Can someone run for the office of Vice President independently of a presidential candidate?

You start your own “party”. Call it the “Czarcasm Party”. If you wanted to do this in 2016, you simply name Trump or Clinton as your party’s Presidential candidate. Then all you’ve got to do is convince voters to vote for “trump/Czarcasm” rather than “trump/Pence”. I think that the trump votes would be cumulative. Then it’s just a question of the VP totals.

Is naming someone without their consent legal?

I don’t think so. Even if you could name another candidate without their permission, when you vote in a presidential election, you’re actually voting for a slate of people who wish to be electors. The “Trump/Czarcasm” ticket would have completely different elector-candidates than the “Trump/Pence” ticket. If there are 500 votes for the Bob-Jane-Sally group of electors (Trump/Czarcasm), 500 for the Tim-John-Mary group (Trump/Pence), and 750 for the Ted-Mike-Susan group (Clinton/Kaine), then Ted, Mike, and Susan got the most votes and are elected.

Even if you somehow got the same people to be electors for both tickets (if that’s even legal in enough states), most states ban the practice of “fusion” and count votes on separate ballot lines separately.

That’s right. They’re two separate elections, as 1824 and 1836 show.

You would have to get a majority of the electoral votes for V-P. If you do, you’re in, regardless of what happens to the presidential election, as with Calhoun in 1824.

If you don’t get a majority of electoral votes, but come in first or second in the electoral votes, then you have to get a majority of the Senators to vote for you, as happened with Johnson in 1836.

IDK. The way the political climate is you don’t think the Dems would deny Trump a Pub VP for an independent or vice-versa if the Pubs controlled the Senate and Clinton won?

Valid point. I was thinking more along the lines of the two finalists being one from a major party and one independent. I can’t imagine either a Democrat or Republican Senator voting for the independent candidate. More likely they’d simply be absent from the Senate. Of course, if either party has a majority in the Senate (as the Republicans do right now) they’d simply vote for their own candidate, and an independent candidate would be irrelevant, even if they got more electoral votes than either party’s candidate.

But it’s only the top two, remember. If we’re positing that an independent came in either first or second in the EC vote, then that means that either the Dems or Repubs in the Senate have to choose between voting for the independent, or the candidate from the other party.

Suppose the Republican V-P candidate came in third, but the Republicans have a majority in the Senate. They have to choose between the Independent or the Democrat. The third place Republican candidate isn’t in the running. Would they vote for the Democrat or the independent candidate?

Or flip it so the independent and the Republican V-P candidates are the top two, but the Democrats hold the Senate. Who do they vote for?

Who won the presidential election? If the candidate from Party A wins the presidential electoral vote, but the party’s candidate finishes third in the vice presidential vote (and ends up out of the running) then I suppose the senators from Party A would consider whether independent candidate fits more closely with Party A’s values.

But if Party A is center right while Party B is center left and independent candidate C is an extreme extremist, I think at least enough Senators from Party A would probably vote for B rather than give C a platform to espouse those weird, extreme views.

The electors vote separately for the two offices but it’s the same group of electors. Which is what makes this a really unlikely scenario.

Suppose it’s 2000 and a group of people are okay with George W. Bush as a presidential candidate but they really don’t like Dick Cheney being the vice-presidential candidate. So they decide to start a new party, the Dickless Party, and they nominate Bush as their presidential candidate and John McCain as their vice-presidential candidate.

It’s Election Day and you go to the polls. It might look like you’re voting for a President and Vice President, but you’re really voting for an Elector. And the basis on which you’re choosing an Elector is that they’ve all promised to vote for a particular President and Vice President.

You have a choice. You can vote for:
John Smith, the Republican Party Elector, who has pledged to vote for Bush and Cheney
Bob Johnson, the Democratic Party Elector, who has pledged to vote for Gore and Lieberman
Walter Peck, the Dickless Party Elector, who has pledged to vote for Bush and McCain
(You wouldn’t actually just be voting on a single Elector. You’re voting for a group of Electors whose number equals your state’s Electoral College representation. Unless you live in Maine or Nebraska.)

The thing is you can only vote for one of them. And the Elector who gets the most votes wins. So Smith and Peck can’t combine their votes even though they’re both pledged to vote for Bush.

The likelihood is that with some Bush supporters voting for Smith and some Bush supporters voting for Peck, it’ll be Johnson who ends up getting the plurality of votes.