And of course, the "look how awesome I am" answer isn't useful at all, because there are unproven assertions made to make the question tractable, and unknown realities not brought into the problem space(for example, people having genetic predispositions towards birthing sons rather than daughters, or vice versa)

That's one of my productivity secrets. Always read the top 4 answers before deciding on a course.

Answer #3 is right far too often for my liking. And sometimes answer #4 brings up corner cases the others missed.

Why is three better? In any family with k brothers, each male will have k-1 brothers, while each female (if any exist) will have k brothers. So the number of brothers in S(x) is gender dependent, despite the the third answer's claim that it isn't.

Absolutely. I actually upvoted #3[1] before coming here and seeing your comment.

[1] http://math.stackexchange.com/a/1794617/63267