Once you introduce any meaningful uncertainty into a non-Archimedean utility framework, it collapses into an Archimedean one. This is because even a very small difference in the probabilities of some highly positive or negative outcome outweighs a certainty of a lesser outcome that is not Archimedean-comparable. And if the probabilities are exactly aligned, it is more worth your time to do more research so that they will be less aligned, than to act on the basis of a hierarchically less important outcome.
I don’t think this is true. As an example, when I wake up in the morning I make the decision between granola and cereal for breakfast. Universe Destruction is undoubtedly high up on the severity scale (certainly higher than crunch satisfaction utility), so your argument suggests that I should spend time researching which choice is more likely to impact that. However, the difference in expected impact in these options is so averse to detection that, despite the fact that I literally act on this choice every single day of my life, it would never be worth the time to research breakfast foods instead of other choices which have stronger (i.e. measurable by the human mind) impacts on Universe Destruction.
This is not a bug, but an incredible feature of the non-Archimedean framework. It allows you to evaluate choices only on the highest severity level at which they actually occur, which is in fact how humans seem to make their decisions already, to some approximation.
As for the car example, your analysis seems sound (assuming there’s no positive expected utility at or above the severity level of car crash injuries to counterbalance it, which is not necessarily the case—e.g. driving somewhere increases the chance that you meet more people and consequently find the love(s) of your life, which may well be worth a broken limb or two. Alternatively, if you are driving to a workshop on AI risk then you may believe yourself to be reducing the expected disutility from unaligned AI, which appears to be incomparable with a car crash). But, forgiving my digression and argument of the hypothetical: the claim that not driving is (often) preferable to driving feels much more reasonable to me than the claim that some number of dust specks is worse than torture.
if SPECKS is preferable to TORTURE, then for some N and some level of torture X, you must prefer 10N people to be tortured at level X than N to be tortured at a slightly higher level X’. This is unreasonable, since X is only slightly higher than X’, while you are forcing 10 times as many people to suffer the torture
I’m not sure I understand this properly. To clarify, I don’t believe that any non-torture suffering is incomparable with torture, merely that dust specks are. I think “slightly higher level” is potentially misleading here—if it’s in a different severity class, then by definition there is nothing slight about it. Depending on the order type, there may not even be a level immediately above torture X, and it may be that there are infinitely many severity classes sitting between X and any distinct X’ (think: or ).
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.