Sigh, we seem to be talking past each other.
There are two issues here: 1) What the most plausible cashing-out of an unbounded utility function recommends 2) Whether that cashing-out is a sensible summary of someone's values. I agree with you on 2) but think that you are giving bogus examples for 1). As with previous posts, if you concoct examples that have many independent things wrong with them, they don't clearly condemn any particular component.
My understanding is that you want to say, with respect to 2), that you don't want to act in accord with any such cashing-out, i.e. that your utility function is bounded insofar as you have one. Fine with me, I would say my own utility function is bounded too (although some of the things I assign finite utility to involve infinite amounts of stuff, e.g. I would prefer living forever to living 10,000 years, although boundedly so). Is that right?
But you also keep using what seem to be mistaken cashing-outs in response to 1). For instance, you say that:
Keeping a few dollars is like eating lunch, so if you can't rationally decide to eat lunch,
But any decision theory/prior/utility function combination that gives in to Pascal's Mugging will also recommend eating lunch (if you don't eat lunch you will be hungry and have reduced probability of gaining your aims, whether infinite or finite). Can we agree on that?
If we can, then you should use examples where a bounded utility function and an unbounded utility function actually give conflicting recommendations about which action to take. As far as I can see, you haven't done so yet.
I think you mean Arguments for - and against - probabilism. If you meant something else, please correct me.
I meant the paper that I already linked to earlier in this thread.
There are two issues here: 1) What the most plausible cashing-out of an unbounded utility function recommends 2) Whether that cashing-out is a sensible summary of someone's values. I agree with you on 2) but think that you are giving bogus examples for 1). As with previous posts, if you concoct examples that have many independent things wrong with them, they don't clearly condemn any particular component.
I agree that we agree on 2).
The conflict here seems to be that you're trying to persist and do math after getting unbounded utilities, and I'm inclined...
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: