[3np]

Did not finish reading either yet, but is this not addressed (without explicitly addressing your work) early on in the article?

As I read their reasoning, even if the by far most likely outcome is that your conclusion holds in practice, there is a non-zero probability that assumptions are wrong in a way that allows for infinite causality, and therefore (by assuming their infinite-fanatical stance), attempting that is still a sane conclusion.

More fundamentally, they are reasoning within the infinite set of imaginable universes whereas you reason within our current one and that current consensus of physical limitations hold. Your scope is "only" our morally relevant universe. Different fundamental assumptions yield fundamentally different conclusions.

Does that make sense?

[kubanczyk]

If you want to use the concept of "probability" to deal with reality, you better decide first if the reality offers infinite payoff/risk. If it does, your tool (the naive probability) is inadequate and quite easily broken, as you just have demonstrated.

The tool will sway to 100% and back to 0% on like a broken compass, depending on which infinities you thought about this very minute.

[3np]

Good point - it should follow that given assumption that with infinitesimal probability of infinite payoff, there is also a corresponding non-zero probability of infinite risk.

Overall I think OP is mostly about them struggling to reduce hypothetical outcomes involving infinities to real numbers in order to be able to rank them. For example:

> Agent-neutrality: If there is a welfare-preserving bijection from the agents in w1 to the agents in w2, then w1 and w2 are equally good. > By “welfare-preserving bijection,” I mean a mapping that pairs each agent in w1 with a single agent in w2, and each agent in w2 with a single agent in w1, such that both members of each pair have the same welfare level.

They then proceed to compare a w1 with a 1/0 of 1:1 vs w2 with a 1:3 ratio, "skipping" 2/3 of 0s in w2, claiming a contradiction. So they're really doing a injective non-surjective mapping, not a bijective one, and them being infinite doesn't really absolve that. I think they could get some insight from algorithmic analysis and limits. Just like (probably sloppy notation here) O(0.25n) is faster than O(0.5n) even if both are O(0.5n).

[penteract]

> They then proceed to compare a w1 with a 1/0 of 1:1 vs w2 with a 1:3 ratio, "skipping" 2/3 of 0s in w2, claiming a contradiction. So they're really doing a injective non-surjective mapping, not a bijective one.

There is in fact a bijection between indices that maps the sequences to each other -

  index: 0 1 2 3 4 5 6 7 ...
  w1:    1 0 1 0 1 0 1 0 ...
  w2:    1 0 0 0 1 0 0 0 ...

bijective map such that w2(f(i))=w1(i) :

  f(n) = if (n is even) then n*2 else floor((n*2+1)/3)
  f_inverse(n) = if (n is a multiple of 4) then n/2 else floor((n*3)/4)*2+1