Are you certain that the likeliness of all your claims being true is not proportional to the size of the change in universe you are claiming to affect.
Almost any person can reasonably claim to be a utility generating god for small values of n for some set of common utility functions (and we don't even have to give up our god-like ability). That is how most of us are able to find gainful employment.
The implausible claim is the ability to generate universe changes of arbitrary utility value.
My proposal is that any claim of utility generation ability has plausibility in inverse proportion to the size of effect that one claims to be able to produce. If I say I can produce delta-U ~$1000, that is somewhat plausible. If I say I can produce delta-U of $1,000,000 that might be plausible for some very high skill people, or given a long time to do it, but as a random person with little time, it's extremely implausible. If I claim to be able to produce delta-U ~ (some amount of wealth > world GDP), that's exceedingly implausible no matter who I am.
And of course, in order to make your mugging function, you would need to be able to produce unbounded utility. Your claim to unbounded utility generation is unboundedly implausible.
Admittedly, this is somewhat unsatisfactory as it effectively treats the unbounded implausibility of a classic onmipotent God figure as an axiom. But this is essentially the same trick as using a Bayesian Occam's Razor to demonstrate atheism. If you aren't happy with this line of reasoning, than I can't see how you'd be happy with Occam's Razor as an axiom, nor how you could legitimately claim that there's a solid rational case for hard atheism.
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: