Doesn't the USA already have a system in place where if you are... well... deemed insane you can't vote?
As a City (State? Party?) Election worker in the City of New York, I can confirm that anyone able to show up who shows up in our filing may vote. There are rules and regulations whereby I (as an election worker, although legally anyone allowed in the site also holds this right) may challenge any voter, for any reason, including no reason at all. Being challenged does not prevent you from voting, however, it merely puts a person into a double-check such that the city will review later whether they had the right to vote at the time. If you are found to have misrepresented who you are or your legal ability to vote (either in general or in my district in particular) you will be arrested and charged with perjury, as well as probably other stuff. However, as election workers we are also on guard for any seniors, elderly, or the disabled, such that their rights to vote are not infringed, and that whoever is assisting them is not using them for a vote (which, unfortunately, happens). But to answer your question no. There's no legal determination of sanity that bars you from voting as far as I am aware. The only determination that matters is whether you are currently committed to a psych ward, and only then because you can't physically show up (and these people may be able to vote for all I know, I'll ask next time I'm in one.) I, for one, aided an autistic man and his mother vote.
It's also my chance to say I got to see Tiffany Trump at my polling place. She was there for a grand total of five seconds it seemed (I remember a pink and blonde flash as she passed, followed by the scent of perfume). Incidentally, much less cool than meeting former Mayor Dinkins.
Limited sufferage was the very first form of democracy. Look up how Athens did it. Practically starship troopers in implementation.
Athens and the other greek city states were all just that: city states, and the
Polis is not necessarily a very helpful model for countries much larger than St. Marino. So even ceteris paribus (and needless to say, there's been 2000 years of stuff since then, so ceteris non paribus but work with me here), it's not necessarily wise to look to Athens on this issue. Frankly I'm of the opinion that its barely worth discussing.
The only popular limits I know of are
1) Citizen based: For example only second generation or even third generation immigrants can vote.
Isn't this just restricting the vote to whoever has citizenship? Doesn't
everybody do that? Or are you proposing that voting rights be restricted in
jus soli states? Can you think of a legitimate reason why legal citizens of a country should not have voting rights because their parents were not born here, or even their grandparents? I mean in a
jus sanguinous situation that's another thing entirely, but why use
jus soli citizenship and
jus sanguinous voting rights? Are you purposely trying to create a class of second-class citizens?
I mean that's so incredibly broad it even manages to disenfranchise
me, and if
anyone deserves the right to vote, it's me (in fact, I'm of the opinion that I'm the
only person who should have the right to vote, but sadly this view has not yet caught on among leading constitutional scholars.)