I suspect that calling your utility function itself into question like that isn't valid in terms of expected utility calculations.
I think what you're suggesting is that on top of our utility function we have some sort of meta-utility function that just says "maximize your utility function, whatever it is." That would fall into your uncertainty trap, but I don't think that is the case, I don't think we have a meta-function like that, I think we just have our utility function.
If you were allowed to cast your entire utility function into doubt you would be completely paralyzed. How do you know you don't have an unbounded utility function for paperclips? How do you know you don't have an unbounded utility function for, and assign infinite utility to, the universe being exactly the way it would be if you never made a fully rational decision again and just went around your life on autopilot? The end result is that there are a number of possible courses of action that would all generate infinity utility and no way to choose between them because infinity=infinity. The only reason your argument sounds logical is because you are allowing the questioning of the boundedness of the utility function, but not its contents.
I think that knowledge of your utility function is probably a basic, prerational thing, like deciding to use expected utility maximization and Bayesian updating in the first place. Attempting to insert your utility function itself into your calculations seems like a basic logical error.
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.
Also, "infinity=infinity" is not the case. Infinity ixs not a number, and the problem goes away if you use limits. otherwise, yes, I even probaböly have unbounded but very slow growing facotrs for s bunch of thigns like that.
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: