As for your first paragraph, well, this is a straightforward application of Bayes' theorem. If you're sure that 2 is even, then learning that 2 was randomly selected from some distribution over primes should not be enough to change your credence very much.
As for your second and third paragraphs: Yes, the argument of Eliezer you're talking about doesn't refute the existence of universally compelling arguments; it merely means that you shouldn't believe you have a universally compelling argument unless you have a good reason for believing so. If you think you have a good reason, then you don't have to worry about this argument.
There's a very simple argument refuting the existence of universally compelling arguments, and I believe it was stated elsewhere in this thread. It's that argument you have to refute, not this one.
There's a very simple argument refuting the existence of universally compelling arguments, and I believe it was stated elsewhere in this thread. It's that argument you have to refute, not this one.
Please point this out to me if you get a chance, as I haven't noticed it. And thanks for the discussion. I mean that: I can see that this wasn't helpful or interesting for you, but rest assured it was for me, so your indulgence is appreciated.
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.