What, exactly, would the guard would say in different situations? Using the standard, utterly unrealistic, interpretation of probability problems like this, the guard is supposed to say this:
VM: If you are on Vulcan, you are in the Mountain VD: I have nothing to tell you. EM: If you are on Vulcan, you are in the Mountain ED: If you are on Vulcan, you are in the Mountain
in which case the probability is 1⁄3. But I have a hard time believing that the guard is willing to talk to you here, but wouldn’t be willing to talk if you were in the Vulcan Desert.
Since the guard refused to talk at first, but then told you something later, it seems pretty clear that they’re trying to help you out. The most obvious way for them to communicate to you where you are is like this:
VM: If you are on Vulcan, you are in the Mountain VD: If you are on Vulcan, you are in the Desert EM: If you are on Earth, you are in the Mountain ED: If you are on Earth, you are in the Desert
But there are other possibilities. Perhaps there’s a policy of executing guards that reveal information about where you are, so the guard wants plausible deniability by lying to you:
VM: If you are on Vulcan, you are in the Desert VD: If you are on Vulcan, you are in the Mountain EM: If you are on Earth, you are in the Desert ED: If you are on Earth, you are in the Mountain
It seems that you’ve ruled that out in the problem statement, though.
Altogether, as Dacyn says, “it depends on what you know about the psychology of the guard.”
Somewhere in Rationality, there’s a post about this.
What, exactly, would the guard would say in different situations? Using the standard, utterly unrealistic, interpretation of probability problems like this, the guard is supposed to say this:
in which case the probability is 1⁄3. But I have a hard time believing that the guard is willing to talk to you here, but wouldn’t be willing to talk if you were in the Vulcan Desert.
Since the guard refused to talk at first, but then told you something later, it seems pretty clear that they’re trying to help you out. The most obvious way for them to communicate to you where you are is like this:
But there are other possibilities. Perhaps there’s a policy of executing guards that reveal information about where you are, so the guard wants plausible deniability by lying to you:
It seems that you’ve ruled that out in the problem statement, though.
Altogether, as Dacyn says, “it depends on what you know about the psychology of the guard.”
Somewhere in Rationality, there’s a post about this.
“Somewhere in Rationality, there’s a post about this.”—do you have any idea where such a post is?
I believe I was thinking of this one:
https://www.lesswrong.com/posts/f6ZLxEWaankRZ2Crv/probability-is-in-the-mind