What would happen if no one ran for president?

[minionofmidas]

As far as the Constitution is concerned, no one votes for President on Election Day, rather the State Legislatures have chosen to allow them to vote for Electors. If for some strange reason, all 538 Electors nominate different people, then it would be a wide open race in the Congress with the House having 538 choices for President and the Senate having 538 choices for Vice President.

Isn't it limited to only the top three?

Yes... but if 538 people tie for first slot...

Of course, in theory electors do not have to cast a valid vote (also, what are state procedures if noone wants to be an elector?) so it could still theoretically happen.

And no, the Constitution does not address such fancy issues. Very little of actual US constitutional law and custom is actually Constitutional text.

[minionofmidas]

As far as the Constitution is concerned, no one votes for President on Election Day, rather the State Legislatures have chosen to allow them to vote for Electors. If for some strange reason, all 538 Electors nominate different people, then it would be a wide open race in the Congress with the House having 538 choices for President and the Senate having 538 choices for Vice President.

Isn't it limited to only the top three?

Technically they're all tied for first if every elector nominated a different person, so that rule isn't relevant.

The 12th amendment does not account for a tie any diffrently, so the house would have to pick 3 to decide from.

That is absurd. The House would pick three for itself to decide from - so a two-round vote between all 538? Where do you believe to be drawing that from, exactly?

[minionofmidas]

The most straightforward reading of the clause you quote is that, if four or more persons are tied at the top, then nobody is eligible to be chosen by the House.
Which is... interesting.

The "highest numbers" language resurfaces in the VP tiebreaking procedure, though... and there it seems likely that the intended meaning is indeed "all the people with the two highest occurring [non-0] totals"  as opposed to "the two people with the highest totals".

The House language is slightly different in including that "not exceeding" though.

[minionofmidas]

What if the Senate were still able to pick the Vice President? Do they go under different rules?

Somewhat, yes.

If the House hasn't settled on a President yet by the time term starts, the VP-elect serves as Acting President. That question is settled IIRC.