It’s a bit late to play the “Don’t question the hypothetical” card, given that a lot of the discussion, and not just between us, has been about variations on the original. Hypotheticals do not exist in a vacuum. In the space of hypotheticals it can be illuminating to explore the neighbourhood of the proposed problem, and in the world in which the hypothetical is proposed, there is usually an unstated agenda behind the design of the puzzle that should be part of the discourse around it.
Or to put that more pithily:
“I didn’t give you that option!”
“That’s right, you didn’t. I took it.”
I suggested some valid ways of fighting the hypothetical within my framing. If you want to take additional ways not compatible with the framing, feel free to suggest a different framing to use. We might just not disagree on the appropriate answer within that framing.
You have connected them in exact parallelism to your description of the mad scientist’s decision, but all that does is shift the bump in the carpet to that description, which now does not correspond to the actual rules of the problem as you stated them. The rules of the mad scientist’s decision are that if half or more press button K he kills those who didn’t, and if fewer than half do, he kills no-one. An equivalent way of describing it is that if fewer than half press button P he kills them, and if at least half do, he kills no-one. The idea that the PEACE button does nothing is wrong, because everyone is required to press one or the other. Pressing one has exactly the same consequences as not pressing the other.
“You have to pick either yellow or green” is a mathematical idealization of an underlying reality. I see no reason to believe that the most robust decision-making algorithm would ignore the deeper mechanistic factors that get idealized.
The mad scientist is presumably using some means to force you (e.g. maybe threatening your family), and there’s always some risk of other disturbances (e.g. electrical wiring errors) whose effects would differ depending on the specifics of the problem.
“You have to pick either yellow or green” is a mathematical idealization of an underlying reality. I see no reason to believe that the most robust decision-making algorithm would ignore the deeper mechanistic factors that get idealized.
If no variation on the hypothetical is allowed, the problem is isomorphic to the original red-blue question, and the story about the mad scientist is epiphenomenal, mere flavourtext, not a “deeper mechanistic factor”.
If you allow variation (the only way in which the presence of the mad scientist can make any difference), then I think my variation is as good as yours.
You are trying to maintain the isomorphism while making the flavourtext have real import. This is not possible.
Are we talking about transgenderism yet? (I have been wondering this for the last few exchanges.)
By “variation” I mean things like preventing the mad scientist from carrying out his dastardly plan, keeping people away from the misleadingly named PEACE button, and so on. Things that are excluded by the exact statement of the problem.
Unless you mean something like, you try to argue with the mad scientist about who should be included? Or try to force the mad scientist to exclude people who are clueless?
so I’m not sure why you are saying that I’m saying that you are not allowed to talk about that sort of stuff.
So OK I guess. Let’s say you’re all standing in a line, and he’s holding a gun to threaten you. You’re first in the line, and he explains the game to you and shows you the buttons.
If I understand correctly, you’re then saying that you’d yell “everyone! press yellow!”? And that if e.g. he introduces a new rule of “no talking to each other!” and threatens you with his gun, you’d assault him to try to stop his mad experiment?
That is, by my logic, a valid answer. I don’t know whether you’ll survive or what would happen in such a case. I probably wouldn’t do it, because it is too brave.
It’s your puzzle. You can make up whatever rules you like. I understood your purpose to be making a version of the red-blue puzzle that would have the same underlying structure but would persuade a different answer. But if isomorphism is maintained, the right answer must be the same. If isomorphism is not maintained, the right answer will be whatever it designed to be, at the expense of not bearing on the original problem.
Presumably this specific aspect is still isomorphic to the red-blue puzzle. With the red-blue puzzle, when you are standing in line for the pills, you could also yell out “take red!”, or assault the scientist threatening you with his gun.
Of course there do seem to be other nonisomorphisms, such as if you press the buttons multiple times. I admit that it is reasonable to say that these nonisomorphisms distinguish my scenario, but I think that still disproves your claim that framing shouldn’t matter, because the framing determines the nonisomorphisms and is the place where you’d actually end up making the decisions.
Games in decision theory are typically taken to be models of real-world decision problems, with the goal being to help you make better decisions. But real-world decision problems are open-ended in ways that games are not, so logically speaking the games must be an idealization that don’t reflect your actual options.
I suggested some valid ways of fighting the hypothetical within my framing. If you want to take additional ways not compatible with the framing, feel free to suggest a different framing to use. We might just not disagree on the appropriate answer within that framing.
“You have to pick either yellow or green” is a mathematical idealization of an underlying reality. I see no reason to believe that the most robust decision-making algorithm would ignore the deeper mechanistic factors that get idealized.
The mad scientist is presumably using some means to force you (e.g. maybe threatening your family), and there’s always some risk of other disturbances (e.g. electrical wiring errors) whose effects would differ depending on the specifics of the problem.
If no variation on the hypothetical is allowed, the problem is isomorphic to the original red-blue question, and the story about the mad scientist is epiphenomenal, mere flavourtext, not a “deeper mechanistic factor”.
If you allow variation (the only way in which the presence of the mad scientist can make any difference), then I think my variation is as good as yours.
You are trying to maintain the isomorphism while making the flavourtext have real import. This is not possible.
Are we talking about transgenderism yet? (I have been wondering this for the last few exchanges.)
I don’t know what you mean by “variation” in this comment.
By “variation” I mean things like preventing the mad scientist from carrying out his dastardly plan, keeping people away from the misleadingly named PEACE button, and so on. Things that are excluded by the exact statement of the problem.
This sounds similar to what I was saying with
so I’m not sure why you are saying that I’m saying that you are not allowed to talk about that sort of stuff.
So OK I guess. Let’s say you’re all standing in a line, and he’s holding a gun to threaten you. You’re first in the line, and he explains the game to you and shows you the buttons.
If I understand correctly, you’re then saying that you’d yell “everyone! press yellow!”? And that if e.g. he introduces a new rule of “no talking to each other!” and threatens you with his gun, you’d assault him to try to stop his mad experiment?
That is, by my logic, a valid answer. I don’t know whether you’ll survive or what would happen in such a case. I probably wouldn’t do it, because it is too brave.
It’s your puzzle. You can make up whatever rules you like. I understood your purpose to be making a version of the red-blue puzzle that would have the same underlying structure but would persuade a different answer. But if isomorphism is maintained, the right answer must be the same. If isomorphism is not maintained, the right answer will be whatever it designed to be, at the expense of not bearing on the original problem.
This circle cannot be squared.
Presumably this specific aspect is still isomorphic to the red-blue puzzle. With the red-blue puzzle, when you are standing in line for the pills, you could also yell out “take red!”, or assault the scientist threatening you with his gun.
Of course there do seem to be other nonisomorphisms, such as if you press the buttons multiple times. I admit that it is reasonable to say that these nonisomorphisms distinguish my scenario, but I think that still disproves your claim that framing shouldn’t matter, because the framing determines the nonisomorphisms and is the place where you’d actually end up making the decisions.
Games in decision theory are typically taken to be models of real-world decision problems, with the goal being to help you make better decisions. But real-world decision problems are open-ended in ways that games are not, so logically speaking the games must be an idealization that don’t reflect your actual options.