
Katie L. answered 05/07/19
School Moving Online? I'm Here to Help
This is a great question! Interesting stuff happens when you read these documents closely.
Here's the bit you're missing: When the amendment talks about ballots, they aren't talking about your ballot. They're talking about the electoral collage.
Let's look at that text again:
"The Electors shall meet in their respective states, and vote by ballot for President and Vice-President, one of whom, at least, shall not be an inhabitant of the same state with themselves; they shall name in their ballots the person voted for as President, and in distinct ballots the person voted for as Vice-President..."
So you're absolutely right about the separate ballots, but look at the beginning. It's not the electorate's votes, it's the electors' votes.
And the electors do vote separately for each, but since all major parties have nominated a single president and VP candidate in nearly all cases since the Civil War, the winner for VP is always the winner for Pres' running mate.
I have no idea if it's theoretically possible for individual states to change their ballot rules resulting in a President and VP from different parties. Maybe! But right now, all states allow you to have a running mate on the ballot.