Why on earth wouldn’t I consider whether or not I would play again? Am I barred from doing so?
If I know that the card game will continue to be available, and that Omega can truly double my expected utility every draw, either it’s a relatively insignificant increase of expected utility over the next few minutes it takes me to die, in which case it’s a foolish bet, compared to my expected utility over the decades I have left, conservatively, or Omega can somehow change the whole world in the radical fashion needed for my expected utility over the next few minutes it takes me to die to dwarf my expected utility right now.
This paradox seems to depend on the idea that the card game is somehow excepted from the 90% likely doubling of expected utility. As I mentioned before, my expected utility certainly includes the decisions I’m likely to make, and it’s easy to see that continuing to draw cards will result in my death. So, it depends on what you mean. If it’s just doubling expected utility over my expected life IF I don’t die in the card game, then it’s a foolish decision to draw the first or any number of cards. If it’s doubling expected utility in all cases, then I draw cards until I die, happily forcing Omega to make verifiable changes to the universe and myself.
Now, there are terms at which I would take the one round, IF you don’t die in the card game version of the gamble, but it would probably depend on how it’s implemented. I don’t have a way of accessing my utility function directly, and my ability to appreciate maximizing it is indirect at best. So I would be very concerned about the way Omega plans to double my expected utility, and how I’m meant to experience it.
In practice, of course, any possible doubt that it’s not Omega giving you this gamble far outweighs any possibility of such lofty returns, but the thought experiment has some interesting complexities.
Why on earth wouldn’t I consider whether or not I would play again? Am I barred from doing so?
If I know that the card game will continue to be available, and that Omega can truly double my expected utility every draw, either it’s a relatively insignificant increase of expected utility over the next few minutes it takes me to die, in which case it’s a foolish bet, compared to my expected utility over the decades I have left, conservatively, or Omega can somehow change the whole world in the radical fashion needed for my expected utility over the next few minutes it takes me to die to dwarf my expected utility right now.
This paradox seems to depend on the idea that the card game is somehow excepted from the 90% likely doubling of expected utility. As I mentioned before, my expected utility certainly includes the decisions I’m likely to make, and it’s easy to see that continuing to draw cards will result in my death. So, it depends on what you mean. If it’s just doubling expected utility over my expected life IF I don’t die in the card game, then it’s a foolish decision to draw the first or any number of cards. If it’s doubling expected utility in all cases, then I draw cards until I die, happily forcing Omega to make verifiable changes to the universe and myself.
Now, there are terms at which I would take the one round, IF you don’t die in the card game version of the gamble, but it would probably depend on how it’s implemented. I don’t have a way of accessing my utility function directly, and my ability to appreciate maximizing it is indirect at best. So I would be very concerned about the way Omega plans to double my expected utility, and how I’m meant to experience it.
In practice, of course, any possible doubt that it’s not Omega giving you this gamble far outweighs any possibility of such lofty returns, but the thought experiment has some interesting complexities.