A fined tuned argument.....Heywood style.

[Alex K]

No I didn't, I never mentioned daughter universes. Here the argument is rather that you have a huge ensemble of universes with varying properties (they aren't necessarily daughter universes) with parameters distributed according to certain rules. If you then apply a "complexity filter" as a I kind of loose anthropic principle, you can do statistics with the set of universes that pass this filter, and see which properties are more likely than others.

I don't think the paper damages my case.

Do you agree the paper says nothing about how many of all possible universes are capable of producing long chains of emergent complexity?

My intuition is telling me that of all possible universes....very few would be capable of producing long chains of emergent complexity. What does your intuition tell you?

There is possibly an infinite number of possible universes, so you'd have to be more specific what you mean by few.