The hypothetical person you describe would beg for the suffering to stop even if continuing to experience it was necessary and sufficient to avoid an even more intense or longer episode of extreme suffering.

Yeah, I agree with this. More explicitly, I agree that it's bad that the person won't continue to experience suffering if it will cause them to experience worse suffering and that this implies that lexical trade-offs in suffering are weird. However

• I said that "in terms of preferences, [suffering] bottoms out." In this situation, you're changing my example by proposing that there is a hypothetical yet worse form of suffering when I'm not convinced there is one after that point
• The above point only addresses more intense suffering, not longer suffering. However I think you're wrong about bringing up different lengths of suffering. When I talk about lexicality, I'm talking about valuing different experiences in different ways. A longer episode of extreme suffering and a shorter form of the same level of extreme suffering are in the same lexicality and can be traded off

It's even harder to understand what it's like to experience comparably extreme happiness, since evolutionary pressures selected for brains capable of experiencing wider intensity ranges of suffering than of happiness.

I agree with this and touched briefly on this in my writing. Even without the evolutionary argument, I'll grant that imagining lexically worse forms of suffering also implies lexically better forms of happiness just as much. After all, in the same way that suffering could bottom out at "this is the worst thing ever and I'd do anything to make it stop", happiness could ceiling at "this is the most amazing thing ever and I'd do anything to make it continue longer."

Then you have to deal with the confusing problem of reconciling trade-offs between those kinds of experiences. Frankly, I have no idea how to do that.

Humans have all sorts of weird and inconsistent attitudes. Regardless of whether you are a realist or an anti-realist, you need to reconcile this particular belief of yours with all the other beliefs you have

I actually don't need to do this for a couple reasons:

• I said that I thought negative lexical utilitarianism was plausible. I think there's something to it but I don't have particularly strong opinions on it. This is true for total utilitarianism as well (though, frankly, I actually learn slightly more in favor of total utilitarianism at the moment)
• The sorts of situations where lexical threshold utilitarianism differs from ordinary utilitarianism are extreme and I think my time is more pragmatically spent trying to help the world than it is on making my brain ethically self-consistent
• As a side-note, negative lexical utilitarianism has infinitely bad forms of suffering so even giving it a small credence in your personal morality should imply that it dominates your personal morality. But, per the above bullet, this isn't something I'm that interested in figuring out

Or, if you want a more vivid example, the belief that it would not be worth subjecting a quadrillion animals having perfectly happy lives to a lifetime of agony in factory farms solely to spare a single animal a mere second of slightly more intense agony just above the relevant critical threshold.

I would not trade a quadrillion animals having perfectly happy lives instead of agony in factory farms just to avoid a second of slightly more intense agony here. However, this isn't the model of negative lexical utilitarianism I find plausible. The one I find plausible implies that there is no continuous space of subjective experiences spanning from bad to good; at some point things just hop from finitely bad suffering that can be reasoned about and traded to infinitely bad suffering that can't be reasoned about and traded.

I guess you could argue that moralities are about how we should prefer subjective experiences as opposed to the subjective experiences themselves (...and thus that the above is completely compatible with total utilitarianism). However, as I mentioned

We don't actually have a great definition of what suffering is and, if we model it in terms of preferences, it bottoms out. AKA, there's a point in suffering when I could imagine myself saying something like "This is the worst thing ever; get me out of here no matter what."

so I'm uncertain about the truth behind distinguishing subjective experience from preferences about them.

It is in the context of that uncertainty that I think negative lexical utilitarianism is plausible.

Concerning the merits of lexical NU, I just don't see how it's plausible to postulate a sharp value discontinuity along the suffering continuum. As discussed many times in the past, one can construct a series of pairwise comparisons involving painful experiences that differ only negligibly in their intensity.

So, I agree that sharp values in discontinuity are not a great aspect for a moral system to have but consider

• We put suffering and happiness on the same scale to reflect how they look in our utility functions. But really, there are lots of kinds of suffering that are qualitatively different. While we can do it sometimes, I'm not sure if we are always capable of making direct, optimized comparisons of qualitatively different experiences
• We don't actually have a great definition of what suffering is and, if we model it in terms of preferences, it bottoms out. AKA, there's a point in suffering when I could imagine myself saying something like "This is the worst thing ever; get me out of here no matter what." Our subjective experience of suffering and our actual ability to report it breaks down
• It's also super hard to really understand what it's like to be in edge-case extreme suffering situations without actually being in one, and most people haven't. Without that (and even potentially with it), trying to model ourselves in extreme suffering would require us to separate logical fallacies we would make in such a situation with our de-facto utility function. From an AI alignment perspective, this is hard.
• If you're an agent and you can't reason about how bad something is while you're in a situation and you don't have a mental model of what that situation is like, getting into that kind of situation is a really bad idea. This isn't just instrumentally inconvenient; it's inconvenient in a "you know you're suffering really badly but you can only model your experience as arbitrarily bad"
• Even if we agree that our utility functions shouldn't have strange discontinuities in suffering, there may still be a strange and discontinuous landscape of levels of suffering we can experience in the landscape of world-states. This is not directly incompatible with any kind of utilitarianism but it makes arguments along the lines of "imagine that we make this suffering just slightly, and virtually unnoticeably, worse" kind of weird. Especially in the context of extreme experiences that exist in a landscape we don't fully understand and especially in a landscape where the above points apply
• I'm a moral anti-realist. There's no strict reason why we can't have weird dicontinuities in our utility functions if that's what we actually have. The "you wouldn't want to trade a dramatic amount of resources to move from one state of suffering to an only infinitesimally worse one" makes sense but, per the above, we need to be careful about what that actually implies about how suffering works

This is all to say that suffering is really complicated and disentangling concerns about how utility functions and suffering work in reality from what logically makes sense is not an easy task. And I think part of the reason people are suffering-focused is because of these general problems. I'm still agnostic on whether something like negative lexical threshold utilitarianism is actually true but the point is that, in light of the above things, I don't think that weird discontinuities is enough to dismiss it from the zone of plausibility.

As pointed out recently, suffering focused views imply that a population where everyone experiences extreme suffering is better than a population where everyone experiences extreme happiness plus a brief, mild instance of suffering, provided the latter population is sufficiently more numerous.

This is an overgeneralization of suffering-focused views. You can believe in Lexical Threshold Negative Utilitarianism (ie there is some point at which suffering is bad enough where it becomes infinitely worse than less bad experiences) where the threshold itself is applied at the person-level rather than the aggregate suffering over all beings level. In this case, many people experiencing mild suffering is trivially better than a smaller number of people experiencing extreme suffering. Not sure if I completely buy into this kind of philosophy but I think it's plausible.