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.
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.