You are, in this very post, questing and saying that your utility function PROBABLY this and that you dont think there's uncertainty about it... That is, you display uncertainty about your utility function. Check mate.
Even if I was uncertain about my utility function, you're still wrong. The factor you are forgetting about is uncertainty. With a bounded utility function infinite utility scores the same as a smaller amount of utility. So you should always assume a bounded utility function, because unbounded utility functions don't offer any more utility than bounded ones and bounded ones outperform unbounded ones in situations like Pascal's Mugging. There's really no point to believing you have an unbounded function.
I just used the same logic you did. But the difference is that I assumed a bounded utility function was the default standard for comparison, whereas you assumed, for no good reason, that the unbounded one was.
I don't know what the proper way to calculate utility when you are uncertain about your utility function. But I know darn well that doing an expected-utility calculation about what utility each function will yield and using one of the two functions that are currently in dispute to calculate that utility is a crime against logic. If you do that you're effectively assigning "having an unbounded function" a probability of 1. And 1 isn't a probability.
Your formulation of "unbounded utility function always scores infinity so it always wins" is not the correct way to compare two utility functions under uncertainty. You could just as easily say "unbounded and bounded both score the same, except in Pascal's mugging where bounded scores higher, so bounded always wins."
I think that using expected utility calculation might be valid for things like deciding whether you assign any utility at all to object or consequence. But for big meta-level questions about what your utility function even is attempting to use them is a huge violation of logic.
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: