(What I'm about to say is I think the same as Jiro has been saying, but I have the impression that you aren't quite responding to what I think Jiro has been saying. So either you're misunderstanding Jiro, in which case another version of the argument might help, or I'm misunderstanding Jiro, in which case I'd be interested in your response to my comments as well as his/hers :-).)
It seems to me pretty obvious that one can construct a scale that goes something like this:
with, say, at most a million steps on the scale from the stubbed toe to 50 years' torture, and with the property that any reasonable person would prefer N people suffering problem n+1 to (let's say) (1000N)^2 people suffering problem n. So, e.g. if I have to choose between a million people getting 13 months' torture and a million million million people getting 12 months' torture, I pick the former.
(Why not just say "would prefer 1 person suffering problem n+1 to 1000000 people suffering problem n"? Because you might take the view that large aggregates of people matter sublinearly, so that 10^12 stubbed toes aren't as much worse than 10^6 stubbed toes as 10^6 stubbed toes are than 1. The particular choice of scaling in the previous paragraph is rather arbitrary.)
If so, then we can construct a chain: 1 person getting 50 years' torture is less bad than 10^6 people getting 49 years, which is less bad than 10^18 people getting 48 years, which is less bad than [... a million steps here ...] which is less bad than [some gigantic number] getting stubbed toes. That final gigantic number is a lot less than 3^^^3; if you replace (1000N)^2 with some faster-growing function of N then it might get bigger, but in any case it's finite.
If you want to maintain that TORTURE is worse than SPECKS in view of this sort of argument, I think you need to do one of the following:
Incidentally, for my part I am uncertain about TORTURE versus SPECKS on two grounds. (1) I do think it's possible that for really gigantic numbers of people badness stops depending on numbers, or starts depending only really really really weakly on numbers, so weakly that you need a lot more arrows to make a number large enough to compensate -- precisely on the grounds that when the exact same life is duplicated many times its (dis)value might be a slowly growing function of the number of duplicates. (2) The question falls far outside the range of questions on which my moral intuitions are (so to speak) trained. I've never seriously encountered any case like it (with the outlandishly large numbers that are required to make it work), nor have any of my ancestors whose reproductive success indirectly shaped my brain. And, while indeed it would be nice to have a consistent and complete system of ethics that gives a definite answer in every case and never contradicts itself, in practice I bet I don't. And cases like this I think it's reasonable to mistrust both whatever answers emerge directly from my intuitions (SPECKS is better!) and the answers I get from far-out-of-context extrapolations of other intuitions (TORTURE is better!).
[EDITED immediately after posting, to fix a formatting screwup.]
(Small nitpicking: The pain from "a multiply-fractured leg" may bother you longer than "an hour of expertly applied torture", but the general idea behind the scale is clear.)
If I have to choose between a million people getting 13 months' torture and a million million million people getting 12 months' torture, I pick the former.
In this case I'd choose as you do, just as in Jiro's example:
3^^^3 people with a certain pain [versus] 1 person with a very slightly bigger pain.
The problem with these scenarios, however, is that they intr...
As per a recent comment this thread is meant to voice contrarian opinions, that is anything this community tends not to agree with. Thus I ask you to post your contrarian views and upvote anything you do not agree with based on personal beliefs. Spam and trolling still needs to be downvoted.