Let's say it's December 10th, 2016 and Joe Smith has just been elected president, but since the election he has decided he no longer wants to be president. In January 2017, who would be inaugurated instead of him?
There are no laws, Constitutional or otherwise, to directly address this situation. The easy answer would be for him to take office and then immediately resign, breaking William Henry Harrison's record of 32 days for shortest Presidential term, and triggering the already-tested resignation process.
However, assuming that the candidate refuses to do that, there's at least one logical flow which seems likely to be the path taken. And just as with Harrison and the succession of "His Accidency", John Tyler to the Presidency, new precedent would be set regardless of what happened.
Article II, Section 1, Clause 8 of the Constitution specifies:
Before [the President] enter on the execution of his office, he shall take the following oath or affirmation:--"I do solemnly swear (or affirm) that I will faithfully execute the office of President of the United States, and will to the best of my ability, preserve, protect and defend the Constitution of the United States."
If the President-elect doesn't take this oath, he is unable to execute his office. I don't think anyone disagrees with that. However, by my reading, his becoming President is not conditional upon taking the oath - only executing it. So what happens?
Clause 6, while partially overridden by the 25th Amendment, states:
In case of the removal of the President from office, or of his death, resignation, or inability to discharge the powers and duties of the said office, the same shall devolve on the Vice President, and the Congress may by law provide for the case of removal, death, resignation or inability, both of the President and Vice President, declaring what officer shall then act as President, and such officer shall act accordingly, until the disability be removed, or a President shall be elected.
The 20th Amendment adds
If, at the time fixed for the beginning of the term of the President, the President elect shall have died, the Vice President elect shall become President. If a President shall not have been chosen before the time fixed for the beginning of his term, or if the President elect shall have failed to qualify, then the Vice President elect shall act as President until a President shall have qualified;
Finally, the 25th Amendment modifies this by adding:
In case of the removal of the President from office or of his death or resignation, the Vice President shall become President.
Whenever the Vice President [and others], transmit to the President pro tempore of the Senate and the Speaker of the House of Representatives their written declaration that the President is unable to discharge the powers and duties of his office, the Vice President shall immediately assume the powers and duties of the office as Acting President.
The cleanest possibility here is that by refusing to take the oath, the President-elect renders himself "unable to discharge the powers and duties of his office". The VP will notify Congress, and become Acting President. He will stay Acting President for the entire 4-year term, and then be eligible for a single extra term as President.
Anything beyond that could spark a constitutional crisis. These tend to be resolved by whoever is most dedicated to their interpretation or who can apply the most force. It's possible it would end up before the Supreme Court, but unless someone's proposed solution was wildly outside the implied default of the VP acting as or becoming President, that's unlikely 1.
Some possible scenarios:
- Like in Tyler's case, the new VP decides he is President, not just Acting President. He declares that the President-elect effectively resigned, rather than just being unable to take the office.
- The question is thrown back to the Electoral College, and the various state's electors would need to re-convene and revote for President/VP.
- An emergency amendment is passed to clarify the situation between the pre-resignation and the inauguration. I would expect that most Congressmen and most state's legislatures would be willing to rush a one-line amendment through to avoid months of arguments. However, this may fail if the minority party prefers one of the other solutions and has enough representation to block the amendment.
- The President-elect is impeached, or plans are made to impeach him as of inauguration day. Again, I would expect most Congressmen to go along with it, regardless of party affiliation (the President's party wants the VP in office, the other side wants to make a big deal about it).
1 One other thing worth noting is that any solution which ends up with a new or acting President from a different political party than the President-elect will run afoul of the spirit of the 12th Amendment which was specifically created to ensure that the President and the VP (his successor) came from the same party, instead of being antagonistic (as per the original Constitution). While there may not be any direct answers there, if it came before the Supreme Court, they would probably base at least part of their decision on the intent of the 12th.
There is no concrete answer to this question. Most likely, the VP would at least become Acting President for the duration of the term. If enough politicians really don't like that result, it would likely create a constitutional crisis, which would set new precedent, which might later be encoded into law.
On Inauguration Day the Vice President elect takes the oath of office first. The President elect is then asked by the Chief Justice if he is ready to take the oath of office. If he says "no, I am no longer interested in the job" the Vice President would automatically become President. A new Vice President would then have to be selected.
President and vice president are elected as a single ticket. You vote for the president and get a vice-president included. You do not vote for each individually. So if the President Elect drops out before being sworn in the VP Elect would be sworn in as The President and He/She would appoint a VP (subject to the approval of the Senate).