This question depends entirely on whether there is a right to vote or whether there is a right for citizens to vote.
In the first case, you take anyone who shows up.
In the 2nd case, you take only citizens who show up.
FWIW the founders never intended for the citizens to have a direct vote for either the President or the Senate. They wanted those offices free from the political pressure of the masses in order to assure that we never had the kind of government that we now have, i.e., a Robin-Hood style democratic electorate that could vote themselves money from the treasury.