You said that you would be okay with losing $5 to a mugger who raised your posterior by a factor of 10^(500), because they would have to do a lot of work to do so. I responded by pointing out that they wouldn't have to do much work after all. If this doesn't change the decision problem (which I agree with) then I don't see how your original reasoning that it's okay to get mugged because the mugger would have to work hard to mug you makes any sense.
What determines how much I am willing to pay is not how hard the mugger works per se, but how credible the threat is compared to its severity. (I thought this went without saying, and that you would be able to automatically generalize from "the mugger working hard" to "the mugger's credibility increasing by whatever means".) Going from p = 10^(-1000) to p = 10^(-500) may not sound like a "huge" increase in credibility, but it is. Or at least, if you insist that it isn't, then you also have to concede that going from p = 10^(-500) to p = 1/2 isn't that big of a credibility increase either, because it's the same number of bits. In fact, measured in bits, going from p = 10^(-1000) to p = 10^(-500) is one-third of the way to p = 1-10^(-500) !
Now I presume you understand this arithmetic, so I agree that this is a distraction. In the same way, I think the simple mathematical arguments that you have been presenting are also a distraction. The real issue is that you apparently don't believe that there exist outcomes with utilities in the range of 10^(750). Well, I am undecided on that question, because at this point I don't know what "my" values look like in the limit of superintelligent extrapolation on galactic scales. (I like to think I'm pretty good at introspection, but I'm not that good!) But there's no way I'm going to be convinced that my utility function has necessarily to be bounded without some serious argument going significantly beyond the fact that the consequences of an unbounded utility function seem counterintuitive to another human whose style of thought has already been demonstrated to be different from my own.
If you've got serious, novel arguments to offer for why a human-extracted utility function must be bounded, I'm quite willing to consider them, of course. But as of now I don't have much evidence that you do have such arguments, because as far as I can tell, all you've said so far is "I can't imagine anything with such high utility!"
Fair enough.
P.S. Given that we've apparently had protracted disagreements on two issues so far, I just wanted you to know that I'm not trying to troll you or anything (in fact, I hadn't realized that you were the same person who had made the Amanda Knox post). I will try to keep in mind in the future that our thinking styles are different and that appeals to intuition will probably just result in frustration.
For background, see here.
In a comment on the original Pascal's mugging post, Nick Tarleton writes:
Coming across this again recently, it occurred to me that there might be a way to generalize Vassar's suggestion in such a way as to deal with Tarleton's more abstract formulation of the problem. I'm curious about the extent to which folks have thought about this. (Looking further through the comments on the original post, I found essentially the same idea in a comment by g, but it wasn't discussed further.)
The idea is that the Kolmogorov complexity of "3^^^^3 units of disutility" should be much higher than the Kolmogorov complexity of the number 3^^^^3. That is, the utility function should grow only according to the complexity of the scenario being evaluated, and not (say) linearly in the number of people involved. Furthermore, the domain of the utility function should consist of low-level descriptions of the state of the world, which won't refer directly to words uttered by muggers, in such a way that a mere discussion of "3^^^^3 units of disutility" by a mugger will not typically be (anywhere near) enough evidence to promote an actual "3^^^^3-disutilon" hypothesis to attention.
This seems to imply that the intuition responsible for the problem is a kind of fake simplicity, ignoring the complexity of value (negative value in this case). A confusion of levels also appears implicated (talking about utility does not itself significantly affect utility; you don't suddenly make 3^^^^3-disutilon scenarios probable by talking about "3^^^^3 disutilons").
What do folks think of this? Any obvious problems?