Can the president and vice president be running for office and living in the same state?

Answer 1

No, they can be from the same state, but there is a rule in the US Constitution, in the first sentence of the 12th Amendment, that an elector (a member of the electoral college) cannot cast both his presidential and vice presidential votes for candidates from his home state. So if Dick Cheney had not moved from Texas back to Wyoming after becoming George W. Bush's running mate in 2000, each of the 32 Texas electors would have been prohibited from voting for BOTH George W. Bush for president AND Dick Cheney for vice president.

Answer 2

Because the U.S. Constitution disallows it... even though George W. Bush and Dick Cheney were both living in Texas at the time of the 2000 election. (Cheney changed his legal residence to Wyoming, proving that the requirement is rather easy to circumvent.)

Answer 3

There is no law prohibiting such a pairing, but doing so is usually avoided. Candidates tend to pick running mates from a different part of the country in order to appeal to a wider demographic.

Answer 4

Yes, they always do, in fact, since the parties want to balance the ticket. Also, each elector can not vote for both president and vice-president from their own state. If the candidates for president and vice-president were both from the same state, they could not both get votes from their own state, so if the election were close it could result in a vice-president from the other party being elected.