President and Vice President from the same state?

[minionofmidas]

Note that under our current system it is conceivable that a candidate could win election as both President and Vice President since the rule does not require that an elector place different names as President and Vice President, if he doesn't live in the same state.   That happened in 2004 when a Minnesota elector chose to vote for John Edwards for both President and Vice President.

I consider that interpretation to be faulty, and the decision to count that guy's votes to be false.

[minionofmidas]

So what would happen if Bloomberg/Giuliani were to win NY?

Bloomberg isn't a Republican anymore, so you can count out any chance of those two being on a ticket together.

But hypothetically, the electors from NY would be prohibited to vote for a President and Vice President from NY.

One of the two could call another State "home"
ie Dick Chaney goes to Wyoming

...and they would. However, they'd have to do that before the election.

The NY electors, in your scenario, would just vote for some counting candidate for VP. Which gets interesting if that means Bloomberg's election goes to the Senate.

[minionofmidas]

Let's say the race is Clinton vs. Romney vs. Bloomberg, and no one wins a majority in the electoral college.  However, Romney's VP is Giuliani.

The election goes to the House and either Clinton or Bloomberg wins.

Then, Giuliani somehow wins the Senate election.  Is that a circumstance where a VP and Pres could be from the same state?

Absolutely.