Pay attention next time you eat something. Do you look at the food and eat what you like or what you think will improve your health, or do you try to prioritize eating the food against sending me money because I might be a god, and against giving all of the other unlikely gods what they might want?
I would like to do whichever of these two alternatives leads to more utility.
We are human and cannot really do that.
If an AI is doing that, I have no confidence at all that it will weigh these things the way I would like, especially given that it's not likely to search all of the space.
Are you saying that we shouldn't maximize utility because it's too hard?
Someone who thinks about a million unlikely gods to decide whether to eat an apple is broken.
If your actual utility function is unbounded and thinking about a million "unlikely gods" is worth the computational resources that could be spent on likely gods (though you specified that small changes to likely gods are unlikely gods, there is a distinction in that there are not a metaphorical million of them), than that is your actual preference. The utility function is not up for grabs.
Your argument seems to be that maximizing an unbounded utility function is impractical, so we should maximize a bounded utility function instead. I find it improbable that you would make this argument, so, if I am missing anything, please clarify.
Yes, the utility function is not up for grabs, but introspection doesn't tell you what it is either. In particular, the statement "endoself acts approximately consistently with utility function U" is an empirical statement for any given U (and any particular notion of "approximately", but let's skip that part for now). I believe I have provided fine arguments that you are not acting approximately consistently with an unbounded utility function, and that you will never be able to do so. If those arguments are valid, and you say you ha...
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: