downvoted because you actually said "I would like to do whichever of these two alternatives leads to more utility."
A) no one or almost no one thinks this way, and advice based on this sort of thinking is useless to almost everyone.
B) The entire point of the original post was that, if you try to do this, then you immediately get completely taken over by consideration of any gods you can imagine. When you say that thinking about unlikely gods is not "worth" the computational resources, you are sidestepping the very issue we are discussing. You have already decided it's not worth thinking about tiny probabilities of huge returns.
I think he actually IS making the argument that you assign a low probability to, but instead of dismissing it I think it's actually extremely important to decide whether to take certain courses based on how practical they are. The entire original purpose of this community is research into AI, and while you can't choose your own utility function, you can choose an AI's. If this problem is practically insoluble, then we should design AIs with only bounded utility functions.
downvoted because you actually said "I would like to do whichever of these two alternatives leads to more utility."
Tim seemed to be implying that it would be absurd for unlikely gods to be the most important motive for determining how to act, but I did not see how anything that he said showed that doing so is actually a bad idea.
When you say that thinking about unlikely gods is not "worth" the computational resources, you are sidestepping the very issue we are discussing.
What? I did not say that; I said that thinking about unlike...
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: