For background on how an electoral college tie is broken, please read my previous article on that subject first. The short version of it is that the House will pick the President and the Senate will pick the Vice President. I adequately addressed the scenario where the House cannot arrive at a decision, but I rather glossed over what would happen if the Senate cannot pick the Vice President.
First off, I should say that many people give the answer that in the event of a 50-50 tie, the current Vice President would break that tie. (In this particular election, that means that Joe Biden would be voting for himself.) For example, Philip Klein of the Washington Times offers this view.
I believe that this view is incorrect, though, based on the 12th Amendment. The operative passage from the 12th Amendment is, “the Senate shall choose the Vice-President; a quorum for the purpose shall consist of two-thirds of the whole number of Senators, and a majority of the whole number shall be necessary to a choice.”
We’re going to dwell on the quorum in a bit, but let’s look at the phrase “majority of the whole number” first. This same phrase is used earlier in the amendment to say that in order to be elected, a President or Vice President must receive the votes of “a majority of the whole number of Electors appointed”. If we had a situation where some third party candidate received electoral college votes and deprived either candidate of a majority, we all understand and agree that the House and Senate would choose the President and Vice President, respectively — a “plurality” does not count as “a majority of the whole number of Electors appointed”. If words have meaning, then we would have to agree that a plurality of the Senate is not sufficient to appoint a Vice President — you must have a majority.
Now, you may correctly point out that Article I of the constitution says of the Vice President, “The Vice President of the United States shall be President of the Senate, but shall have no Vote, unless they be equally divided.” That is true — the Vice President does have a vote on ordinary business. But the Vice President is not a Senator and the 12th Amendment specifically says that a majority of SENATORS must cast a vote to select a Vice President.
In fact, even if the Vice President (who is not a Senator) did get a tie-breaking vote (which he does not, but we’re pretending), that tie-breaking vote could be thwarted by one Republican senator abstaining. 50-49 is not a majority of the “whole number” of Senators – it’s a majority of votes cast, but not a majority of the “whole number” of Senators. Since Biden only gets a vote in the event of a tie, he gets no vote there. And even if a Democrat were to match the Republican abstention and thus Biden gets his tie-breaking vote, we’re still at 50-49, which is not a majority of the whole number of Senators.
Now, let’s take crazy hypotheticals one step further. A two-thirds quorum of the Senate (meaning, 67 Senators) are required to pick the Vice President. That means that the minority party, provided that they have at least 34 seats, could skip town to prevent a quorum. Now, the Sergent-at-Arms does have the power to arrest Senators to compel their attendance, but, much like the Wisconsin state senators did during their recent fight over unions, the Senators could simply leave the jurisdiction of the United States were they so inclined.
The “Fugitive Senate” scenario is presumably a highly unlikely one that would never happen in the real world (it would be a guaranteed way for the party doing it to never win another election), but, incidentally, the Constitution does not specifically say what would happen in that case. The 20th amendment tells what to do if the President has not been chosen by January 20, but does not specify what to do if the President has, but the Vice President has not. So it could be argued that at any point in time, when the fugitives return, the Senate would be able to pick the Vice President. On the other hand, under the 25th amendment, the President has a right to appoint a Vice President subject to confirmation any time a vacancy occurs.