Since I finally changed the colors on my maps to match what everyone expects after the 2000 election, this has now become the most asked question I get! I've answered here before but since it still gets asked so often I'll elaborate. The first thing to note is that it matters when the person dies.

Let's tackle the easy one first. If a winning candidate dies after the election in November AND after the Electoral College votes in December then his running mate will be sworn in as President. After being sworn in he would then choose a Vice President who would then have to be confirmed by both Houses of Congress.

Here's where it gets tricky, though!

If a candidate wins on election day in November and then dies before the Electoral College counts the votes in December, then there is a problem! Technically the electors can already vote for whomever they want to even if the candidate is alive. So the most likely outcome with a death is that the electors would decide who would become president. Obviously the party of the candidate would have something to say about who they should vote for. But the electors would not be bound by the party's opinion. The best outcome would be for all the dead candidate's electors to come together and choose who to vote for in a single block. But that is complicated by the fact that the electors never really all come together at all -- the electors vote in their individual state capitals, not in one big group.

My thought is that most electors would probably vote for the vice presidential candidate for president. But then that opens up a whole new can of worms about who gets the VP slot on the electoral ballots! Once again the party would have suggestions, but once again electors would not be bound to that.

One last complication is the states that have laws that bind electors to vote for the candidate they were elected to vote for. If those laws don't have provisions for the death of a candidate then that person will get votes!

So with electors able to vote for whomever they wish, some electors stuck voting for a dead guy, and a probable mishmash of vice presidential candidates getting votes, what does the result look like? Maybe an election sent to Congress to decide! It's easy to imagine. Assume DEAD CANDIDATE wins the election with 300 electoral votes while LOSER CANDIDATE loses with 238 votes. DEAD CANDIDATE then dies before the Electoral College votes. Here is one very possible count of the votes:

LOSER CANDIDATE: 238
DEAD CANDIDATE: 100 (from electors in states required to vote him)
DEAD CANDIDATE's VP: 150
OTHER GUY: 50 (from electors who decide to vote for someone else)

In that scenario no one has reached the required 270 votes to become president. The Constitution says the House of Representatives would have to pick the President from among the top three vote getters -- in this case LOSER CANDIDATE, DEAD CANDIDATE, and DEAD CANDIDATE's VP. So it is possible the House could pick the losing candidate to become the next president!

Assuming the same scenario above, we would now have to look at the electoral vote for Vice President. And here things could get much more hairy as there would be no obvious replacement as there was for the presidential pick. For this example, let's assume that several possible replacement VP's are lobbying for the votes:

LOSER CANDIDATE's VP: 238
DEAD CANDIDATE's VP: 100 (from electors in states required to vote for him)
OTHER GUY A: 90
OTHER GUY B: 75
OTHER GUY C: 35

In that scenario we have a big problem. Because the Constitution says that the Senate would pick the VP from the top TWO vote getters -- here LOSER CANDIDATE's VP and DEAD CANDIDATE's VP. But DEAD CANDIDATE's VP is already being voted on in the House for President! Could the same person be elected for both posts? Constitutionally I don't think so. What would probably happen is the House would vote for President first and then the Senate, knowing those results, would then vote for VP. But that again presents another problem. What if the House chooses DEAD CANDIDATE's VP for President? Since the Senate only has two choices to pick from and one of those has just been elected President does that mean they could only pick LOSER CANDIDATE's VP from the other party as the new Vice President?

Another scenario would be the electors settling on a different candidate for VP rather than splitting their votes, but again we could have another interesting situation arise:

LOSER CANDIDATE's VP: 238
DEAD CANDIDATE's VP: 100 (from electors in states required to vote for him)
OTHER GUY: 200

In that scenario we lose the risk of only having one choice for VP as the Senate will now be choosing between LOSER CANDIDATE's VP and OTHER GUY. Where's the problem? What if DEAD CANDIDATE's VP is not chosen by the House to become President? There's no way he could then be voted Vice President either in this case and the peoples' choice for both offices in the election will get neither post!

There is one last thing to consider -- precedent. In 1872, Horace Greeley died after the election but before the Electoral College voted. Since he lost the election (and therefore what happened afterwards didn't change a thing, technically) not many people even remember him or this story. As I mentioned as possibilities above, some electors voted for his running mate and some voted for other people as well -- besides his VP three other people got his electoral votes. But three of his electors went ahead and voted for him anyway. When it came time to count the votes Congress decided to toss the three votes of the dead candidate. But as he lost there was no real significance to it, other than the possible precedent it may have set.

Looking at my first scenario again:

LOSER CANDIDATE: 238
DEAD CANDIDATE: 100 (from electors in states required to vote him)
DEAD CANDIDATE's VP: 150
OTHER GUY: 50 (from electors who decide to vote for someone else)

Let's assume Congress followed the Greeley precedent and tossed the 100 votes cast for him. Since no one has 270 electoral votes we now have a scenario where Congress chooses from LOSER CANDIDATE, DEAD CANDIDATE's VP, and OTHER GUY. Right?

Not so fast! Following the Greeley precedent when Congress tossed the dead candidate's votes, that also changed the number required to win. Since it was just 3 votes it really didn't matter. But in this case it changes things massively. With 538 votes you need 270 to win. Toss 100 of those votes and you're left with 438. That means you just need 220 to win. And in this scenario LOSER CANDIDATE is now the clear winner without it ever having to go to the House for a decision!

Keep in mind this is all speculation. While it is very possible an opposing party candidate or someone who didn't even run could win office, it's also possible that things could work out fine. And if electors aren't bound to vote for a dead candidate or his running mate then that clears the way considerably for the winning party.

But, anything is possible in this scenario and that is why so many people seem to be interested in it!

(People think this is an interesting scenario? Just imagine the possibilities if both a presidential candidate AND his running mate die before the Electoral College counts the votes!)

UPDATE: One other scenario people have been asking about that was not addressed is "what happens if a candidate were to die very close to the election". There would probably be nothing that could be done. Ballots would have been printed and there would be no time to fix them. Even electronic voting probably wouldn't be able to be changed statewide in time. So what would probably happen is that the party of the dead candidate would tell voters "go ahead and vote for him and your vote will actually count for xxx". They would then instruct their electors to vote for xxx for President and yyy for VP. But the scenarios above would definitely be in play after that point.