There can be a very real issue if HN accounts have an age or birthdate associated with them which indicate that the user is under 13. In that situation where knowledge of age is in the hands of the website operator, the FTC has taken notice, and action. See Path's recent FTC COPPA ruling as an example.
So, if HN internally keeps a reference from votes in the under-10 category of this poll to the accounts they came from, and if any of those people are under 13, there may be cause for real concern re: COPPA.
There are sort of 3 ways to approach this safely...
1. don't ask, don't tell (eg: Google's main search page)
2. ask, and reject (eg: Facebook account signup)
3. ask, accept, and get consent (eg: some child focused sites)
HN is pretty clearly not a child-oriented website, but if there is concrete knowledge of age, COPPA can apply.
Does it really apply to a user-generated poll? I mean, this would be no different than a user of a forum or chat service asking another their age, with the server keeping some kind of message records. I think it's hard to make the claim that the administrators have concrete knowledge; it's just an anonymous record in the database.
Path's case is different, since the form asking for the birthdate was made by them, so they knew they had that information.
If the First Amendment allows children to traffic in snuff films, Nazi regalia, bomb making manuals, Satanist tracts, classified nuclear information, and so forth while in a government school, it's safe to assume that COPPA is an unconstitutional prior restraint on free speech. I am astonished that the ACLU has not already handed the FTC their ass.
"The ACLU has long been strongly supportive of COPPA. It is an important first step on the road to universal baseline privacy protections that ensure that every American—young and old—has meaningful control over their personal information online. (...) The ACLU protects privacy and free speech simultaneously, and the two interests are rarely at cross-purposes. Right now, COPPA is a great law and it does both effectively."
..you could let them send in a note from their parents to get unbanned :-)
1. http://en.wikipedia.org/wiki/Childrens_Online_Privacy_Protec...