To know that such a number cannot represent an altogether esoteric feature of the universe that can nevertheless be the legitimate subject of infinite value I would need to know the smallest number that can be assigned to a quantum state.
I think you are conflating quantum probabilities with Bayesian probabilities here, but I'm not sure. Unless you think this point is worth discussing further I'll move on to your more significant disagreement.
Someone can assign infinite utility to Australia winning the ashes if that is what they really want. I'd think them rather silly but that is just my subjective evaluation, nothing to do with maths.
Hm...I initially wrote a two-paragraph explanation of why you were wrong, then deleted it because I changed my mind. So, I think we are making progress!
I initially thought I accorded disdain to unbounded utility functions for the same reason that I accorded disdain to ridiculous priors. But the difference is that your priors affect your epistemic state, and in the case of beliefs there is only one right answer. On the other hand, there is nothing inherently wrong with being a paperclip maximizer.
I think the actual issue I'm having is that I suspect that most people who claim to have unbounded utility functions would have been unwilling to make the trades implied by this before reading about VNM utility / "Shut up and multiply". So my objection is not that unbounded utility functions are inherently wrong, but that they cannot possibly reflect the preferences of a human.
I think the actual issue I'm having is that I suspect that most people who claim to have unbounded utility functions would have been unwilling to make the trades implied by this before reading about VNM utility / "Shut up and multiply". So my objection is not that unbounded utility functions are inherently wrong, but that they cannot possibly reflect the preferences of a human.
On this I believe we approximately agree.
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?