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Comment by BenthamsBulldog | Hacker News Reader

No, that isn't true. We can consider some metric like being at some temperature for an hour. Start with some truly torturous pain like being at 500 degrees for an hour (you'd die quickly, ofc). One person being at 500 degrees is less bad than 10 at 499 degrees which is less bad than 100 at 498 degrees...which is less bad than some number at 85 degrees (not torture, just a bit unpleasant).

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I think OP's objection is that - even granting that a "badness value" can be assigned to headaches and that 3 people with headaches is worse than 2 - there's no clear reason to suppose that 3 is exactly half again as bad as 2. It may be that the function mapping headaches to badness is logarithmic, or even that it asymptotes towards some limit. In mathematical terms it can be both monotonic and bounded.

Thus, when comparing headaches to a man being tortured, there's no clear reason to suppose that there is a number of headaches that is worse than the torture.

That's reversed. The number of people can be mapped linearly, but not the intensity of the pain.

(Intuitively, it's hard to say saving 100 people is 100x as good as saving 1, because we can't have 100 best friends, but it doesn't affect the math at all)

Right but Norcross gives an argument against that. You either have to think that slightly reducing pain and making it 1000 times as prevalent doesn't always make a worse state of affairs or deny that worse than is transitive.

What are the arguments for "worse than" being transitive? It's not immediately clear to me that it ought to be.

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