I can see various possibilities of ways around de Blanc's argument besides bounding utility, but those are whole nother questions.
Can you elaborate on these?
Not with any great weight, it's just a matter of looking at each hypothesis and thinking up a way of making it fail.
Maybe utility isn't bounded below by a computable function (and a fortiori is not itself computable). That might be unfortunate for the would-be utility maximizer, but if that's the way it is, too bad.
Or -- this is a possibility that de Blanc himself mentions in the 2009 version -- maybe the environment should not be allowed to range over all computable functions. That seems quite a strong possibility to me. Known physical bounds on the density of information processing would appear to require it. Of course, those bounds apply equally to the utility function, which might open the way for a complexity-bounded version of the proof of bounded utility.
Maybe utility isn't bounded below by a computable function (and a fortiori is not itself computable). That might be unfortunate for the would-be utility maximizer, but if that's the way it is, too bad.
Good point, but I find it unlikely.
Or -- this is a possibility that de Blanc himself mentions in the 2009 version -- maybe the environment should not be allowed to range over all computable functions. That seems quite a strong possibility to me. Known physical bounds on the density of information processing would appear to require it.
This requires assigning zero probability to the hypothesis that there is no limit on the density of information processing.
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: