I really care whether they can pay attention to an apple when they're hungry to decide whether to eat the apple, as opposed to considering obscure consequences of how various possible unlikely gods might react to the eating of the apple.
Personal survival makes it a lot easier to please unlikely gods, so eating the apple is preferred.
Eating an apple was meant to be an example of a trivial thing. Inflating it to personal survival misses the point. Eating an apple should be connected to your own personal values concerning hunger and apples, and there should be a way to make a decision about eating an apple or not eating it and being slightly hungry based on your personal values about apples and hunger. If we have to think about unlikely gods to decide whether to eat an apple, something is broken.
For more general situations, some paths to infinity are much more probable than others. For example, perhaps we can build a god [SIAI pointer].
That's a likely god, not an unlikely god, so it's a little bit different. Even then, low-probability interactions between eating an apple and the nature of the likely god seem likely to lead to bizarre decision processes about apple-eating, unless you have bounded utilities.
Even then, low-probability interactions between eating an apple and the nature of the likely god seem likely to lead to bizarre decision processes about apple-eating, unless you have bounded utilities.
I don't see why this is a problem. What causes you to find it so unlikely that our desires could work this way?
This post describes an infinite gamble that, under some reasonable assumptions, will motivate people who act to maximize an unbounded utility function to send me all their money. In other words, if you understand this post and it doesn't motivate you to send me all your money, then you have a bounded utility function, or perhaps even upon reflection you are not choosing your actions to maximize expected utility, or perhaps you found a flaw in this post.
Briefly, we do this with The St. Petersburg Paradox, converted to a mugging along the lines of Pascal's Mugging. I then tweaked it to extract all of the money instead of just a fixed sum.
I have always wondered if any actual payments have resulted from Pascal's Mugging, so I intend to track payments received for this variation. If anyone does have unbounded utility and wants to prove me wrong by sending money, send it with Paypal to tim at fungible dot com. Annotate the transfer with the phrase "St. Petersburg Mugging", and I'll edit this article periodically to say how much money I received. In order to avoid confusing the experiment, and to exercise my spite, I promise I will not spend the money on anything you will find especially valuable. SIAI would be better charity, if you want to do charity, but don't send that money to me.
Here's the hypothetical (that is, false) offer to persons with unbounded utility:
If I am lying and the offer is real, and I am a god, what utility will you receive from sending me a dollar? Well, the probability of me seeing N Tails followed by a Head is (1/2)**(N + 1), and your utility for the resulting universe is UTILITY(UN(N)) >= DUT * 2**N, so your expected utility if I see N tails is (1/2)**(N + 1) * UTILITY(UN(N)) >= (1/2)**(N + 1) * DUT * 2 ** N = DUT/2. There are infinitely many possible values for N, so your total expected utility is positive infinity * DUT/2, which is positive infinity.
I hope we agree that it is unlikely that I am a god, but it's consistent with what you have observed so far, so unless you were born with certain knowledge that I am not a god, you have to assign positive probability to it. Similarly, the probability that I'm lying and the above offer is real is also positive. The product of two positive numbers is positive. Combining this with the result from the previous paragraph, your expected utility from sending me a dollar is infinitely positive.
If you send me one dollar, there will probably be no result. Perhaps I am a god, and the above offer is real, but I didn't do anything beyond flipping the first coin because it came out Tails. In that case, nothing happens. Your expected utility for the next dollar is also infinitely positive, so you should send the next dollar too. By induction you should send me all your dollars.
If you don't send money because you have bounded utility, that's my desired outcome. If you do feel motivated to send me money, well, I suppose I lost the argument. Remember to send all of it, and remember that you can always send me more later.
As of 7 June 2011, nobody has sent me any money for this.
ETA: Some interesting issues keep coming up. I'll put them here to decrease the redundancy: