignorant) third party that pays off $100 if the announced result is tails.
Aha. In that case, I’d say it’s analogous, but I might just be granting that since the correct answer there is 1⁄3 as well. Or are there folks that would answer 1⁄2 to this scenario?
Yes, the answer is 1⁄3, because I am more likely to be asked if it was tails. But in the original problem, I am not more likely to be asked, I am just asked more often, so there is no analogy.
I have a question for those more familiar with the discussions surrounding this problem: is there anything really relevant about the sleeping/waking/amnesia story here? What if instead the experimenter just went out and asked the next random passerby on the street each time?
It seems to me that the problem could be formulated less confusingly that way. Am I missing something?
Yes, I think that there is something very important about the memory loss/waking.
Suppose we perform the really extreme sleeping beauty problem but each interview is with a different person, chose at random from a very large pool.
I don’t think many people here would take the “1/2” approach; they would reason “Since if the die came up 1, there would be 400 interviews, and I am being interviewed, it almost certainly came up 1″.
I’m not sure I understand your “really extreme” formulation fully. Is the amnesia supposed to make the wins in chocolate bars non-cumulative?
I’m confused about how that’s supposed to have the same relevant features, so the answer to your question is probably “Yes”.
Are you suggesting the following?: Flip a coin. Go out and ask a random passerby what the probability is that the coin came up heads.
If so, you’ve entirely eliminated Beauty’s subjective uncertainty about whether she’s been woken up once or more than once, which is putatively relevant to subjective probability.
The exact equivalent of the original problem would be as follows. You announce that:
(1) You’re about to flip a coin at some secret time during the next few days, and the result will be posted publicly in (say) a week.
(2) Before the flip, you’ll approach a random person in the street and ask about their expectation about the result that’s about to be posted. After the flip, if and only if it lands tails, you’ll do the same with one additional person before the result is announced publicly. The persons are unaware of each other, and have no way to determine if they’re being asked before or after the actual toss.
So, does anyone see relevant differences between this problem and the original one?
I’m guessing you already understood this, but as a person accosted and informed of this procedure, I know it’s more likely that I heard about it because the result was tails (than I was to hear about it before the toss). Those experiments that resulted in heads, I (most likely) never got to hear about.
So in asking if there’s any relevant thing that’s different, you expect a halfer to come forth and explain himself. Unfortunately, I’m not one. But it does seem to me that the only possible important difference is that Beauty knows about the experiment before the coin is tossed; but perhaps the amnesia compensates exactly for that.
As far as your “an instrument sold by a (so far completely ignorant) third party that pays off $100 if the announced result is tails”, then of course Beauty would value it exactly as your interviewees, provided she knew that the offer was to be made at every interview.
Well you also have to note in the problem description that a particular person is asked, and ask what should their guess be (so far you just got as far as the announcement).
But I think that’s equivalent.
Well, yes, I should also specify that you’ll actually act on the announcement.
But in any case, would anyone find anything strange or counterintuitive about this less exotic formulation, which could be readily tried in the real world? As soon as the somewhat vague “expectation about the result” is stated clearly, the answer should be clear. In particular, if we ignore risk aversion and discount rate, each interviewee should be willing to pay, on the spot, up to $66.66 for an instrument sold by a (so far completely ignorant) third party that pays off $100 if the announced result is tails.
If the coin is tails, you would ask two random passerbies.
Aha. In that case, I’d say it’s analogous, but I might just be granting that since the correct answer there is 1⁄3 as well. Or are there folks that would answer 1⁄2 to this scenario?
Yes, the answer is 1⁄3, because I am more likely to be asked if it was tails. But in the original problem, I am not more likely to be asked, I am just asked more often, so there is no analogy.