Is there any decision theory that works well when faced with infinite choice?
Suppose you meet a benevolent genie, who says “pick a number, any real number, and I will give you that many utils”.
It seems like this isn’t about your decision theory, since knowing about busy beaver numbers gives you an advantage over everyone that doesn’t.
On your last problem, if you want to output a number higher than you normally could:
Run a lottery (If you have company):
At the end of the day, the lottery is run. When someone wins the lottery, they leave the next day (or are ‘unsubscribed’). Then it is run again.
This method relies on the number of beings in purgatory, and not the highest number which you can output/conceive of.
It seems like this isn’t about your decision theory, since knowing about busy beaver numbers gives you an advantage over everyone that doesn’t.
On your last problem, if you want to output a number higher than you normally could:
Run a lottery (If you have company):
At the end of the day, the lottery is run. When someone wins the lottery, they leave the next day (or are ‘unsubscribed’). Then it is run again.
This method relies on the number of beings in purgatory, and not the highest number which you can output/conceive of.