Nice! Right now I’m faced with an exercise in catching loopholes of exactly that kind, while trying to write a newbie-friendly text on UDT. Basically I’m going through a bunch of puzzles involving perfect predictors, trying to reformulate them as crisply as possible and remove all avenues of cheating. It’s crazy.
For your particular puzzle, I think you can rescue it by making the gods go into an infinite loop when faced with a paradox. And when faced with a regular non-paradoxical question, they can wait for an unknown but finite amount of time before answering. That way you can’t reliably distinguish an infinite loop from an answer that’s just taking a while, so your only hope of solving the problem in guaranteed finite time is to ask non-paradoxical questions. That also stops you from manipulating gods into doing stuff, I think.
For example, I just decided that the symmetric Prisoner’s Dilemma should be introduced quite late in the text, not near the beginning as I thought. The reason is that it’s tricky to formalize, even if you assume that participants are robots.
“Robot, I have chosen you and another robot at random, now you must play the PD against each other. My infallible predictor device says you will either both cooperate or both defect. What do you do?”—The answer depends on how the robots were chosen, and what the owner would do if the predictor didn’t predict symmetry. It’s surprisingly hard to patch up.
Nice! Right now I’m faced with an exercise in catching loopholes of exactly that kind, while trying to write a newbie-friendly text on UDT. Basically I’m going through a bunch of puzzles involving perfect predictors, trying to reformulate them as crisply as possible and remove all avenues of cheating. It’s crazy.
For your particular puzzle, I think you can rescue it by making the gods go into an infinite loop when faced with a paradox. And when faced with a regular non-paradoxical question, they can wait for an unknown but finite amount of time before answering. That way you can’t reliably distinguish an infinite loop from an answer that’s just taking a while, so your only hope of solving the problem in guaranteed finite time is to ask non-paradoxical questions. That also stops you from manipulating gods into doing stuff, I think.
Can you give me some examples of those exercises and loopholes you have seen?
For example, I just decided that the symmetric Prisoner’s Dilemma should be introduced quite late in the text, not near the beginning as I thought. The reason is that it’s tricky to formalize, even if you assume that participants are robots.
“Robot, I have chosen you and another robot at random, now you must play the PD against each other. My infallible predictor device says you will either both cooperate or both defect. What do you do?”—The answer depends on how the robots were chosen, and what the owner would do if the predictor didn’t predict symmetry. It’s surprisingly hard to patch up.