I've been re-reading this thread, and think I've found an even bigger problem with FNC, even if it is just restricted to "small" finite universes.

As discussed above, in such universe models, FNC causes us to weight our probability estimates towards models with a high density of civilizations e.g. ones where practically ever star system that can gives rise to life and an intelligent civilization. And then, if we take our observations seriously, none of those civilizations can have ever expanded into our own solar system, so they must have a very low expansion probability. (Incidentally, even if they were blocked somehow from entering our own solar system, because of quarantine policy, Prime Directive, Crystal Spheres etc, and the block was somehow enforced universally and over geological timeframes, we still ought to see some evidence of them occupying other nearby star systems - radio emissions, large scale engineering projects, Dyson spheres etc.)

But the worse problem is that FNC creates an even stronger weight towards not taking our observations seriously in the first place. It seems there is even higher probability under FNC that some civilizations have expanded, have occupied the whole universe, and have populated it very densely with observers. We are then part of some subset of observers who have been deliberately "fooled" into thinking that the universe is largely unoccupied, and that we're in a primitive civilization. Probably we're in some form of simulation or experiment.

Unfortunately, I think this is all pretty devastating to FNC:

1. If infinite universes are allowed at all, then under FNC they will receive weighted probability very close to one.
2. If infinite universes are ruled out (prior probability zero), then very large finite universes will now receive weighted probability very close to one.
3. If very large finite universes are also ruled out (also probability zero), then skeptical hypotheses where the universe is not as it seems, and we are instead in some sort of simulation or experiment, receive weighted probability close to one.
4. If skeptical hypotheses are also ruled out (let's give them probability zero as well) then we are still weighted towards universes with a high density of civilizations, and a "Great Filter" which lies in front of us. This still gives pretty doomerish conclusions.

So we have to do a lot of ad hoc tweaking to get FNC to predict anything sensible at all. And then what it does predict doesn't sound very optimistic anyway.