The thing you called "pseudograding" is normally called "filtration".
Ah, thanks! I knew there had to be something for that, just couldn't remember what it was. I was embarrassed posting with a made-up word, but I really did look (and ask around) and couldn't find what I needed.
...Although, reading the definition, I'm not sure it's exactly the same...the severity classes aren't nested, and I think this is probably an important distinction to the conceptual framing, even if the math is equivalent. If I start with a filtration proper, I need to extract the severity classes in a way that seems slightly more convoluted than what I did.
In practice, because of the complexity of the world, and especially because of the presence of probabilistic uncertainty, an agent following a non-Archimedean utility function will always consider only the component corresponding to the absolute maximum of I, since there will never be a choice between A and B such that these components just happen to be exactly equal. So it will be equivalent to an Archimedean agent whose utility is this worst component.
See my response to Dacyn.
we find the need for a weird cut off point, like a broken arm
For the cut-off point on a broken arm, I recommend the elbow [not a doctor].
Suppose there was a strong clustering effect in human psychology, such that less than a week of torture left peoples minds in one state, and more than a week left them broken. I would still expect the possibility of some intermediate cases on the borderlines. Things as messy as human psychology, I would expect there to not be a perfectly sharp black and white cutoff. If we zoom in enough, we find that the space of possible quantum wavefunctions is continuous.
I agree! You've made my point for me: it is precisely this messiness which grants us continuity on average. Some people will take longer than others to have qualitatively incomparably damaging effects from torture, and as such the expected impact of any significant torture will have a component on the severity level of 50 years torture. Hence, comparable (on expectation).
I agree that delineating the precise boundaries of comparability classes is a uniquely challenging task. Nonetheless, it does not mean they don't exist--to me your claim feels along the same lines as classical induction "paradoxes" involving classifying sand heaps. While it's difficult to define exactly what a sand heap is, we can look at many objects and say with certainty whether or not they are sand heaps, and that's what matters for living in the world and making empirical claims (or building sandcastles anyway).
I suspect it's quite likely that experiences you may be referring to as "higher quantities of themselves" within a single person are in fact qualitatively different and no longer comparable utilities in many cases. Consider the dust specks: they are assumed to be minimally annoying and almost indetectable to the bespeckèd. However, if we even slightly upgrade them so as to cause a noticeable sting in their targeted eye, they appear to reach a whole different level. I'd rather spend my life plagued by barely noticeable specks (assuming they have no interactions) than have one slightly burn my eyeball.
Yes! This is all true. I thought set differences of infinite unions and quotients would only make the post less accessible for non-mathematicians though. I also don't see a natural way to define the filtration without already having defined the severity classes.