Thomas Hurka’s St Petersburg Paradox: Suppose you are offered a deal—you can press a button that has a 51% chance of creating a new world and doubling the total amount of utility, but a 49% chance of destroying the world and all utility in existence. If you want to maximise total expected utility, you ought to press the button—pressing the button has positive expected value. But the problem comes when you are asked whether you want to press the button again and again and again—at each point, the person trying to maximise expected utility ought to agree to press the button, but of course, eventually they will destroy everything.[2]
I have two gripes with this thought experiment. First, time is not modelled. Second, it’s left implicit why we should feel uneasy about the thought experiment. And that doesn’t work due to highly variable philosophical intuitions. I honestly don’t feel uneasy about the thought experiment at all (only slightly annoyed). But maybe I would have it been completely specified.
I can see two ways to add a time dimension to the problem. First, you could let all the presses be predetermined and in one go, where we get into Satan’s apple territory. Second, you could have 30 seconds pause between all presses. But in that case, we would accumulate massive amounts of utility in a very short time—just the seconds in-between presses would be invaluable! And who cares if the world ends in five minutes with probability 1−0.4910 when every second it survives is so sweet? :p
What is the “Satan’s apple” reference? I don’t get that, sorry.
I think I agree with you that the version of the example I offered did not fully specify the time dimension. But it’s crucial to the original St Petersburg game that your winnings at stage n are not collected until the game is finished, so that if you lose at stage n+1 you don’t get to enjoy your winnings. So presumably, in Hurka’s variant, the extra world(s) should not be created until after you walk away from the button, so the seconds in-between presses would not be valuable at all. But I take your point that this wasn’t specified well enough in OP.
Satan cuts an apple into a countable infinity of slices and offers it to Eve, one piece at a time. Each slice has positive utility for Eve. If Eve eats only finitely many pieces, there is no difficulty; she simply enjoys her snack. If she eats infinitely many pieces, however, she is banished from Paradise. To keep things simple, we may assume that the pieces are numbered: in each time interval, the choice is Take piece n or Don’t take piece n. Furthermore, Eve can reject piece n, but take later pieces. Taking any countably infinite set leads to the bad outcome (banishment). Finally, regardless of whether or not she is banished, Eve gets to keep (and eat) her pieces of apple. Call this the original version of Satan’s apple.
We shall sometimes discuss a simplified version of Satan’s apple, different from the original version in two respects. First, Eve is banished only if she takes all the pieces. Second, once Eve refuses a piece, she cannot take any more pieces. These restrictions make Satan’s apple a close analogue to the two earlier puzzles.
I have two gripes with this thought experiment. First, time is not modelled. Second, it’s left implicit why we should feel uneasy about the thought experiment. And that doesn’t work due to highly variable philosophical intuitions. I honestly don’t feel uneasy about the thought experiment at all (only slightly annoyed). But maybe I would have it been completely specified.
I can see two ways to add a time dimension to the problem. First, you could let all the presses be predetermined and in one go, where we get into Satan’s apple territory. Second, you could have 30 seconds pause between all presses. But in that case, we would accumulate massive amounts of utility in a very short time—just the seconds in-between presses would be invaluable! And who cares if the world ends in five minutes with probability 1−0.4910 when every second it survives is so sweet? :p
People should be allowed to destroy the button (aka “x-risk reduction”) ;-)
What is the “Satan’s apple” reference? I don’t get that, sorry.
I think I agree with you that the version of the example I offered did not fully specify the time dimension. But it’s crucial to the original St Petersburg game that your winnings at stage n are not collected until the game is finished, so that if you lose at stage n+1 you don’t get to enjoy your winnings. So presumably, in Hurka’s variant, the extra world(s) should not be created until after you walk away from the button, so the seconds in-between presses would not be valuable at all. But I take your point that this wasn’t specified well enough in OP.
Source: Satan, Saint Peter and Saint Petersburg