I changed my mind from “1/3 is the right answer” to “The answer is obviously 1⁄2 or 1⁄3 once you’ve gotten clear on what question is being asked”. I’m not sure if I did so publicly. It seems to me that other folks have changed their minds similarly. I think I see an isomorphism to POAT here, as well as any classic Internet debate amongst intelligent people.
I’m also not sure if you’re serious, but if you assign a 50% probability to the relevant question being the one with the correct answer of ‘1/2’ and a 50% probability to the relevant question being the one with the correct answer of ‘1/3’ then ‘5/12’ should maximize your payoff over multiple such cases if you’re well-calibrated.
Phil and I seem to think the problem is sufficiently clearly specified to give an answer to. If you think 1⁄2 is a defensible answer, how would you reply to Robin Hanson’s comment?
FWIW, on POAT I am inclined towards “Whoever asked this question is an idiot”.
there are some problems similar to this one for which the answer is 1⁄2
there are some problems similar to this one for which the answer is 1⁄3
people seem to be disagreeing which sort of problem this is
all debate has devolved to debate over the meanings of words (in the problem statement and elsewhere)
Given this, I think it’s obvious that the problem is ambiguous, and arguing whether the problem is ambiguous is counterproductive as compared to just sorting out which sort of problem you’re responding to and what the right answer is.
IMHO, different people giving different answers to problems does not mean it is ambiguous. Nor does people disagreeing over the meanings of words. Words do have commonly-accepted meanings—that is how people communicate.
I changed my mind from “1/3 is the right answer” to “The answer is obviously 1⁄2 or 1⁄3 once you’ve gotten clear on what question is being asked”. I’m not sure if I did so publicly. It seems to me that other folks have changed their minds similarly. I think I see an isomorphism to POAT here, as well as any classic Internet debate amongst intelligent people.
I’m not sure whether this is legitimate or a joke, but if the question is unclear about whether 1⁄2 or 1⁄3 is better, maybe 5⁄12 is a good answer.
I’m also not sure if you’re serious, but if you assign a 50% probability to the relevant question being the one with the correct answer of ‘1/2’ and a 50% probability to the relevant question being the one with the correct answer of ‘1/3’ then ‘5/12’ should maximize your payoff over multiple such cases if you’re well-calibrated.
Phil and I seem to think the problem is sufficiently clearly specified to give an answer to. If you think 1⁄2 is a defensible answer, how would you reply to Robin Hanson’s comment?
FWIW, on POAT I am inclined towards “Whoever asked this question is an idiot”.
Actually I think it would make more sense to reply to my own comment in response to this. link
I am not sure that is going anywhere.
Personally, I think I pretty-much nailed what was wrong with the claim that the problem was ambiguous here.
I think that we’ve established the following:
there are some problems similar to this one for which the answer is 1⁄2
there are some problems similar to this one for which the answer is 1⁄3
people seem to be disagreeing which sort of problem this is
all debate has devolved to debate over the meanings of words (in the problem statement and elsewhere)
Given this, I think it’s obvious that the problem is ambiguous, and arguing whether the problem is ambiguous is counterproductive as compared to just sorting out which sort of problem you’re responding to and what the right answer is.
IMHO, different people giving different answers to problems does not mean it is ambiguous. Nor does people disagreeing over the meanings of words. Words do have commonly-accepted meanings—that is how people communicate.