- At the federal level (the actual direct presidential election) we technically don't have FPTP, technically its majority rules election.
- At the state level (the indirect election of the president via electors) the details depend state to state.
Elector college representative's voting procedures are defined by US Code title 3 chapter 1 section 8, which states
Manner of voting
§ 8. The electors shall vote for President and Vice President, respectively, in the manner directed by the Constitution.
Amendment XII of the constitution states
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, and they shall make
distinct lists of all persons voted for as President, and all persons
voted for as Vice-President and of the number of votes for each, which
lists they shall sign and certify, and transmit sealed to the seat of
the government of the United States, directed to the President of the
The President of the Senate shall, in the presence of the Senate and
House of Representatives, open all the certificates and the votes
shall then be counted.
The person having the greatest Number of votes for President, shall be
the President, if such number be a majority of the whole number of
Electors appointed; and if no person have such majority, then from the
persons having the highest numbers not exceeding three on the list of
those voted for as President, the House of Representatives shall
choose immediately, by ballot, the President. But in choosing the
President, the votes shall be taken by states, the representation from
each state having one vote; a quorum for this purpose shall consist of
a member or members from two-thirds of the states, and a majority of
all the states shall be necessary to a choice. And if the House of
Representatives shall not choose a President whenever the right of
choice shall devolve upon them, before the fourth day of March next
following, then the Vice-President shall act as President, as in the
case of the death or other constitutional disability of the
The person having the greatest number of votes as Vice-President,
shall be the Vice-President, if such number be a majority of the whole
number of Electors appointed, and if no person have a majority, then
from the two highest numbers on the list, 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. But no person constitutionally
ineligible to the office of President shall be eligible to that of
Vice-President of the United States.
In other words, if someone manages to get a majority, they win. If they don't there is a run-off-ish election in the congress and senate for President/VP respectfully. (Side Note: If you heard the story about Evan McMullin potentially becoming president after only winning one state, this is how that would have happened). This is technically a majority rules election, not a FPTP election (Thanks Brythan).
Note that this is only for the second, direct presidential election by the electoral college representatives. The more known general election (IE what we all did on Nov 8th) which, in most cases, binds the electoral college representatives to their state's popular vote have different laws governing them that vary state to state. I randomly picked Delaware as an example:
§ 4303 Meeting and voting of electors.
(a) The electors chosen or appointed in this State for the election of
a President and Vice-President of the United States shall meet and
give their votes at Dover on the day determined by Congress for that
(b) In all cases, the electors chosen or appointed in this State for
the election of a President and Vice-President of the United States
under this chapter shall be required to cast their individual votes in
accordance with the plurality vote of the voters in this State.